message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
n,k=int(input()),int(input())
ans=1
for i in range(n):
ans=min(ans*2,ans+k)
print(ans)
``` | instruction | 0 | 633 | 5 | 1,266 |
Yes | output | 1 | 633 | 5 | 1,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
n=int(input())
m=int(input())
s=1
for i in range(n):
s = min(s*2, s+m)
print(s)
``` | instruction | 0 | 634 | 5 | 1,268 |
Yes | output | 1 | 634 | 5 | 1,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
from sys import stdin
N=int(stdin.readline().rstrip())
K=int(stdin.readline().rstrip())
num = 1
cnt = 0
while num < N:
num = num * 2
cnt += 1
for _ in range(N-cnt):
num += K
print(num)
``` | instruction | 0 | 635 | 5 | 1,270 |
No | output | 1 | 635 | 5 | 1,271 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
n = int(input())
k = int(input())
num = 2**n
list = [format(str(i),"b").zfill(n) for i in range(num)]
result = []
for i in list:
a = 1
for j in len(i):
if i[j] == "0":
a *= 2
else:
a += k
result.apppend(a)
print(max(result))
``` | instruction | 0 | 636 | 5 | 1,272 |
No | output | 1 | 636 | 5 | 1,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
import math
N = int(input())
K = int(input())
twice_count = int(math.log2(K)) + 1
print(2**twice_count + K*(N - twice_count))
``` | instruction | 0 | 637 | 5 | 1,274 |
No | output | 1 | 637 | 5 | 1,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Square1001 has seen an electric bulletin board displaying the integer 1. He can perform the following operations A and B to change this value:
* Operation A: The displayed value is doubled.
* Operation B: The displayed value increases by K.
Square1001 needs to perform these operations N times in total. Find the minimum possible value displayed in the board after N operations.
Constraints
* 1 \leq N, K \leq 10
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
K
Output
Print the minimum possible value displayed in the board after N operations.
Examples
Input
4
3
Output
10
Input
10
10
Output
76
Submitted Solution:
```
n=int(input())
k=int(input())
a=1
for i in range(n):
if a*2>a+k:
a=a*2
else:
a=a+k
print(a)
``` | instruction | 0 | 638 | 5 | 1,276 |
No | output | 1 | 638 | 5 | 1,277 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 639 | 5 | 1,278 |
"Correct Solution:
```
A,B,C = map(int,input().split())
print('Yes') if A<=C<=B else print('No')
``` | output | 1 | 639 | 5 | 1,279 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 640 | 5 | 1,280 |
"Correct Solution:
```
a,b,c=map(int,input().split())
print("YNeos"[a>c or c>b::2])
``` | output | 1 | 640 | 5 | 1,281 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 641 | 5 | 1,282 |
"Correct Solution:
```
a, b, c = map(int,input().split())
print('Yes') if a <= c <= b else print('No')
``` | output | 1 | 641 | 5 | 1,283 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 642 | 5 | 1,284 |
"Correct Solution:
```
A, B, C = map(int, input().split())
print("Yes") if A <= C and C <= B else print("No")
``` | output | 1 | 642 | 5 | 1,285 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 643 | 5 | 1,286 |
"Correct Solution:
```
a,b,c = map(int,input().split())
print("Yes" if a <= c and c <= b else "No")
``` | output | 1 | 643 | 5 | 1,287 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 644 | 5 | 1,288 |
"Correct Solution:
```
a,b,c = map(int,input().split())
print(('No','Yes')[a<=c and c<=b])
``` | output | 1 | 644 | 5 | 1,289 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 645 | 5 | 1,290 |
"Correct Solution:
```
a,b,c=map(int,input().split())
if (a<=c<=b):
print("Yes")
else:
print("No")
``` | output | 1 | 645 | 5 | 1,291 |
Provide a correct Python 3 solution for this coding contest problem.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes | instruction | 0 | 646 | 5 | 1,292 |
"Correct Solution:
```
A, B, C = map(int, input().split())
ans = 'Yes' if A <= C <= B else 'No'
print(ans)
``` | output | 1 | 646 | 5 | 1,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
A,B,C=map(int,input().split())
if A<=C and C<=B:
print('Yes')
else:
print('No')
``` | instruction | 0 | 647 | 5 | 1,294 |
Yes | output | 1 | 647 | 5 | 1,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
a, b, c = map(int,input().split())
ans = 'Yes' if a <= c <= b else 'No'
print(ans)
``` | instruction | 0 | 648 | 5 | 1,296 |
Yes | output | 1 | 648 | 5 | 1,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
#061_A
a,b,c=map(int,input().split())
print('Yes' if a<=c<=b else 'No')
``` | instruction | 0 | 649 | 5 | 1,298 |
Yes | output | 1 | 649 | 5 | 1,299 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
a,b,c = map(int,input().split())
if a<=c<=b:
print("Yes")
else:
print("No")
``` | instruction | 0 | 650 | 5 | 1,300 |
Yes | output | 1 | 650 | 5 | 1,301 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
a,b,c=map(int,input().split());print('
NYoe s'[a<=c<=b::2])
``` | instruction | 0 | 651 | 5 | 1,302 |
No | output | 1 | 651 | 5 | 1,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
A,B,C = input().split()
print('Yes' if A <= C <= B else 'No')
``` | instruction | 0 | 652 | 5 | 1,304 |
No | output | 1 | 652 | 5 | 1,305 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
a, b, c = map(int, input().split())
if a <= c <= b:
print("Yse")
else:
print("No")
``` | instruction | 0 | 653 | 5 | 1,306 |
No | output | 1 | 653 | 5 | 1,307 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three integers A, B and C. Determine whether C is not less than A and not greater than B.
Constraints
* -100≤A,B,C≤100
* A, B and C are all integers.
Input
Input is given from Standard Input in the following format:
A B C
Output
If the condition is satisfied, print `Yes`; otherwise, print `No`.
Examples
Input
1 3 2
Output
Yes
Input
6 5 4
Output
No
Input
2 2 2
Output
Yes
Submitted Solution:
```
print('YNeos'[eval(input().replace(' ','<='))::2])
``` | instruction | 0 | 654 | 5 | 1,308 |
No | output | 1 | 654 | 5 | 1,309 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 780 | 5 | 1,560 |
"Correct Solution:
```
N=int(input())
A,B=map(int,input().split())
def one(n,A,B):
if n%2==0:
return A-B,B
else:
return A,A+B
N=N%12
for i in range(N):
A,B=one(i,A,B)
print(A,B)
``` | output | 1 | 780 | 5 | 1,561 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 781 | 5 | 1,562 |
"Correct Solution:
```
N = int(input())
A, B = map(int, input().split())
ret = [(A, B)]
for i in range(1, 12) :
if i % 2 == 0 :
B = A + B
else :
A = A - B
ret.append((A, B))
print(*ret[N % 12])
``` | output | 1 | 781 | 5 | 1,563 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 782 | 5 | 1,564 |
"Correct Solution:
```
n=int(input())
a,b=map(int,input().split())
n=n%12
for i in range(n):
if i % 2:
b=a+b
else:
a=a-b
print(a,b)
``` | output | 1 | 782 | 5 | 1,565 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 783 | 5 | 1,566 |
"Correct Solution:
```
n = int(input())
a,b = map(int,input().split())
s = n%12
for i in range(1,s+1):
if i % 2 == 0:
b = a+b
else:
a = a-b
print(a,b)
``` | output | 1 | 783 | 5 | 1,567 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 784 | 5 | 1,568 |
"Correct Solution:
```
N = int(input())
A, B = map(int,input().split())
N = N%12
for k in range(1,N+1):
if k%2 == 1:
A -= B
else:
B += A
print(A,B)
``` | output | 1 | 784 | 5 | 1,569 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 785 | 5 | 1,570 |
"Correct Solution:
```
N = int(input())
A, B = map(int, input().split())
N %= 12
for i in range(1, N + 1):
if i % 2 == 1:
A = A - B
else:
B = A + B
print(A, B)
``` | output | 1 | 785 | 5 | 1,571 |
Provide a correct Python 3 solution for this coding contest problem.
Tashizan Hikizan (Calculation Training)
square1001 You gave E869120 two numbers, $ A $ and $ B $, as birthday presents.
E869120 You decided to use these two numbers for calculation training.
Specifically, E869120 does the following for these numbers exactly $ N $ times:
* Replace $ A $ with $ A-B $ on odd-numbered operations
* Replace $ B $ with $ A + B $ on even-numbered operations
E869120 Find out what the values of $ A $ and $ B $ are after you have operated $ N $ times.
input
Input is given from standard input in the following format.
$ N $
$ A $ $ B $
output
E869120 Please output the values of $ A $ and $ B $ after you have operated $ N $ times in this order, separated by blanks.
However, insert a line break at the end.
Constraint
* $ 1 \ leq N \ leq 1000000000000000000 \ (= 10 ^ {18}) $
* $ 1 \ leq A \ leq 1000000000 \ (= 10 ^ 9) $
* $ 1 \ leq B \ leq 1000000000 \ (= 10 ^ 9) $
* All inputs are integers.
Input example 1
3
3 4
Output example 1
-4 3
The value of $ (A, B) $ changes as $ (3,4) → (-1,4) → (-1,3) → (-4,3) $.
Input example 2
8
6 9
Output example 2
3 -6
Example
Input
3
3 4
Output
-4 3 | instruction | 0 | 787 | 5 | 1,574 |
"Correct Solution:
```
n = int(input())
a,b = map(int,input().split())
n %= 12
for i in range(n):
if i%2 == 0:
a = a-b
else:
b = a+b
print(a,b)
``` | output | 1 | 787 | 5 | 1,575 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
from collections import deque
import math
import os
import random
import re
import sys
#n=list(map(int, input().split()))
#n=map(int, input().split())
def main():
t=int(input())
if (t-2) %3:
print('1 1',t-2)
else:
print('1 2',t-3)
main()
``` | instruction | 0 | 827 | 5 | 1,654 |
Yes | output | 1 | 827 | 5 | 1,655 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
n=int(input())
a=1
b=1
c=n-2
if c%3==0:
c=c-1
b=b+1
print(a,b,c)
``` | instruction | 0 | 828 | 5 | 1,656 |
Yes | output | 1 | 828 | 5 | 1,657 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
x = int(input())
a = 1
b = 1
c = x-(a+b)
if(c%3==0):
a+=1
c-=1
print(a,b,c)
``` | instruction | 0 | 829 | 5 | 1,658 |
Yes | output | 1 | 829 | 5 | 1,659 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
a = int(input())
if ((a-2)%3 != 0):
p = q =1
r = (a-2)
elif ((a-2)%3 == 0):
p = 1
q = 2
r = (a-3)
print (int(p),int(q),int(r))
``` | instruction | 0 | 830 | 5 | 1,660 |
Yes | output | 1 | 830 | 5 | 1,661 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
n=int(input())
k=4
if n==3:
print(1,1,1)
exit()
if (n-3)%3!=0:
print(1,2,n-3)
else:
while ((n-k)%3==0 or k%3==0):
k+=1
print(1,k,n-k)
``` | instruction | 0 | 831 | 5 | 1,662 |
No | output | 1 | 831 | 5 | 1,663 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
n=int(input())
q=n//3
r=n%3
if(q==1):
print("1 1 1")
elif(q%3==0):
print(q-1,q-1,q+2+r)
else:
print(q,q,q+r)
``` | instruction | 0 | 832 | 5 | 1,664 |
No | output | 1 | 832 | 5 | 1,665 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
n=int(input())
if n%3==0:print("1 1 %d"%(n-2))
else:print("2 2 %d"%(n-4))
``` | instruction | 0 | 833 | 5 | 1,666 |
No | output | 1 | 833 | 5 | 1,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little C loves number «3» very much. He loves all things about it.
Now he has a positive integer n. He wants to split n into 3 positive integers a,b,c, such that a+b+c=n and none of the 3 integers is a multiple of 3. Help him to find a solution.
Input
A single line containing one integer n (3 ≤ n ≤ 10^9) — the integer Little C has.
Output
Print 3 positive integers a,b,c in a single line, such that a+b+c=n and none of them is a multiple of 3.
It can be proved that there is at least one solution. If there are multiple solutions, print any of them.
Examples
Input
3
Output
1 1 1
Input
233
Output
77 77 79
Submitted Solution:
```
n = int(input())
if (n - 3) % 3 == 0 and n > 3:
print(2, 2, n - 4)
else:
print(1, 1, n - 2)
``` | instruction | 0 | 834 | 5 | 1,668 |
No | output | 1 | 834 | 5 | 1,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
n, d = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
ans = 0
for i in range(1,n):
if a[i]>a[i-1]:
continue
else:
dif = a[i-1]-a[i]
ans += dif//d + 1
a[i] += (dif//d + 1) * d
print(ans)
``` | instruction | 0 | 909 | 5 | 1,818 |
Yes | output | 1 | 909 | 5 | 1,819 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
n,d = map(int,input().split())
a = list(map(int,input().split()))
ans = 0
for i in range(1,n):
if a[i] == a[i-1]: a[i]+=d; ans += 1
elif a[i] < a[i-1]:
ans += -(-(a[i-1]-a[i])//d);
a[i]+= (-(-(a[i-1]-a[i])//d))*d
if a[i] == a[i-1]: ans += 1; a[i]+=d
print(ans)
``` | instruction | 0 | 910 | 5 | 1,820 |
Yes | output | 1 | 910 | 5 | 1,821 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
l1 = [int(x) for x in input().split()]
n,d = l1[0],l1[1]
l2 = [int(x) for x in input().split()]
l2.reverse()
ans=0
for x in range(len(l2)-1):
while l2[x]<=l2[x+1]:
l2[x]+=d
ans+=1
print(ans)
``` | instruction | 0 | 913 | 5 | 1,826 |
No | output | 1 | 913 | 5 | 1,827 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
from math import ceil
n,d=map(int,input().split())
l=list(map(int,input().split()))
ma=l[0]
m=0
for i in range(1,len(l)):
if l[i]>ma:
ma=l[i]
else:
p=ceil((ma-l[i])/d)
m+=p+1
# print(m)
ma=l[i]
print(m)
``` | instruction | 0 | 914 | 5 | 1,828 |
No | output | 1 | 914 | 5 | 1,829 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
import math
n,d=map(int,input().split())
a=list(map(int,input().split()))
c=0
for i in range(0,n-1):
if(a[i]>a[i+1]):
a[i+1]+=(math.ceil((a[i]-a[i+1])/d))*d
c+=math.ceil((a[i]-a[i+1])/d)
elif(a[i]==a[i+1]):
a[i+1]+=d
c+=1
print(c)
``` | instruction | 0 | 915 | 5 | 1,830 |
No | output | 1 | 915 | 5 | 1,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.
You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?
Input
The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).
Output
Output the minimal number of moves needed to make the sequence increasing.
Examples
Input
4 2
1 3 3 2
Output
3
Submitted Solution:
```
n,d=map(int,input().split())
l=[int(c) for c in input().split()]
t=[]
s=0
for i in range(1,n):
t+=[l[i]-l[i-1]]
for i in range(len(t)):
s+=t[i]//d+1
print(s)
``` | instruction | 0 | 916 | 5 | 1,832 |
No | output | 1 | 916 | 5 | 1,833 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0. | instruction | 0 | 952 | 5 | 1,904 |
Tags: binary search, math
Correct Solution:
```
for qq in range(int(input())):
a, b =map(int, input().split())
if (a+b) > 3*min(a,b):
print("NO")
elif (a+b) % 3 != 0:
print("NO")
continue
else:
if a==b==0:
print("YES")
elif a == 0 or b == 0:
print("NO")
else:
print("YES")
``` | output | 1 | 952 | 5 | 1,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
t = int(input())
for test in range(t):
a,b = map(int,input().split())
if a*b == 0 and max(a,b) > 0:
print('NO')
else:
if a == b:
if a%3 == 0:
print('YES')
else:
print('NO')
else:
if (2*a-b)%3 == 0 and 2*a >= b and 2*b >= a:
print('YES')
else:
print('NO')
``` | instruction | 0 | 957 | 5 | 1,914 |
Yes | output | 1 | 957 | 5 | 1,915 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
t = int(input())
for i in range(t):
x, y = map(int, input().split())
if abs(x - y) > min(x, y):
print("No")
else:
if (x + y) % 3 == 0:
print("Yes")
else:
print("No")
``` | instruction | 0 | 958 | 5 | 1,916 |
Yes | output | 1 | 958 | 5 | 1,917 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
for _ in range(int(input())):
a=list(map(int,input().split()))
a.sort()
if (a[0]+a[1])%3==0 and a[0]*2>=a[1]:
print("YES")
else:
print("NO")
``` | instruction | 0 | 959 | 5 | 1,918 |
Yes | output | 1 | 959 | 5 | 1,919 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
n=int(input())
lst=[]
for i in range(n):
lst1=list(map(int,input().split()))
lst.append(lst1)
for i in range(n):
a=lst[i][0]
b=lst[i][1]
if a>b:
a,b=b,a
if b==2*a:
print('yes')
else:
c=b-a
if (a-c)%3==0 and a-c>=0:
print('yes')
else:
print('no')
``` | instruction | 0 | 960 | 5 | 1,920 |
Yes | output | 1 | 960 | 5 | 1,921 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
import math
t=int(input())
for i in range(t):
s=input().split()
a=int(s[0])
b=int(s[1])
x=min(a,b)
y=max(a,b)
if( y > 2*x):
print("NO")
else:
hc= math.gcd(x,y)
if x==y==2:
print("NO")
elif hc!=1:
print("YES")
else:
af=0
if (x+y-3)%3==0 and (x+y-3)/3 >=0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 961 | 5 | 1,922 |
No | output | 1 | 961 | 5 | 1,923 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
"""
NTC here
"""
from sys import stdin, setrecursionlimit
setrecursionlimit(10**6)
def iin(): return int(stdin.readline())
def lin(): return list(map(int, stdin.readline().split()))
# range = xrange
# input = raw_input
# print("Case #{}: {} {}".format(i, n + m, n * m))
def check(a,b):
x=(2*a-b)/3
return int(x*100000)==int(x)*100000
def main():
n=iin()
for _ in range(n):
a,b=lin()
if a==2*b or b==a*2:print('YES')
else:
if check(a,b) and check(b,a):print('YES')
else:print('NO')
main()
``` | instruction | 0 | 962 | 5 | 1,924 |
No | output | 1 | 962 | 5 | 1,925 |
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