English Language Preparation
Complete Guide to "Can" and "Could" in English
Can and could are modal auxiliary verbs. They are
commonly used to talk about ability, permission, requests, possibility,
suggestions, and hypothetical situations.
Basic
Structure
Subject + can/could + base verb
- I can speak English.
- She could swim when she was five.
- They can come tomorrow.
- We could visit them next week.
Important: After can/could, always use the base form of
the verb.
- ✅ She can speak English.
- ❌ She can speaks English.
- ✅ He could go there.
- ❌ He could went there.
1. CAN – Detailed Uses with Examples
A.
Ability – Present
Can shows that someone has the ability to do something now.
- She can speak three languages.
- I can swim very well.
- He can drive a car.
- They can solve difficult problems.
- We can understand the instructions.
Negative:
Can't / Cannot
- He can't drive yet.
- I can't swim.
- She cannot speak French.
- They can't solve this problem.
Structure
Subject + can + base verb
I can speak English.
Subject + can't + base verb
I can't speak Chinese.
B.
Permission – Informal
Can is commonly used to ask for or give permission in everyday
situations.
Asking
Permission
- Can I use
your phone?
- Can I sit
here?
- Can we leave
early today?
- Can I borrow
your pen?
- Can I open
the window?
Giving
Permission
- You can sit here.
- You can use my computer.
- You can leave now.
- Students can use the library after class.
C.
Possibility – General
Can can describe something that is possible in general or
something that sometimes happens.
- Smoking can cause serious health problems.
- It can get very hot here in summer.
- Anyone can make mistakes.
- Learning English can take time.
- Traffic can be heavy during rush hour.
Important
Difference
Can often describes general possibility, while could
often describes a specific or uncertain possibility.
- It can rain heavily in this region.
→ General possibility. - It could rain this evening.
→ Possible in this particular situation.
D.
Requests – Informal
Can is commonly used to ask someone to do something.
- Can you help
me?
- Can you pass
the salt?
- Can you open
the window?
- Can you explain
this question?
- Can you call
me later?
These are natural and common in
everyday English.
E.
Offers
Can I...? can be used to offer help or service.
- Can I help
you?
- Can I carry
your bag?
- Can I get
you a drink?
- Can I give
you a hand?
- Can I help
you with your homework?
F.
Prohibition – Can't
Can't can mean that something is not allowed.
- You can't park here.
- Students can't use phones during the
examination.
- You can't smoke inside the building.
- Visitors can't enter this room.
- You can't take photographs here.
Here, can't means must not
/ are not allowed to.
2. COULD – Detailed Uses with Examples
A.
Past Ability
Could is used to describe general ability in the past.
- When I was young, I could run very fast.
- She could play the piano at age five.
- My grandfather could speak several languages.
- When we were children, we could swim very well.
- He could read when he was four.
Negative
- I couldn't swim when I was six.
- She couldn't drive last year.
- He couldn't understand English at that time.
- We couldn't speak French when we were children.
Important
Rule: One Specific Past Achievement
For a single successful action in
the past, was/were able to or managed to is often preferred.
- ✅ Despite the storm, we were able to reach the
airport.
- ✅ Despite the storm, we managed to reach the
airport.
- ⚠️ Despite the storm, we could reach the
airport.
Could is normally better for general past ability:
When I was young, I could run
five kilometres.
3. COULD – Polite Requests
Could is often more polite or less direct than can.
- Could you please open
the door?
- Could you help
me with these bags?
- Could you explain
this again?
- Could you give
me a minute?
- Could you send
me the document?
Comparison
- Can you help me?
→ Casual/direct.
- Could you help me?
→ More polite/less direct.
Both are correct.
4. COULD – Polite Permission
Could can be used when asking for permission politely.
- Could I leave
the room for a moment?
- Could I borrow
your pen?
- Could we stay
another night?
- Could I use
your phone?
- Could I speak
to the manager?
Comparison
- Can I use your phone?
→ Informal.
- Could I use your phone? → More polite.
For very formal permission, may
is also possible:
May I use your phone?
5. COULD – Possibility
Could expresses possibility, often when the speaker is not
certain.
- It could rain later.
- She could be at home.
- He could be the person we are looking for.
- This could be the solution.
- They could arrive tomorrow.
Compare
She can be at home.
This is unusual if you mean
"maybe she is at home." Can is generally not used this way for
a specific present possibility.
She could be at home.
This means:
Maybe she is at home.
6. COULD – Suggestions
Could can give a gentle suggestion or possible option.
- You could try restarting your computer.
- We could go to the cinema tonight.
- You could ask your teacher.
- You could take a taxi.
- We could meet tomorrow.
The meaning is often:
"One possible option
is..."
Compare
- You can take a taxi.
→ It is possible/allowed for you to take a taxi. - You could take a taxi.
→ I am suggesting that taking a taxi is one option.
7. COULD – Hypothetical Situations
Could is frequently used in hypothetical or conditional
situations.
Second
Conditional
If + past simple, subject + could +
base verb
- If I had more money, I could buy a car.
- If you studied harder, you could pass the exam.
- If we left early, we could catch the train.
- If she had more time, she could learn another
language.
Meaning:
If the condition became true, the
result would be possible.
Third
Conditional
If + past perfect, subject + could
have + past participle
- If you had asked, I could have helped you.
- If we had left earlier, we could have caught the
bus.
- If she had studied harder, she could have passed
the exam.
- If they had informed us, we could have prepared
earlier.
Meaning:
The opportunity existed in the past,
but the situation did not happen.
8. COULD – Past Permission
Could can describe permission in the past.
- When we were children, we could stay up late on
Saturdays.
- We could play outside until sunset.
- He said I could use his laptop.
- Our teacher said we could leave early.
In reported speech:
"You can use my computer."
becomes:
He said I could use his
computer.
9. CAN vs. COULD – Key Differences
|
Feature |
CAN |
COULD |
|
Present ability |
✓ |
Usually not |
|
Past general ability |
Usually not |
✓ |
|
Informal permission |
✓ |
✓ |
|
Polite permission |
Possible |
More polite |
|
Informal request |
✓ |
✓ |
|
Polite request |
Possible |
More polite |
|
General possibility |
✓ |
✓ |
|
Specific uncertain possibility |
Usually not |
✓ |
|
Suggestion |
Sometimes |
✓ |
|
Hypothetical ability |
Sometimes |
✓ |
|
Past permission |
✓ in some contexts |
✓ |
|
Past specific achievement |
Usually not |
Usually not; use was/were able
to |
10. Comparison Examples
Ability
- I can swim.
→ I have the ability now. - I could swim when I was five.
→ I had the ability in the past.
Requests
- Can you help me?
→ Casual. - Could you help me?
→ More polite.
Permission
- Can I leave now?
→ Informal. - Could I leave now?
→ More polite.
General
vs. Specific Possibility
- It can rain heavily here in July.
→ General possibility. - It could rain tonight.
→ Specific possibility.
Permission
vs. Suggestion
- You can go now.
→ I give you permission. - You could go now.
→ I suggest that you go now.
11. Negative Forms
|
Form |
Main
Meaning |
Example |
|
can't / cannot |
Present inability |
I can't lift this box. |
|
can't / cannot |
Prohibition |
You can't smoke here. |
|
couldn't |
Past inability |
I couldn't swim as a child. |
|
couldn't |
Past impossibility/negative
possibility |
We couldn't find the
address. |
Contractions
- cannot → can't
- could not → couldn't
12. Special Structure: Could Have + Past Participle
Could have + past participle has several important uses.
A.
Past Possibility
- She could have missed the bus.
- He could have forgotten the appointment.
- They could have taken the wrong road.
Meaning:
It is possible that this happened.
B.
Missed Opportunity / Ability
- I could have helped you.
- We could have won the match.
- She could have passed the exam.
Meaning:
It was possible, but it did not
happen.
C.
Criticism
- You could have told me earlier!
- You could have called me.
- He could have been more careful.
Meaning:
You had the opportunity or
possibility to do something, but you did not.
13. Special Structure: Can't Have + Past Participle
Can't have + past participle expresses a strong negative deduction about the past.
- She can't have forgotten the meeting.
- He can't have finished so quickly.
- They can't have left already.
- She can't have seen us.
Meaning:
I am strongly convinced that this
did not happen.
Compare
- She could have forgotten the meeting.
→ Maybe she forgot. - She can't have forgotten the meeting.
→ I am sure she didn't forget.
14. Can and Could with Perception Verbs
Can is commonly used with verbs of perception such as:
- see
- hear
- smell
- taste
- feel
Present
- I can see the mountain.
- I can hear music.
- I can smell something burning.
- I can feel the wind.
Past
- I could see the mountains from our hotel.
- We could hear music from the house.
- She could smell smoke.
- He could feel the cold air.
15. Can't for Strong Deduction
Can't can express a strong belief that something is impossible or
untrue.
- She can't be serious!
- He can't be the manager.
- They can't be at home.
- This can't be the right answer.
Past
Deduction
Can't have + past participle
- He can't have forgotten the meeting.
- She can't have left already.
- They can't have finished the work.
16. Could for Weak or Possible Deduction
Could can express a possibility when the speaker is not certain.
- She could be at the office.
- He could be the person we need.
- They could be waiting outside.
- This could be the answer.
Compare
- She could be at home.
→ Maybe she is. - She must be at home.
→ I am quite sure she is. - She can't be at home.
→ I am sure she isn't.
17. Can vs. Could in Questions
Can
Used for direct, everyday questions:
- Can you help me?
- Can I come in?
- Can we start now?
- Can you explain this?
Could
Used for softer, more polite
questions:
- Could you help me?
- Could I come in?
- Could we start now?
- Could you explain this?
Important
Point
Could does not always refer to the past.
Compare:
Could you help me?
This normally refers to now,
not the past.
18. Common Errors
Error
1: Using "to" after can/could
❌ I can to speak English.
✅ I can speak English.
❌ She could to help us.
✅ She could help us.
Error
2: Adding -s to the main verb
❌ He can speaks English.
✅ He can speak English.
❌ She could goes there.
✅ She could go there.
Error
3: Using "did" with can/could
❌ Did you can swim?
✅ Could you swim?
or
✅ Were you able to swim?
Error
4: Using "will can"
❌ I will can help you tomorrow.
✅ I will be able to help you
tomorrow.
Because can does not normally
have a future form with will.
Error
5: Using "can" for a specific past success
❌ Despite the difficulty, we could
finish the project.
Better:
✅ Despite the difficulty, we were
able to finish the project.
✅ Despite the difficulty, we managed
to finish the project.
19. Can/Could + Be
Can
be – General possibility
- English can be difficult.
- Life can be unpredictable.
- The weather can be dangerous.
Could
be – Specific possibility
- He could be busy.
- She could be at school.
- This could be useful.
20. Can/Could + Have
Can
have
Can have is possible in certain structures, especially for general
possibility:
- Too much sugar can have negative effects.
- This medicine can have side effects.
Could
have
Could have + past participle is very common:
- She could have won.
- He could have helped us.
- They could have arrived earlier.
21. Can vs. Be Able To
Can and be able to often have the same meaning.
- I can swim.
- I am able to swim.
However, be able to is
necessary or more natural in some situations.
Future
❌ I will can help you.
✅ I will be able to help you.
Present
Perfect
❌ I have can finish the work.
✅ I have been able to finish
the work.
Infinitive
❌ I want to can speak English.
✅ I want to be able to speak
English.
22. Can vs. Could – Quick Decision Rules
Use
CAN when:
1.
You are talking about present
ability.
o
I can drive.
2.
You are asking for informal
permission.
o
Can I come
in?
3.
You are making an informal
request.
o
Can you
help me?
4.
You are talking about general
possibility.
o
It can be dangerous.
5.
You are giving permission.
o
You can leave now.
6.
You are expressing prohibition with can't.
o
You can't park here.
Use
COULD when:
1.
You are talking about general
past ability.
o
I could swim when I was
young.
2.
You want to make a polite request.
o
Could you
help me?
3.
You want to ask permission politely.
o
Could I
use your phone?
4.
You are expressing uncertain
possibility.
o
It could rain.
5.
You are making a suggestion.
o
You could try again.
6.
You are talking about a hypothetical
ability or possibility.
o
If I had more time, I could help.
7.
You are talking about a past
possibility or missed opportunity.
o
I could have helped you.
23. Easy Formula Chart
|
Meaning |
Structure |
Example |
|
Present ability |
can + V1 |
I can swim. |
|
Present inability |
can't + V1 |
I can't swim. |
|
Informal permission |
can + subject + V1? |
Can I leave? |
|
Informal request |
can + subject + V1? |
Can you help? |
|
General possibility |
can + V1 |
It can happen. |
|
Past general ability |
could + V1 |
I could swim at five. |
|
Polite request |
could + subject + V1? |
Could you help? |
|
Polite permission |
could + subject + V1? |
Could I leave? |
|
Present possibility |
could + V1 |
She could be busy. |
|
Suggestion |
could + V1 |
You could try again. |
|
Hypothetical ability |
could + V1 |
I could help if I had time. |
|
Past possibility |
could have + V3 |
He could have forgotten. |
|
Missed opportunity |
could have + V3 |
I could have helped. |
|
Strong negative deduction |
can't be / can't have + V3 |
He can't have done it. |
24. Final Summary
CAN
=
Present ability + informal
permission + informal requests + general possibility + offers + prohibition
Examples:
- I can speak English.
- Can I come
in?
- Can you help
me?
- It can be difficult.
- Can I help
you?
- You can't park here.
COULD
=
Past general ability + polite
requests + polite permission + uncertain possibility + suggestions +
hypothetical situations + past possibility
Examples:
- I could swim when I was young.
- Could you help
me?
- Could I use
your phone?
- It could rain tonight.
- You could try again.
- If I had money, I could buy a car.
- She could have forgotten.
The
easiest way to remember:
CAN = ability/possibility/permission
now or generally.
COULD = past ability, politeness,
possibility, suggestion, or hypothetical situation.
5 Conversation
Sets – Hospitality, Hotel Management, Travelling, Shopping & Jobs
SET 1: HOSPITALITY (Restaurant Setting)
People:
Waiter (Ramesh) & Guest (Ms. Sharma)
1.
Ramesh: Good evening, madam. Can I
take your order?
Ms. Sharma: Yes, could I see the menu first, please?
2.
Ms. Sharma: Can I get a table near the
window?
Ramesh: Of course. You can sit anywhere you like.
3.
Ramesh: Could I suggest our special
grilled fish today?
Ms. Sharma: That sounds good. Can you make it less spicy?
4.
Ms. Sharma: Could you bring me some water,
please?
Ramesh: Certainly. Can I get you anything else?
5.
Ms. Sharma: Can I have the bill, please?
Ramesh: Certainly, madam. I can bring it right away.
6.
Ms. Sharma: Could I pay by card?
Ramesh: Yes, you can pay by card or cash.
7.
Ms. Sharma: Can I have a receipt?
Ramesh: Of course. I can print it for you now.
8.
Ramesh: Could I call you a taxi?
Ms. Sharma: Yes, please. That could be very helpful.
SET 2: HOTEL MANAGEMENT (Front Desk)
People:
Receptionist (Anita) & Guest (Mr. Khan)
1.
Anita: Good afternoon. Can I help
you?
Mr. Khan: Yes, could I check in, please? I have a reservation.
2.
Mr. Khan: Could I have a room with a
city view?
Anita: Let me check. I can offer you room 504.
3.
Mr. Khan: Can I get an extra bed in my
room?
Anita: Yes, we can arrange that for you.
4.
Mr. Khan: Could you tell me the Wi-Fi
password?
Anita: Certainly. You can find it on the card in your room.
5.
Mr. Khan: Can I have breakfast in my
room?
Anita: Of course. You can call room service anytime.
6.
Mr. Khan: Could I extend my stay by one
night?
Anita: I can check availability. Could you wait a moment?
7.
Mr. Khan: Can I leave my luggage here
after checkout?
Anita: Yes, you can leave it at the bell desk.
8.
Mr. Khan: Could I speak to the manager,
please?
Anita: Certainly. I can call him now.
SET 3: TRAVELLING (At the Airport /
Tour Desk)
People:
Traveler (Sita) & Agent (Bikash)
1.
Sita: Could you help me find gate
12?
Bikash: Sure. You can take the escalator to the second floor.
2.
Sita: Can I change my flight to tomorrow?
Bikash: Let me check. You can change it for a small fee.
3.
Sita: Could I get a window seat,
please?
Bikash: Yes, I can assign you seat 14A.
4.
Sita: Can I carry this bag as hand
luggage?
Bikash: It could be too big. You can check it in.
5.
Sita: Could you recommend a good
hotel near the beach?
Bikash: You could try the Sea View Resort. I can book it
for you.
6.
Sita: Can I get a map of the city?
Bikash: Yes, you can take this one for free.
7.
Sita: Could I know the boarding
time?
Bikash: Boarding starts at 3:30. You can see it on the screen.
8.
Sita: Can I get a taxi from the
airport?
Bikash: Yes, you can find taxis outside Terminal 2.
SET 4: SHOPPING (Clothing Store)
People:
Customer (Maya) & Shop Assistant (Sunil)
1.
Maya: Could you show me that blue
jacket?
Sunil: Sure. You can try it on in the fitting room.
2.
Maya: Can I get this in a larger
size?
Sunil: Yes, I can bring you a larger size.
3.
Maya: Could I exchange it if it
doesn't fit?
Sunil: Of course. You can exchange it within 7 days.
4.
Maya: Can I get a discount on this?
Sunil: We could offer 10% off today.
5.
Maya: Could you check if you have it
in black?
Sunil: I can check the stock room. Please wait.
6.
Maya: Can I pay with my credit card?
Sunil: Yes, you can pay at the counter.
7.
Maya: Could you gift-wrap it for me?
Sunil: Certainly. I can wrap it in ten minutes.
8.
Maya: Can I have a bag for this?
Sunil: Yes, you can take this paper bag.
SET 5: JOB (Interview Conversation)
People:
Interviewer (Ms. Rai) & Candidate (Arjun)
1.
Ms. Rai: Could you tell me about
yourself?
Arjun: Yes, I can briefly summarize my experience in hospitality.
2.
Ms. Rai: Can you work night shifts?
Arjun: Yes, I can work any shift you need.
3.
Ms. Rai: Could you explain your last
job role?
Arjun: Certainly. I can explain it. I managed front-desk
operations.
4.
Ms. Rai: Can you speak any other
languages?
Arjun: I can speak English, Hindi, and basic French.
5.
Ms. Rai: Could you start next Monday?
Arjun: Yes, I can start next Monday.
6.
Ms. Rai: Can you handle difficult
guests?
Arjun: Yes, I can stay calm and solve problems politely.
7.
Ms. Rai: Could you send us your
references?
Arjun: Certainly. I can email them today.
8.
Ms. Rai: Can I ask why you want this
job?
Arjun: Certainly. I can say that this hotel matches my skills and
career goals.
6 Conversation
Sets – Using Can & Could
Topics:
Hospitality, Hotel Management, Travelling, Shopping, Job Interview, Customer
Service
Each
set has 8 short exchanges between two people.
SET 1: HOSPITALITY (Restaurant)
People:
Waiter (Ramesh) & Guest (Ms. Sharma)
1.
Ramesh: Good evening, madam. Can I
take your order?
Ms. Sharma: Yes, could I see the menu first, please?
2.
Ms. Sharma: Can I get a table near the
window?
Ramesh: Of course. You can sit anywhere you like.
3.
Ramesh: Could I suggest our special
grilled fish today?
Ms. Sharma: That sounds good. Can you make it less spicy?
4.
Ms. Sharma: Could you bring me some water,
please?
Ramesh: Certainly. Can I get you anything else?
5.
Ms. Sharma: Can I have the bill, please?
Ramesh: Certainly, madam. I can bring it right away.
6.
Ms. Sharma: Could I pay by card?
Ramesh: Yes, you can pay by card or cash.
7.
Ms. Sharma: Can I have a receipt?
Ramesh: Of course. I can print it for you now.
8.
Ramesh: Could I call you a taxi?
Ms. Sharma: Yes, please. That could be very helpful.
SET 2: HOTEL MANAGEMENT (Front Desk)
People:
Receptionist (Anita) & Guest (Mr. Khan)
1.
Anita: Good afternoon. Can I help
you?
Mr. Khan: Yes, could I check in, please? I have a reservation.
2.
Mr. Khan: Could I have a room with a
city view?
Anita: Let me check. I can offer you room 504.
3.
Mr. Khan: Can I get an extra bed in my
room?
Anita: Yes, we can arrange that for you.
4.
Mr. Khan: Could you tell me the Wi-Fi
password?
Anita: Certainly. You can find it on the card in your room.
5.
Mr. Khan: Can I have breakfast in my
room?
Anita: Of course. You can call room service anytime.
6.
Mr. Khan: Could I extend my stay by one
night?
Anita: I can check availability. Could you wait a moment?
7.
Mr. Khan: Can I leave my luggage here
after checkout?
Anita: Yes, you can leave it at the bell desk.
8.
Mr. Khan: Could I speak to the manager,
please?
Anita: Certainly. I can call him now.
SET 3: TRAVELLING (Airport / Tour
Desk)
People:
Traveler (Sita) & Agent (Bikash)
1.
Sita: Could you help me find gate
12?
Bikash: Sure. You can take the escalator to the second floor.
2.
Sita: Can I change my flight to
tomorrow?
Bikash: Let me check. You can change it for a small fee.
3.
Sita: Could I get a window seat,
please?
Bikash: Yes, I can assign you seat 14A.
4.
Sita: Can I carry this bag as hand
luggage?
Bikash: It could be too big. You can check it in.
5.
Sita: Could you recommend a good
hotel near the beach?
Bikash: You could try the Sea View Resort. I can book it
for you.
6.
Sita: Can I get a map of the city?
Bikash: Yes, you can take this one for free.
7.
Sita: Could I know the boarding
time?
Bikash: Boarding starts at 3:30. You can see it on the screen.
8.
Sita: Can I get a taxi from the
airport?
Bikash: Yes, you can find taxis outside Terminal 2.
SET 4: SHOPPING (Clothing Store)
People:
Customer (Maya) & Shop Assistant (Sunil)
1.
Maya: Could you show me that blue
jacket?
Sunil: Sure. You can try it on in the fitting room.
2.
Maya: Can I get this in a larger
size?
Sunil: Yes, I can bring you a larger size.
3.
Maya: Could I exchange it if it
doesn't fit?
Sunil: Of course. You can exchange it within 7 days.
4.
Maya: Can I get a discount on this?
Sunil: We could offer 10% off today.
5.
Maya: Could you check if you have it
in black?
Sunil: I can check the stock room. Please wait.
6.
Maya: Can I pay with my credit card?
Sunil: Yes, you can pay at the counter.
7.
Maya: Could you gift-wrap it for me?
Sunil: Certainly. I can wrap it in ten minutes.
8.
Maya: Can I have a bag for this?
Sunil: Yes, you can take this paper bag.
SET 5: JOB INTERVIEW
People:
Interviewer (Ms. Rai) & Candidate (Arjun)
1.
Ms. Rai: Could you tell me about
yourself?
Arjun: Yes, I can summarize my experience in hospitality.
2.
Ms. Rai: Can you work night shifts?
Arjun: Yes, I can work any shift you need.
3.
Ms. Rai: Could you explain your last
job role?
Arjun: Certainly. I can explain it. I managed front-desk
operations.
4.
Ms. Rai: Can you speak any other
languages?
Arjun: I can speak English, Hindi, and basic French.
5.
Ms. Rai: Could you start next Monday?
Arjun: Yes, I can start next Monday.
6.
Ms. Rai: Can you handle difficult
guests?
Arjun: Yes, I can stay calm and solve problems politely.
7.
Ms. Rai: Could you send us your
references?
Arjun: Certainly. I can email them today.
8.
Ms. Rai: Can I ask why you want this
job?
Arjun: Certainly. I can say that this hotel matches my skills and
career goals.
SET 6: CUSTOMER SERVICE (Phone Call –
Hotel Booking)
People:
Customer (Priya) & Reservations Agent (Deepak)
1.
Deepak: Good morning, Sunrise Hotel. Can
I help you?
Priya: Yes, could I book a room for two nights?
2.
Priya: Can I get a room with a
balcony?
Deepak: Yes, you can book a deluxe room with a balcony.
3.
Priya: Could you tell me the price
per night?
Deepak: It can cost $80 per night, including breakfast.
4.
Priya: Can I cancel free of charge?
Deepak: You can cancel up to 24 hours before arrival.
5.
Priya: Could I get an early check-in?
Deepak: We can arrange early check-in if the room is ready.
6.
Priya: Can I bring my pet with me?
Deepak: I'm sorry, pets can't stay in the rooms. But you could
use our pet-care service.
7.
Priya: Could you send me a
confirmation email?
Deepak: Of course. I can send it right away.
8.
Priya: Can I pay on arrival?
Deepak: Yes, you can pay at the front desk.