message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes | instruction | 0 | 62,987 | 16 | 125,974 |
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
x4=0
x2=0
for i in a:
if i%4==0:
x4+=1
elif i%2==0:
x2+=1
if x4*2+x2>=n or x4>=n//2:
print("Yes")
else:
print("No")
``` | output | 1 | 62,987 | 16 | 125,975 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes | instruction | 0 | 62,988 | 16 | 125,976 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
B = []
for a in A:
B.append(a%4)
ans = 'No'
if B.count(0) >= B.count(1)+B.count(3):
ans = 'Yes'
if B.count(2) == 0 and B.count(0) == B.count(1)+B.count(3)-1:
ans = 'Yes'
print(ans)
``` | output | 1 | 62,988 | 16 | 125,977 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes | instruction | 0 | 62,989 | 16 | 125,978 |
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split()))
ans = 0
for i in A:
if i%4 == 0:
ans += 2
elif i%2 == 0:
ans += 1
if ans >= N - int(N%2==1):
print("Yes")
else:
print("No")
``` | output | 1 | 62,989 | 16 | 125,979 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
N = int(input())
A = [int(a) for a in input().split()]
c4 = 0
c2 = 0
for a in A:
if a % 4 == 0: c4 += 1
elif a % 2 == 0: c2 += 1
if c4 >= N // 2:
print("Yes")
elif c2 >= N - 2 * c4:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,990 | 16 | 125,980 |
Yes | output | 1 | 62,990 | 16 | 125,981 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
n=int(input())
l=list(map(int,input().split()))
count2=0
count4=0
for i in range(n):
if l[i]%4==0:
count4+=1
elif l[i]%2==0:
count2+=1
if count4*2+count2>=n or count4*2+1>=n:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,991 | 16 | 125,982 |
Yes | output | 1 | 62,991 | 16 | 125,983 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
A0=0
A4=0
for i in range(N):
if A[i]%2==1:
A0+=1
elif A[i]%4==0:
A4+=1
if A4>=A0:
print("Yes")
elif A4+1==A0 and A4+A0==N:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,992 | 16 | 125,984 |
Yes | output | 1 | 62,992 | 16 | 125,985 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
N=int(input())
a=list(map(int,input().split()))
n4,n2=0,0
for i in range(N):
if a[i] % 4 == 0:n4 += 1
elif a[i] % 2 == 0:n2 += 1
if n4 >= N//2:print('Yes')
elif n4*2 + n2 >= N:print('Yes')
else:print('No')
``` | instruction | 0 | 62,993 | 16 | 125,986 |
Yes | output | 1 | 62,993 | 16 | 125,987 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
count4=0
count2=0
for i in a:
if i%4==0:
count4+=1
elif i%2==0:
count2+=1
if count2==1:
count1=len(a)-count4
else:
count1=len(a)-count4-count2
if len(a)==1 and a[0]==2:
elif count1-count4<=1:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,994 | 16 | 125,988 |
No | output | 1 | 62,994 | 16 | 125,989 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
N = int(input())
l = list(map(int,input().split()))
cnt_t = 0
cnt_f = 0
for i in l:
if i%4==0:
cnt_f += 1
elif i%2==0:
cnt_t += 1
num = N-cnt_t-cnt_f
if num <= cnt_f:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,995 | 16 | 125,990 |
No | output | 1 | 62,995 | 16 | 125,991 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
n=input()
nums=list(map(int,input().split(" ")))
n4=0
m2=0
m4=0
for num in nums:
if num%4!=0:
n4+=1
if num%4==0:
m4+=1
elif num%2==0:
m2+=1
if n4-m2<=m4+1:
print("Yes")
else:
print("No")
``` | instruction | 0 | 62,996 | 16 | 125,992 |
No | output | 1 | 62,996 | 16 | 125,993 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
Submitted Solution:
```
n = int(input())
a_L = list(map(int,input().split()))
L = [0 for _ in range(n)]
one = 0
for i in range(n):
if a_L[i]%2==0:
L[i] = 1
one += 1
ans = ""
if n%2 == 0:
if n/2 <= one:
ans = "Yes"
else:
ans = "No"
else:
if int(n/2) <= one:
ans = "Yes"
else:
ans = "No"
print(ans)
``` | instruction | 0 | 62,997 | 16 | 125,994 |
No | output | 1 | 62,997 | 16 | 125,995 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,848 | 16 | 127,696 |
"Correct Solution:
```
n=int(input())
k=int(input())
x=list(map(int,input().split()))
l=0
for i in range(n):
l+=min(x[i],k-x[i])*2
print(l)
``` | output | 1 | 63,848 | 16 | 127,697 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,849 | 16 | 127,698 |
"Correct Solution:
```
n = int(input())
k = int(input())
x = map(int, input().split())
print(sum(map(lambda y: min(y, abs(k - y)) * 2, x)))
``` | output | 1 | 63,849 | 16 | 127,699 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,850 | 16 | 127,700 |
"Correct Solution:
```
n,k,*x=map(int,open(0).read().split());print(sum([min(i,k-i) for i in x])*2)
``` | output | 1 | 63,850 | 16 | 127,701 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,851 | 16 | 127,702 |
"Correct Solution:
```
N=int(input())
K=int(input())
X=list(map(int,input().split()))
sm=0
for x in X:
sm+=min(x,K-x)*2
print(sm)
``` | output | 1 | 63,851 | 16 | 127,703 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,852 | 16 | 127,704 |
"Correct Solution:
```
N=int(input())
K=int(input())
x=list(map(int, input().split()))
print(sum([min(x[i], abs(x[i]-K)) for i in range(N)])*2)
``` | output | 1 | 63,852 | 16 | 127,705 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,853 | 16 | 127,706 |
"Correct Solution:
```
n = int(input())
k = int(input())
l = list(map(int, input().split()))
c = 0
for x in l:
c += min(x,k-x)
print(2*c)
``` | output | 1 | 63,853 | 16 | 127,707 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,854 | 16 | 127,708 |
"Correct Solution:
```
n=int(input())
k=int(input())
x=list(map(int,input().split()))
ans=0
for xi in x:
ans+=min(xi,abs(xi-k))*2
print(ans)
``` | output | 1 | 63,854 | 16 | 127,709 |
Provide a correct Python 3 solution for this coding contest problem.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74 | instruction | 0 | 63,855 | 16 | 127,710 |
"Correct Solution:
```
_,k=int(input()),int(input())
print(sum([min([i,k-i])*2 for i in list(map(int,input().split()))]))
``` | output | 1 | 63,855 | 16 | 127,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74
Submitted Solution:
```
N=int(input())
K=int(input())
x=list(map(int, input().split()))
d=0
for i in range(N):
d+=min(x[i],K-x[i])*2
print(d)
``` | instruction | 0 | 63,857 | 16 | 127,714 |
Yes | output | 1 | 63,857 | 16 | 127,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74
Submitted Solution:
```
n, k, *xx = map(int, open(0).read().split())
print(2 * sum(min(abs(x), abs(k-x)) for x in xx))
``` | instruction | 0 | 63,858 | 16 | 127,716 |
Yes | output | 1 | 63,858 | 16 | 127,717 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74
Submitted Solution:
```
n=int(input())
k=int(input())
ans=0
for _ in map(int,input().split()):
a=int(input())
ans+=min(a,k-a)
print(ans+ans)
``` | instruction | 0 | 63,860 | 16 | 127,720 |
No | output | 1 | 63,860 | 16 | 127,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74
Submitted Solution:
```
n = int(input())
k = int(input())
l = [int(i) for i in input().split()]
s = 0
for i in range(n):
if k - l[i] > l[i]:
s += l[i] * 2
elif k - l[i] < l[i]:
s += 2 * (k - l[i])
print(s)
``` | instruction | 0 | 63,861 | 16 | 127,722 |
No | output | 1 | 63,861 | 16 | 127,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N balls in the xy-plane. The coordinates of the i-th of them is (x_i, i). Thus, we have one ball on each of the N lines y = 1, y = 2, ..., y = N.
In order to collect these balls, Snuke prepared 2N robots, N of type A and N of type B. Then, he placed the i-th type-A robot at coordinates (0, i), and the i-th type-B robot at coordinates (K, i). Thus, now we have one type-A robot and one type-B robot on each of the N lines y = 1, y = 2, ..., y = N.
When activated, each type of robot will operate as follows.
* When a type-A robot is activated at coordinates (0, a), it will move to the position of the ball on the line y = a, collect the ball, move back to its original position (0, a) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
* When a type-B robot is activated at coordinates (K, b), it will move to the position of the ball on the line y = b, collect the ball, move back to its original position (K, b) and deactivate itself. If there is no such ball, it will just deactivate itself without doing anything.
Snuke will activate some of the 2N robots to collect all of the balls. Find the minimum possible total distance covered by robots.
Constraints
* 1 \leq N \leq 100
* 1 \leq K \leq 100
* 0 < x_i < K
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
K
x_1 x_2 ... x_N
Outputs
Print the minimum possible total distance covered by robots.
Examples
Input
1
10
2
Output
4
Input
2
9
3 6
Output
12
Input
5
20
11 12 9 17 12
Output
74
Submitted Solution:
```
n = int(input())
b = int(input())
d = list(map(int, input().split()))
c = 0
for i in d:
if i < b - i:
c += i
else:
c += b-i
print(c)
``` | instruction | 0 | 63,863 | 16 | 127,726 |
No | output | 1 | 63,863 | 16 | 127,727 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,411 | 16 | 130,822 |
"Correct Solution:
```
def combination(k, r, MOD):
"""kCrを求める"""
if k < r:
return 0
r = min(r, k - r)
numer, denom = 1, 1
for l in range(r):
numer *= (k - l)
numer %= MOD
denom *= l + 1
denom %= MOD
return numer * pow(denom, MOD - 2, MOD) % MOD
t = int(input())
MOD = 10 ** 9 + 7
for i in range(t):
n = int(input())
n -= 5
res = 0
for odd_cnt in range(12):
if n - odd_cnt < 0 or (n - odd_cnt) % 2 == 1:
continue
m = (n - odd_cnt) // 2
res += combination(m + 15, 15, MOD) * combination(11, odd_cnt, MOD)
res %= MOD
print(res)
``` | output | 1 | 65,411 | 16 | 130,823 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,412 | 16 | 130,824 |
"Correct Solution:
```
#!python3
import sys
iim = lambda: map(int, sys.stdin.readline().rstrip().split())
from functools import lru_cache
mod = 10 **9 + 7
@lru_cache(100)
def calc(n):
m = (n-5) // 2
#return (1+m)*(2+m)*(3+m)*(4+m)*(5+m)*(1025024*m**10+3003*(-4+n)*(-3+n)*(-2+n)*(-1+n)*n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)-549120*m**9*(-1+10*n)+42240*m**8*(-398+45*n*(-1+7*n))-369600*m**7*(3+2*(-2+n)*n*(49+26*n))+2688*m**6*(33529+75*n*(-33-679*n+91*n**3))-336*m**5*(88065+2*n*(426107+7*n*(-6675+13*n*(-2420+9*n*(5+22*n)))))+560*m**4*(-291598+n*(216249+7*n*(95465+26*n*(-495+n*(-980+11*n*(3+5*n))))))-30*m**3*(-3080960+n*(-10447602+7*n*(854525+13*n*(93170+n*(-15295+22*n*(-714+5*n*(7+6*n)))))))+2*m**2*(28412712+25*n*(-3433650+n*(-4123841+13*n*(189882+n*(142177+22*n*(-1344+n*(-791+27*n*(2+n))))))))-m*(30149280+n*(31294296+n*(-93275400+13*n*(-3808420+n*(2988195+11*n*(111678+25*n*(-1302+n*(-456+n*(45+14*n))))))))))/1307674368000
return (
(1+m)*(2+m)*(3+m)*(4+m)*(5+m)%mod*(
1025024*pow(m,10,mod)+3003*(-4+n)%mod*(-3+n)%mod*(-2+n)%mod*(-1+n)*n*(1+n)%mod*(2+n)%mod*(3+n)%mod*(4+n)%mod*(5+n)%mod
-549120*pow(m,9,mod)*(-1+10*n)%mod
+42240*pow(m,8,mod)*(-398+45*n*(-1+7*n)%mod)%mod
-369600*pow(m,7,mod)*(3+2*(-2+n)*n*(49+26*n)%mod)%mod
+2688*pow(m,6,mod)*(33529+75*n*(-33-679*n+91*n**3)%mod)%mod
-336*pow(m,5,mod)*(88065+2*n*(426107+7*n*(-6675+13*n*(-2420+9*n*(5+22*n)%mod)%mod)%mod)%mod)%mod
+560*pow(m,4,mod)*(-291598+n*(216249+7*n*(95465+26*n*(-495+n*(-980+11*n*(3+5*n)%mod)%mod)%mod)%mod)%mod)%mod
-30*pow(m,3,mod)*(-3080960+n*(-10447602+7*n*(854525+13*n*(93170+n*(-15295+22*n*(-714+5*n*(7+6*n)%mod)%mod)%mod)%mod)%mod)%mod)%mod
+2*pow(m,2,mod)*(28412712+25*n*(-3433650+n*(-4123841+13*n*(189882+n*(142177+22*n*(-1344+n*(-791+27*n*(2+n)%mod)%mod)%mod)%mod)%mod)%mod)%mod)%mod
-m*(30149280+n*(31294296+n*(-93275400+13*n*(-3808420+n*(2988195+11*n*(111678+25*n*(-1302+n*(-456+n*(45+14*n)%mod)%mod)%mod)%mod)%mod)%mod)%mod)%mod)%mod
)%mod*pow(1307674368000%mod, mod-2, mod)%mod
)
def resolve():
it = map(int, sys.stdin.read().split())
N = next(it)
ans = [0] * N
for i in range(N):
n = next(it)
ans[i] = calc(n)
print(*ans, sep="\n")
if __name__ == "__main__":
resolve()
``` | output | 1 | 65,412 | 16 | 130,825 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,413 | 16 | 130,826 |
"Correct Solution:
```
mod = 10**9 + 7
k = 5
class Lagrange:
def __init__(self, lst):
self.lst = lst
self.mod = mod
def prd(self, j, x):
tmp = 1
for i, (xi, yi) in enumerate(self.lst):
if j != i:
tmp *= (x - xi)
tmp %= self.mod
return tmp
def pln(self, x):
tmp = 0
for i, (xi, yi) in enumerate(self.lst):
tmp += yi * (self.prd(i, x) *
pow(self.prd(i, xi), self.mod - 2, self.mod))
tmp %= self.mod
return tmp
def cmb(x, y):
if x < y:
return 0
tmp = 1
for i in range(y):
tmp *= x - i
tmp *= pow(y - i, mod - 2, mod)
tmp %= mod
return tmp
def pln(n):
tmp = 0
for x in range(n):
tmp += cmb(x + k - 1, k - 1) * cmb(n - (2 * x) + k, 2 * k)
tmp %= mod
return tmp
lst_eve = [(i, pln(i)) for i in range(0, 2 * (3 * k + 1), 2)]
lst_odd = [(i, pln(i)) for i in range(1, 2 * (3 * k + 1) + 1, 2)]
lag_eve = Lagrange(lst_eve)
lag_odd = Lagrange(lst_odd)
t = int(input())
for _ in range(t):
n = int(input())
if n % 2 == 0:
print(lag_eve.pln(n))
else:
print(lag_odd.pln(n))
``` | output | 1 | 65,413 | 16 | 130,827 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,414 | 16 | 130,828 |
"Correct Solution:
```
import sys
def I(): return int(sys.stdin.readline().rstrip())
T = I()
mod = 10**9+7
for i in range(T):
N = I()
if N % 2 == 0:
M = N//2+1
a = pow(M,15,mod)*pow(1277025750,mod-2,mod)
a %= mod
a += pow(M,14,mod)*pow(48648600,mod-2,mod)
a %= mod
a += pow(M,13,mod)*29*pow(145945800,mod-2,mod)
a %= mod
a += pow(M,12,mod)*pow(1425600,mod-2,mod)
a %= mod
a += -pow(M,11,mod)*571*pow(449064000,mod-2,mod)
a %= mod
a += -pow(M,10,mod)*pow(62208,mod-2,mod)
a %= mod
a += -pow(M,9,mod)*6269*pow(228614400,mod-2,mod)
a %= mod
a += pow(M,8,mod)*109*pow(1360800,mod-2,mod)
a %= mod
a += pow(M,7,mod)*23227*pow(81648000,mod-2,mod)
a %= mod
a += -pow(M,6,mod)*7*pow(518400,mod-2,mod)
a %= mod
a += -pow(M,5,mod)*301729*pow(359251200,mod-2,mod)
a %= mod
a += -pow(M,4,mod)*4409*pow(8553600,mod-2,mod)
a %= mod
a += pow(M,3,mod)*1081139*pow(1513512000,mod-2,mod)
a %= mod
a += pow(M,2,mod)*10037*pow(21621600,mod-2,mod)
a %= mod
a += -pow(M,1,mod)*47*pow(360360,mod-2,mod)
a %= mod
print(a)
else:
M = N//2+1
a = pow(M,15,mod)*pow(1277025750,mod-2,mod)
a %= mod
a += pow(M,14,mod)*pow(37837800,mod-2,mod)
a %= mod
a += pow(M,13,mod)*53*pow(145945800,mod-2,mod)
a %= mod
a += pow(M,12,mod)*pow(399168,mod-2,mod)
a %= mod
a += pow(M,11,mod)*319*pow(40824000,mod-2,mod)
a %= mod
a += -pow(M,10,mod)*11*pow(3628800,mod-2,mod)
a %= mod
a += -pow(M,9,mod)*21893*pow(228614400,mod-2,mod)
a %= mod
a += -pow(M,8,mod)*31*pow(141120,mod-2,mod)
a %= mod
a += pow(M,7,mod)*9307*pow(81648000,mod-2,mod)
a %= mod
a += pow(M,6,mod)*3769*pow(3628800,mod-2,mod)
a %= mod
a += pow(M,5,mod)*297287*pow(359251200,mod-2,mod)
a %= mod
a += -pow(M,4,mod)*4841*pow(3991680,mod-2,mod)
a %= mod
a += -pow(M,3,mod)*87223*pow(56056000,mod-2,mod)
a %= mod
a += pow(M,2,mod)*6631*pow(16816800,mod-2,mod)
a %= mod
a += pow(M,1,mod)*23*pow(32760,mod-2,mod)
a %= mod
print(a)
``` | output | 1 | 65,414 | 16 | 130,829 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,415 | 16 | 130,830 |
"Correct Solution:
```
MOD = 1000000007
def mult(a, b):
da = len(a)
db = len(b)
res = [0] * (da + db - 1)
for i in range(da):
for j in range(db):
res[i+j] = (res[i+j] + a[i] * b[j]) % MOD
return res
plus = [1, 1]
minus = [1, -1]
d = [1]
for i in range(5):
d = mult(d, plus)
for i in range(16):
d = mult(d, minus)
a = [0] * 6
a[5] = 1
def flip_odd(d):
dd = d[:]
for i in range(1, len(dd), 2):
dd[i] = -dd[i]
return dd
def get(a, d, n):
if n == 0:return a[0]
dd = flip_odd(d)
if n % 2 == 1:
return get(mult(a,dd)[1::2], mult(d, dd)[::2], (n-1) // 2)
else:
return get(mult(a,dd)[::2], mult(d,dd)[::2], n // 2)
for _ in range(int(input())):
n = int(input())
print(get(a, d, n))
``` | output | 1 | 65,415 | 16 | 130,831 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,416 | 16 | 130,832 |
"Correct Solution:
```
#!python3
import sys
iim = lambda: map(int, sys.stdin.readline().rstrip().split())
mod = 10 **9 + 7
def calc(n):
ans = 0
if n & 1:
Y = [33746491, 897911890, 741553367, 922649390, 82466138, 30593036, 407570181, 119032926, 718747607, 27251510, 15690675, 2549638, 225225, 11620, 330, 4]
else:
Y = [0, 296640693, 751721723, 240221668, 869628520, 30593036, 407570181, 119032926, 718747607, 27251510, 15690675, 2549638, 225225, 11620, 330, 4]
x = 1
for y in Y:
ans = (ans + x*y%mod) % mod
x = x*n%mod
ans = ans * pow(167382319104000, mod-2, mod) % mod
return ans
def resolve():
it = map(int, sys.stdin.read().split())
N = next(it)
ans = [0] * N
for i in range(N):
n = next(it)
ans[i] = calc(n)
print(*ans, sep="\n")
if __name__ == "__main__":
resolve()
``` | output | 1 | 65,416 | 16 | 130,833 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,417 | 16 | 130,834 |
"Correct Solution:
```
T = int(input())
for _ in range(T):
n = int(input())
if n < 5:
print(0)
elif n % 2 == 0:
x = n // 2 - 2
ans = (37476432000*(x) + 187243792560*(x**2) + 399117903732*(x**3) + 485269948800*(x**4) + 379718819935*(x**5) + 204017288475*(x**6) + 78161197114*(x**7) + 21814113750*(x**8) + 4477585255*(x**9) + 675269595*(x**10) + 73895276*(x**11) + 5705700*(x**12) + 294560*(x**13) + 9120*(x**14) + 128*(x**15))//163459296000
print(ans % 1000000007)
else:
x = n // 2 - 1
ans = ((-4490640000) * (x) - 9469891440 * (x**2) + 5980311612 * (x**3) + 38927921760 * (x**4) + 55757252005 * (x**5) + 44011832865 * (x**6) + 22464496054 * (x**7) + 7902767730 * (x**8) + 1972993165 * (x**9) + 353017665 * (x**10) + 45000956 * (x**11) + 3991260 * (x**12) + 234080 * (x**13) + 8160 * (x**14) + 128 * (x**15))//163459296000
print(ans % 1000000007)
``` | output | 1 | 65,417 | 16 | 130,835 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556 | instruction | 0 | 65,418 | 16 | 130,836 |
"Correct Solution:
```
m=10**9+7
x=[[0,765144583,346175634,347662323,5655049,184117322,927321758,444014759,542573865,237315285,417297686,471090892,183023413,660103155,727008098,869418286],[539588932,729548371,700407153,404391958,962779130,184117322,927321758,444014759,542573865,237315285,417297686,471090892,183023413,660103155,727008098,869418286]]
for _ in range(int(input())):
n=int(input())
print(sum([n**j*x[n&1][j]for j in range(16)])%m)
``` | output | 1 | 65,418 | 16 | 130,837 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
mod = 10**9+7
def mul(f,g):
n = len(f)
m = len(g)
h = [0]*(n+m-1)
for i in range(n):
for j in range(m):
h[i+j] += f[i]*g[j]
h[i+j] %= mod
return h
def rev(f):
h = [0]*len(f)
for i in range(len(f)):
h[i] += f[i]
if i%2==1:
h[i] *= -1
h[i] %= mod
return h
def add(f,g):
if len(f)<len(g):
f,g = g,f
g += [0]*(len(f)-len(g))
h = [0]*len(f)
for i in range(len(f)):
h[i] = f[i]+g[i]
h[i] %= mod
return h
def coef(n,P,Q):
if n==0:
return P[0]%mod
q = mul(Q,rev(Q))[::2]
if n%2==0:
p = mul(P,rev(Q))[::2]
else:
p = mul(P,rev(Q))[1::2]
return coef(n//2,p,q)
P = [0,0,0,0,0,1]
Q = [1]
for i in range(5):
Q = mul(Q,[1,1])
for i in range(16):
Q = mul(Q,[1,-1])
T = int(input())
for i in range(T):
N = int(input())
print(coef(N,P,Q))
``` | instruction | 0 | 65,419 | 16 | 130,838 |
Yes | output | 1 | 65,419 | 16 | 130,839 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
MOD=10**9+7
def matmul(A,B): # A,B: 行列
res = [[0]*len(B[0]) for _ in [None]*len(A)]
for i, resi in enumerate(res):
for k, aik in enumerate(A[i]):
for j,bkj in enumerate(B[k]):
resi[j] += aik*bkj
resi[j] %= MOD
return res
def matpow(A,p): #A^p mod M
if p%2:
return matmul(A, matpow(A,p-1))
elif p > 0:
b = matpow(A,p//2)
return matmul(b,b)
else:
return [[1 if i == j else 0 for j in range(len(A))] for i in range(len(A))]
def solve(n):
pass
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline
#n,k,*a = map(int,read().split())
T, = map(int,readline().split())
c = [1, -11, 50, -110, 65, 253, -648, 440, 610 , -1430 ,+ 780 ,+ 780, - 1430 , 610 , 440, - 648, + 253, + 65, - 110, + 50, - 11, + 1]
m = 21
A = [[0]*m for _ in range(m)]
for i in range(m-1):
A[i+1][i] = 1
for i in range(m):
A[i][-1] = -c[i]
#print(A)
v = [[0]*(m-1)+[1]]
c = matmul(v,matpow(A,15))
#print(c)
for _ in range(T):
n, = map(int,readline().split())
x = matmul(c,matpow(A,n))
print(x[0][0])
``` | instruction | 0 | 65,420 | 16 | 130,840 |
Yes | output | 1 | 65,420 | 16 | 130,841 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
m=1000000007
x=[[0,765144583,346175634,347662323,5655049,184117322,927321758,444014759,542573865,237315285,417297686,471090892,183023413,660103155,727008098,869418286],[539588932,729548371,700407153,404391958,962779130,184117322,927321758,444014759,542573865,237315285,417297686,471090892,183023413,660103155,727008098,869418286]]
for _ in range(int(input())):
n=int(input())
print(sum([pow(n,j,m)*x[n&1][j]%m for j in range(16)])%m)
``` | instruction | 0 | 65,421 | 16 | 130,842 |
Yes | output | 1 | 65,421 | 16 | 130,843 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
# Ref: https://betrue12.hateblo.jp/entry/2020/07/12/060026
import sys
sys.setrecursionlimit(10**6)
def ext_euc(a, b):
if b == 0:
return 1, 0, a
y, x, v = ext_euc(b, a % b)
y -= (a // b) * x
return x, y, v
def mod_inv(a, mod):
x, _, _ = ext_euc(a, mod)
return x % mod
def generate_points(is_odd, mod):
# Lagrange補完するためのデータ点を計算
n_points = 16
points = [None] * n_points
if is_odd:
comb_1 = [0] * n_points # (n+4)_C_4
comb_2 = [0] * n_points # (2n+10)_C_10
comb_1[0] = 1
comb_2[0] = 1
for n in range(1, n_points):
comb_1[n] = comb_1[n - 1] * (n + 4) * mod_inv(n, mod) % mod
v = comb_2[n - 1] * (2 * n + 10) * (2 * n + 9) % mod
v *= mod_inv(2 * n, mod) * mod_inv(2 * n - 1, mod) % mod
comb_2[n] = v % mod
for n in range(n_points):
N = 2 * n + 5
val = 0
for k in range(n + 1):
val += comb_1[k] * comb_2[n - k]
val %= mod
points[n] = (N, val)
else:
comb_1 = [0] * n_points # (k+4)_C_4
comb_2 = [0] * n_points # (2n+11)_C_10
comb_1[0] = 1
comb_2[0] = 11 # 11_C_10
for n in range(1, n_points):
comb_1[n] = comb_1[n - 1] * (n + 4) * mod_inv(n, mod) % mod
v = comb_2[n - 1] * (2 * n + 11) * (2 * n + 10) % mod
v *= mod_inv(2 * n + 1, mod) * mod_inv(2 * n, mod) % mod
comb_2[n] = v % mod
for n in range(n_points):
N = 2 * n + 6
val = 0
for k in range(n + 1):
val += comb_1[k] * comb_2[n - k]
val %= mod
points[n] = (N, val)
return points
def lagrange_interpolation(points, k, mod):
n_points = len(points)
# points を通る n_points - 1 次の多項式 の k での値を求める
# ref: https://mathtrain.jp/hokan
ret = 0
for n in range(n_points):
x, y = points[n]
y_coef = 1
for i in range(n_points):
if i == n:
continue
xi, _ = points[i]
y_coef *= k - xi
y_coef *= mod_inv(x - xi, mod)
ret += y * y_coef
ret %= mod
return ret
def main():
MOD = 10**9 + 7
T = int(input())
test_cases = [int(input()) for _ in range(T)]
odd_points = generate_points(True, MOD)
even_points = generate_points(False, MOD)
for N in test_cases:
if N < 5:
print(0)
elif N % 2 == 0:
print(lagrange_interpolation(even_points, N, MOD))
else:
print(lagrange_interpolation(odd_points, N, MOD))
if __name__ == '__main__':
main()
``` | instruction | 0 | 65,422 | 16 | 130,844 |
Yes | output | 1 | 65,422 | 16 | 130,845 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
import numpy as np
conv=np.convolve
def beki(P,Q,n):
while n:
Q1=Q.copy()
Q1[1::2]=-Q[1::2]
P=conv(P,Q1)[n&1::2]
Q=conv(Q,Q1)[::2]
n>>=1
return P[0]
mod=10**9+7
t=int(input())
p=[0,0,0,0,0,1]
q=[1]
for _ in range(16):
q=conv(q,[-1,1])
for _ in range(5):
q=conv(q,[1,1])
for i in range(t):
n=int(input())
print(beki(p,q,n)%mod)
``` | instruction | 0 | 65,423 | 16 | 130,846 |
No | output | 1 | 65,423 | 16 | 130,847 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
import numpy as np
MOD = 10 ** 9 + 7
l_matrix = np.zeros((32, 32), np.int64)
for i in range(16):
l_matrix[i+16][i] = 1
l_matrix[i][i+16] = 1
for i in range(15):
l_matrix[i+1][i] = 1
for i in range(5, 15):
l_matrix[i+1][i+16] = 1
doubling = [l_matrix] #doubling[i] = (l_matrix) ** (2 ** i) % MOD
for _ in range(30):
doubling.append(doubling[-1] @ doubling[-1] % MOD)
T = int(input())
for _ in range(T):
N = int(input())
N += 10
dp = np.zeros(32, np.int64)
dp[0] = 1
for i, c in enumerate(reversed(format(N, 'b'))):
if c == '1':
dp = doubling[i] @ dp
dp %= MOD
print((dp[15] + dp[31]) % MOD)
#print(dp)
``` | instruction | 0 | 65,424 | 16 | 130,848 |
No | output | 1 | 65,424 | 16 | 130,849 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
def main():
"""
形式的冪級数を用いる問題。maspyさん解説と以下の解説を参照。
将来解き直す時のメモとしてのせておく。
https://atcoder.jp/contests/aising2020/tasks/aising2020_f
"""
T = int(input())
for _ in range(T):
N = int(input())
print(0)
if __name__ == "__main__":
main()
``` | instruction | 0 | 65,425 | 16 | 130,850 |
No | output | 1 | 65,425 | 16 | 130,851 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:
* 0 \leq s_1 < s_2
* 0 \leq n_1 < n_2
* 0 \leq u_1 < u_2
* 0 \leq k_1 < k_2
* 0 \leq e_1 < e_2
* s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N
For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).
Solve this problem for each of the T test cases given.
Constraints
* All values in input are integers.
* 1 \leq T \leq 100
* 1 \leq N \leq 10^{9}
Input
Input is given from Standard Input in the following format:
T
\mathrm{case}_1
\vdots
\mathrm{case}_T
Each case is given in the following format:
N
Output
Print T lines. The i-th line should contain the answer to the i-th test case.
Example
Input
4
4
6
10
1000000000
Output
0
11
4598
257255556
Submitted Solution:
```
#!python3
import sys
iim = lambda: map(int, sys.stdin.readline().rstrip().split())
mod = 10 **9 + 7
def calc(n):
ans = 0
#if n & 1:
# Y = [37033746750,-19102088250,-75258447165,+8922649446,+41082466425,+12030593120,-2592429840,-1880967088,-281252400,+27251510,+15690675,+2549638,+225225,+11620,+330,+4]
#else:
# Y = [0, -98703360000,-108248279040,+4240221696,+40869628800,+12030593120,-2592429840,-1880967088,-281252400,+27251510,+15690675,+2549638,+225225,+11620,+330,+4]
if n & 1:
Y = [33746491, 897911890, 741553367, 922649390, 82466138, 30593036, 407570181, 119032926, 718747607, 27251510, 15690675, 2549638, 225225, 11620, 330, 4]
else:
Y = [0, 296640693, 751721723, 240221668, 869628520, 30593036, 407570181, 119032926, 718747607, 27251510, 15690675, 2549638, 225225, 11620, 330, 4]
x = 1
for i, y in enumerate(Y):
ans = (ans + x*y%mod) % mod
x = x*n%mod
ans = ans * pow(167382319104000, mod-2, mod) % mod
return ans
def resolve():
it = map(int, sys.stdin.read().split())
N = next(it)
if N == 4: raise 1
ans = [0] * N
for i in range(N):
n = next(it)
ans[i] = calc(n)
print(*ans, sep="\n")
if __name__ == "__main__":
resolve()
``` | instruction | 0 | 65,426 | 16 | 130,852 |
No | output | 1 | 65,426 | 16 | 130,853 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,021 | 16 | 134,042 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 7)
from collections import deque
N,K,*P=map(int,sys.stdin.read().split())
Kmin = []
deq = deque()
for i in range(K):
while deq and P[deq[-1]] > P[i]:
deq.pop()
deq.append(i)
Kmin.append(deq[0])
for i in range(K,N):
if deq[0] == i-K:
deq.popleft()
while deq and P[deq[-1]] > P[i]:
deq.pop()
deq.append(i)
Kmin.append(deq[0])
Kmax = []
deq = deque()
for i in range(K):
while deq and P[deq[-1]] < P[i]:
deq.pop()
deq.append(i)
Kmax.append(deq[0])
for i in range(K,N):
if deq[0] == i-K:
deq.popleft()
while deq and P[deq[-1]] < P[i]:
deq.pop()
deq.append(i)
Kmax.append(deq[0])
is_new_seq = [Kmin[i] != i or Kmax[i+1] != i+K for i in range(N-K)]
is_new_seq
import itertools
incr = [1 if x<y else 0 for x,y in zip(P,P[1:])]
incr_cum = [0] + list(itertools.accumulate(incr))
is_stable = [y-x==K-1 for x,y in zip(incr_cum,incr_cum[K-1:])]
is_new_seq = [x&(not y) for x,y in zip(is_new_seq,is_stable[1:])]
answer = sum(is_new_seq)
if not is_stable[0]:
answer += 1
if any(is_stable):
answer += 1
else:
answer += 1
print(answer)
``` | output | 1 | 67,021 | 16 | 134,043 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,022 | 16 | 134,044 |
"Correct Solution:
```
import heapq
def main():
N, K = map(int, input().split())
P = list(map(int, input().split()))
ans = 1
inside_que = [0] * N
min_que, max_que = [], []
for i in range(K):
heapq.heappush(min_que, P[i])
heapq.heappush(max_que, - P[i])
inside_que[P[i]] = 1
for i in range(N - K):
old_p, new_p = P[i], P[i + K]
if not(old_p == min_que[0] and new_p >= - max_que[0]):
ans += 1
inside_que[old_p] = 0
inside_que[new_p] = 1
heapq.heappush(min_que, new_p)
heapq.heappush(max_que, - new_p)
while inside_que[min_que[0]] == 0:
heapq.heappop(min_que)
while inside_que[-max_que[0]] == 0:
heapq.heappop(max_que)
desc_index = 0
exists_asc_section = False
for i in range(1, N):
if P[i - 1] > P[i]:
if i - desc_index >= K:
ans -= 1
exists_asc_section = True
desc_index = i
if N - desc_index >= K:
exists_asc_section = True
ans -= 1
if exists_asc_section:
ans += 1
print(ans)
if __name__ == '__main__':
main()
``` | output | 1 | 67,022 | 16 | 134,045 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,023 | 16 | 134,046 |
"Correct Solution:
```
from collections import Counter, deque
N, K = map(int, input().split())
P = list(map(int, input().split()))
ans = N - K + 1
# 変化しないものを数える
LIS = [-1] * N
LIS[-1] = 1
LIS_MIN_NOW = P[-1]
for i in reversed(range(N - 1)):
p = P[i]
if p < LIS_MIN_NOW:
LIS_MIN_NOW = p
LIS[i] = LIS[i + 1] + 1
else:
LIS_MIN_NOW = p
LIS[i] = 1
LIS = LIS[:N - K + 1]
# スライド最小値を計算
slide_min = deque([])
MIN = []
for k in range(N):
while slide_min and P[slide_min[-1]] >= P[k]:
slide_min.pop()
slide_min.append(k)
if k < K - 1:
continue
if slide_min[0] + K <= k:
slide_min.popleft()
MIN.append(P[slide_min[0]])
# スライド最大値を計算
slide_max = deque([])
MAX = []
for k in range(N):
while slide_max and P[slide_max[-1]] <= P[k]:
slide_max.pop()
slide_max.append(k)
if k < K - 1:
continue
if slide_max[0] + K <= k:
slide_max.popleft()
MAX.append(P[slide_max[0]])
for i in range(N - K + 1):
flg = False
if LIS[i] >= K:
flg = True
if (i + 1 < N - K + 1) and (P[i] == MIN[i]) and (P[i + K] == MAX[i + 1]):
flg = True
ans -= flg
if len([l for l in LIS if l >= K]):
ans += 1
print(ans)
``` | output | 1 | 67,023 | 16 | 134,047 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,024 | 16 | 134,048 |
"Correct Solution:
```
from collections import deque
from bisect import bisect_right
N,K = map(int,input().split())
P = list(map(int,input().split()))
Lmax = []
Lmin = []
if P[1]>P[0]:
flag = 1
else:
flag = -1
for i in range(2,N):
if P[i]>P[i-1]:
if flag==1:continue
else:
Lmin.append([i-1,P[i-1]])
flag = 1
else:
if flag==1:
Lmax.append([i-1,P[i-1]])
flag = -1
else:continue
cnt = 0
flagMono = 0
indmin = bisect_right(Lmin,[K-1,P[K-1]])
Smax = deque([0])
Smin = deque([0])
for i in range(1,K):
while Smax:
if P[Smax[-1]]<P[i]:
Smax.pop()
else:break
Smax.append(i)
while Smin:
if P[Smin[-1]]>P[i]:
Smin.pop()
else:break
Smin.append(i)
if P[0]==P[Smin[0]] and P[K-1]==P[Smax[0]] and (len(Lmin)==0 or indmin==0 or Lmin[indmin-1][0]==0):
flagMono=1
cnt += 1
elif P[0]==P[Smin[0]] and K<N and P[K]>P[Smax[0]]:
pass
else:
cnt += 1
for i in range(1,N-K+1):
if Smax[0]==i-1:
Smax.popleft()
while Smax:
if P[Smax[-1]]<P[i+K-1]:
Smax.pop()
else:break
Smax.append(i+K-1)
if Smin[0]==i-1:
Smin.popleft()
while Smin:
if P[Smin[-1]]>P[i+K-1]:
Smin.pop()
else:break
Smin.append(i+K-1)
indmin = bisect_right(Lmin,[i+K-1,P[i+K-1]])
if P[i]==P[Smin[0]] and P[i+K-1]==P[Smax[0]] and (len(Lmin)==0 or indmin==0 or Lmin[indmin-1][0]<=i):
if flagMono==0:
flagMono = 1
cnt += 1
else:
pass
elif P[i]==P[Smin[0]] and i+K<N and P[i+K]>P[Smax[0]]:
continue
else:
cnt += 1
print(cnt)
``` | output | 1 | 67,024 | 16 | 134,049 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,025 | 16 | 134,050 |
"Correct Solution:
```
from collections import deque
from itertools import accumulate
def slide_min(A, K):
res = []
Q = deque()
for i, a in enumerate(A):
while Q and A[Q[-1]] > a:
Q.pop()
Q.append(i)
if Q[0] == i - K:
Q.popleft()
res.append(Q[0])
return res[K - 1:]
N, K, *P = map(int, open(0).read().split())
mi = slide_min(P, K)
ma = slide_min([-p for p in P], K)
B = [mi != i or ma != i + K for i, (mi, ma) in enumerate(zip(mi, ma[1:]))]
A = [0] + list(accumulate(x < y for x, y in zip(P, P[1:])))
S = [y - x != K - 1 for x, y in zip(A, A[K - 1:])]
ans = 1 + sum(b for b, s in zip(B, S[1:]) if s)
if S[0] and not all(S):
ans += 1
print(ans)
``` | output | 1 | 67,025 | 16 | 134,051 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,026 | 16 | 134,052 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda:sys.stdin.readline().rstrip()
class SparseTable(object):
def __init__(self,A):
n=len(A)
logn=max(0,(n-1).bit_length())
maxtable=[[0]*n for _ in range(logn)]
maxtable[0]=A[:]
mintable=[[0]*n for _ in range(logn)]
mintable[0]=A[:]
from itertools import product
for i,k in product(range(1,logn),range(n)):
if(k+(1<<(i-1))>=n):
maxtable[i][k]=maxtable[i-1][k]
mintable[i][k]=mintable[i-1][k]
else:
maxtable[i][k]=max(maxtable[i-1][k],maxtable[i-1][k+(1<<(i-1))])
mintable[i][k]=min(mintable[i-1][k],mintable[i-1][k+(1<<(i-1))])
self.__n=n
self.__maxtable=maxtable
self.__mintable=mintable
def max(self,l,r):
n=self.__n
assert 0<=l<r<=n
i=max(0,(r-l-1).bit_length()-1)
maxtable=self.__maxtable
return max(maxtable[i][l],maxtable[i][r-(1<<i)])
def min(self,l,r):
n=self.__n
assert 0<=l<r<=n
i=max(0,(r-l-1).bit_length()-1)
mintable=self.__mintable
return min(mintable[i][l],mintable[i][r-(1<<i)])
def resolve():
n,k=map(int,input().split())
P=list(map(int,input().split()))
table=SparseTable(P)
ans=n-k+1
for i in range(n-k):
m=table.min(i,i+k)
M=table.max(i+1,i+1+k)
if(m==P[i] and M==P[i+k]):
ans-=1
cnt=0
num=0
P.append(-1) # 番兵
for i in range(n):
if(P[i+1]>P[i]):
cnt+=1
else:
num+=(cnt>=k-1)
cnt=0
ans-=max(num-1,0)
print(ans)
resolve()
``` | output | 1 | 67,026 | 16 | 134,053 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,027 | 16 | 134,054 |
"Correct Solution:
```
N,K = map(int,input().split())
P = list(map(int,input().split()))
if K==N:
print(1)
exit()
cum_asc = [0]
for p,q in zip(P,P[1:]):
cum_asc.append(cum_asc[-1] + int(p<q))
all_asc = []
for i in range(N-K+1):
all_asc.append(cum_asc[i+K-1] - cum_asc[i] == K-1)
from collections import deque
sldmin = []
sldmax = []
qmin = deque()
qmax = deque()
for i,p in enumerate(P):
while qmin and qmin[-1] > p:
qmin.pop()
qmin.append(p)
if i-K-1 >= 0 and P[i-K-1] == qmin[0]:
qmin.popleft()
while qmax and qmax[-1] < p:
qmax.pop()
qmax.append(p)
if i-K-1 >= 0 and P[i-K-1] == qmax[0]:
qmax.popleft()
if i >= K:
sldmin.append(qmin[0])
sldmax.append(qmax[0])
class UnionFind:
def __init__(self,N):
self.parent = [i for i in range(N)]
self.rank = [0] * N
self.count = 0
def root(self,a):
if self.parent[a] == a:
return a
else:
self.parent[a] = self.root(self.parent[a])
return self.parent[a]
def is_same(self,a,b):
return self.root(a) == self.root(b)
def unite(self,a,b):
ra = self.root(a)
rb = self.root(b)
if ra == rb: return
if self.rank[ra] < self.rank[rb]:
self.parent[ra] = rb
else:
self.parent[rb] = ra
if self.rank[ra] == self.rank[rb]: self.rank[ra] += 1
self.count += 1
def components(self):
return len(self.parent) - self.count
uf = UnionFind(N-K+2)
for i,(l,r,mn,mx) in enumerate(zip(P,P[K:],sldmin,sldmax)):
if l==mn and r==mx:
uf.unite(i,i+1)
if all(f == False for f in all_asc):
print(uf.components() - 1)
exit()
def_i = N-K+1 #same as default P
for i,f in enumerate(all_asc):
if f:
uf.unite(i, def_i)
print(uf.components())
``` | output | 1 | 67,027 | 16 | 134,055 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6 | instruction | 0 | 67,028 | 16 | 134,056 |
"Correct Solution:
```
from heapq import heappush, heappop
N, K = map(int, input().split())
P = [int(i) for i in input().split()]
dp = [0] * N
dp[0] = 1
for i in range(1, N) :
if P[i] > P[i-1] :
dp[i] = dp[i-1] + 1
else :
dp[i] = 1
ma = []
mi = []
for i in range(K) :
heappush(ma, (-P[i], i))
heappush(mi, (P[i], i))
if dp[K-1] == K :
ret = 0
else :
ret = 1
for i in range(K, N) :
heappush(ma, (-P[i], i))
heappush(mi, (P[i], i))
while ma[0][1] < i - K :
heappop(ma)
while mi[0][1] < i - K :
heappop(mi)
if dp[i] < K and (P[i-K] != mi[0][0] or P[i] != -ma[0][0]) :
ret += 1
if sum([dp[i] >= K for i in range(N)]) > 0 :
ret += 1
print(ret)
``` | output | 1 | 67,028 | 16 | 134,057 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6
Submitted Solution:
```
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007
class SegmentTree:
def __init__(self, init_val, ide_ele, op):
n = len(init_val)
self.num = 2 ** (n - 1).bit_length()
self.seg = [ide_ele] * 2 * self.num
self.ide_ele = ide_ele
self.op = op
for i in range(n):
self.seg[i + self.num - 1] = init_val[i]
# built
for i in range(self.num - 2, -1, -1):
self.seg[i] = self.op(self.seg[2 * i + 1], self.seg[2 * i + 2])
def update(self, k, x):
k += self.num - 1
self.seg[k] = x
while k + 1:
k = (k - 1) // 2
self.seg[k] = self.op(self.seg[k * 2 + 1], self.seg[k * 2 + 2])
def query(self, p, q):
if q <= p:
return self.ide_ele
p += self.num - 1
q += self.num - 2
res = self.ide_ele
while q - p > 1:
if p & 1 == 0:
res = self.op(res, self.seg[p])
if q & 1 == 1:
res = self.op(res, self.seg[q])
p = p // 2
q = (q - 2) // 2
if p == q:
res = self.op(res, self.seg[p])
else:
res = self.op(self.seg[p], self.op(res, self.seg[q]))
return res
n, k = LI()
L = LI()
min_ST = SegmentTree(L, INF, min)
max_ST = SegmentTree(L, -INF, max)
cnt = 1
for i in range(n - k):
if min_ST.query(i, i + k) == L[i] and max_ST.query(i + 1, i + k + 1) == L[i + k]:
continue
else:
cnt += 1
ret = -INF
increasing_block_num = 0
max_len = 0
for j in range(n):
if L[j] >= ret:
max_len += 1
else:
if max_len >= k:
increasing_block_num += 1
max_len = 1
ret = L[j]
if max_len >= k:
increasing_block_num += 1
if increasing_block_num:
print(cnt - (increasing_block_num - 1))
else:
print(cnt)
``` | instruction | 0 | 67,029 | 16 | 134,058 |
Yes | output | 1 | 67,029 | 16 | 134,059 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).
Now, he will perform the following operation exactly once:
* Choose K consecutive elements in P and sort them in ascending order.
Find the number of permutations that can be produced as P after the operation.
Constraints
* 2 \leq N \leq 200000
* 2 \leq K \leq N
* 0 \leq P_i \leq N-1
* P_0,P_1,\cdots,P_{N-1} are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
P_0 P_1 \cdots P_{N-1}
Output
Print the number of permutations that can be produced as P after the operation.
Examples
Input
5 3
0 2 1 4 3
Output
2
Input
4 4
0 1 2 3
Output
1
Input
10 4
2 0 1 3 7 5 4 6 8 9
Output
6
Submitted Solution:
```
class SWAG():
def __init__(self,unit,f,data):
self.unit=unit
self.f=f
self.fold_r=[unit]
self.fold_l=[unit]
self.data_r=[]
self.data_l=[]
sep=len(data)//2
list(map(self.append,data[sep:]))
list(map(self.appendleft,data[sep-1::-1]))
def append(self,x):
self.fold_r.append(self.f(self.fold_r[-1],x))
self.data_r.append(x)
def appendleft(self,x):
self.fold_l.append(self.f(self.fold_l[-1],x))
self.data_l.append(x)
def pop(self):
if not self.data_r:
self.__init__(self.unit,self.f,self.data_l[::-1])
self.fold_r.pop()
return self.data_r.pop()
def popleft(self):
if not self.data_l:
self.__init__(self.unit,self.f,self.data_r)
self.fold_l.pop()
return self.data_l.pop()
def fold_all(self):
return self.f(self.fold_r[-1],self.fold_l[-1])
n,k,*p=map(int,open(0).read().split())
c=[0]
for a,b in zip(p,p[1:]):c+=c[-1]+(a<b),
*c,f=[b-a==k-1for a,b in zip(c,c[k-1:])]
x=not f
s_min=SWAG(10**18,min,p[:k-1])
s_max=SWAG(0,max,p[1:k])
for i,(a,b,c)in enumerate(zip(p,p[k:],c)):
f|=c
s_min.append(p[i+k-1])
s_max.append(b)
if not c and(a!=s_min.fold_all()or b!=s_max.fold_all()):x+=1
s_min.popleft()
s_max.popleft()
print(x+f)
``` | instruction | 0 | 67,030 | 16 | 134,060 |
Yes | output | 1 | 67,030 | 16 | 134,061 |
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