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.
Given is an integer S. Find a combination of six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfies all of the following conditions:
* 0 \leq X_1,Y_1,X_2,Y_2,X_3,Y_3 \leq 10^9
* The area of the triangle in a two-dimensional plane whose vertices are (X_1,Y_1),(X_2,Y_2), and (X_3,Y_3) is S/2.
We can prove that there always exist six integers that satisfy the conditions under the constraints of this problem.
Constraints
* 1 \leq S \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between. If multiple solutions exist, any of them will be accepted.
Examples
Input
3
Output
1 0 2 2 0 1
Input
100
Output
0 0 10 0 0 10
Input
311114770564041497
Output
314159265 358979323 846264338 327950288 419716939 937510582
Submitted Solution:
```
N = int(input())
maxRange = 10**9
sq = N**0.5
if sq.is_integer() :
print('0 0 0 {} {} 0'.format(sq, sq))
else :
if N <= maxRange :
print('0 0 0 {} 1 0'.format(N))
else :
div = 1
for i in range(2, int(sq) + 1) :
if N % i == 0 :
if N // i < maxRange :
div = i
break
print('0 0 0 {} {} 0'.format(div, N // div))
``` | instruction | 0 | 52,874 | 5 | 105,748 |
No | output | 1 | 52,874 | 5 | 105,749 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is an integer S. Find a combination of six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfies all of the following conditions:
* 0 \leq X_1,Y_1,X_2,Y_2,X_3,Y_3 \leq 10^9
* The area of the triangle in a two-dimensional plane whose vertices are (X_1,Y_1),(X_2,Y_2), and (X_3,Y_3) is S/2.
We can prove that there always exist six integers that satisfy the conditions under the constraints of this problem.
Constraints
* 1 \leq S \leq 10^{18}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print six integers X_1,Y_1,X_2,Y_2,X_3, and Y_3 that satisfy the conditions, in this order, with spaces in between. If multiple solutions exist, any of them will be accepted.
Examples
Input
3
Output
1 0 2 2 0 1
Input
100
Output
0 0 10 0 0 10
Input
311114770564041497
Output
314159265 358979323 846264338 327950288 419716939 937510582
Submitted Solution:
```
S = int(input())
X_1 = 0
Y_1 = 0
X_2 = 1
Y_2 = 0
X_3 = 0
Y_3 = S
print("{} {} {} {} {} {}".format(X_1, Y_1, X_2, Y_2, X_3, Y_2))
``` | instruction | 0 | 52,875 | 5 | 105,750 |
No | output | 1 | 52,875 | 5 | 105,751 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,892 | 5 | 105,784 |
"Correct Solution:
```
from collections import Counter
n = int(input())
v = list(map(int, input().split()))
if len(set(v)) == 1:
print(n // 2)
exit()
kisu = Counter(v[::2]).most_common(2)
gusu = Counter(v[1::2]).most_common(2)
if kisu[0][0] == gusu[0][0]:
keep = max(kisu[1][1] + gusu[0][1],
kisu[0][1] + gusu[1][1])
else:
keep = kisu[0][1] + gusu[0][1]
print(n - keep)
``` | output | 1 | 52,892 | 5 | 105,785 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,893 | 5 | 105,786 |
"Correct Solution:
```
from collections import Counter
n=int(input())
V=list(map(int,input().split()))
E=Counter(V[::2]).most_common()+[(0,0)]
O=Counter(V[1::2]).most_common()+[(0,0)]
print(n-E[0][1]-O[0][1] if E[0][0]!=O[0][0] else n-max(E[0][1]+O[1][1],O[0][1]+E[1][1]))
``` | output | 1 | 52,893 | 5 | 105,787 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,894 | 5 | 105,788 |
"Correct Solution:
```
from collections import Counter
N = int(input())
V = list(map(int,input().split()))
if len(set(V)) == 1:
print(N//2)
else:
v1 = Counter(V[0::2]).most_common(2)
v2 = Counter(V[1::2]).most_common(2)
if v1[0][0] == v2[0][0]:
print(N - max(v1[0][1] + v2[1][1], v1[1][1] + v2[0][1]))
else:
print(N - v1[0][1] - v2[0][1])
``` | output | 1 | 52,894 | 5 | 105,789 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,895 | 5 | 105,790 |
"Correct Solution:
```
n = int(input())
v = list(map(int,input().split()))
v1 = v[::2]
v2 = v[1::2]
from collections import Counter
v1c = Counter(v1).most_common()
v2c = Counter(v2).most_common()
v1c.append([0,0])
v2c.append([0,0])
if v1c[0][0] == v2c[0][0]:
ans = max(v1c[0][1] + v2c[1][1], v1c[1][1] + v2c[0][1])
else:
ans = v1c[0][1] + v2c[0][1]
print(n-ans)
``` | output | 1 | 52,895 | 5 | 105,791 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,896 | 5 | 105,792 |
"Correct Solution:
```
from collections import Counter
n, *v = map(int, open(0).read().split())
vo = Counter(v[::2])
ve = Counter(v[1::2])
vomc = vo.most_common() + [(0, 0)]
vemc = ve.most_common() + [(0, 0)]
if vomc[0][0] == vemc[0][0]:
ans = min(n//2 - vomc[0][1] + n//2 - vemc[1][1], n//2 - vomc[1][1] + n//2 - vemc[0][1])
else:
ans = n//2 - vomc[0][1] + n//2 - vemc[0][1]
print(ans)
``` | output | 1 | 52,896 | 5 | 105,793 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,897 | 5 | 105,794 |
"Correct Solution:
```
from collections import Counter
n = int(input())
v = list(map(int, input().split()))
e = Counter(v[::2]).most_common() + [(0, 0)]#最も多いものは書き換えない
#コーナーケース対応、要素が超少ない場合
o = Counter(v[1::2]).most_common() + [(0, 0)]#偶奇で分けて考える
if e[0][0] != o[0][0]:#偶奇で最多が異なるなら、偶奇の最多を引く
print(n - e[0][1] - o[0][1])
else:#偶奇で最多が同じなら、最多の次を検討して、最も書換を少なくする
print(n - max(e[0][1]+o[1][1], e[1][1]+o[0][1]))
``` | output | 1 | 52,897 | 5 | 105,795 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,898 | 5 | 105,796 |
"Correct Solution:
```
from collections import Counter
N = int(input())
V = list(map(int,input().split()))
E = list(Counter(V[0::2]).most_common())
O = list(Counter(V[1::2]).most_common())
E.append((10001,0))
O.append((10002,0))
if E[0][0] != O[0][0]:
print(N - E[0][1] - O[0][1])
else:
print(min([N - E[0][1] - O[1][1],N - E[1][1] - O[0][1]]))
``` | output | 1 | 52,898 | 5 | 105,797 |
Provide a correct Python 3 solution for this coding contest problem.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2 | instruction | 0 | 52,899 | 5 | 105,798 |
"Correct Solution:
```
from collections import Counter
N = int(input())
V = [i for i in input().split()]
odd = Counter(V[::2]).most_common(2)
even = Counter(V[1::2]).most_common(2)
if odd[0][0] != even[0][0]:
print(N - odd[0][1] - even[0][1])
elif len(odd) == 1:
print(N // 2)
else:
o0e1 = N - odd[0][1] - even[1][1]
o1e0 = N - odd[1][1] - even[0][1]
print(min(o0e1, o1e0))
``` | output | 1 | 52,899 | 5 | 105,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
import collections
n=int(input())
v=list(map(int,input().split()))
c1,c2,ans=collections.Counter(v[::2]),collections.Counter(v[1::2]),0
a,b=c1.most_common(),c2.most_common()
if len(a)==len(b)==1:
print(n//2 if a==b else 0)
exit()
ans=n+(-a[0][1]-b[0][1] if a[0][0]!=b[0][0] else (-a[0][1]-b[1][1] if b[1][1]>=a[1][1] else -a[1][1]-b[0][1]))
print(ans)
``` | instruction | 0 | 52,900 | 5 | 105,800 |
Yes | output | 1 | 52,900 | 5 | 105,801 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
from collections import Counter
n = int(input())
v = input().split()
if len(set(v)) == 1:
print(n // 2)
else:
c1 = Counter(v[::2])
c2 = Counter(v[1::2])
c1m = c1.most_common()
c2m = c2.most_common()
if c1m[0][0] == c2m[0][0]:
print(min(n - c1m[0][1] - c2m[1][1], n - c1m[1][1] - c2m[0][1]))
else:
print(n - c1m[0][1] - c2m[0][1])
``` | instruction | 0 | 52,901 | 5 | 105,802 |
Yes | output | 1 | 52,901 | 5 | 105,803 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
def ans():
N = int(input())
V = list(map(int,input().split()))
even = [0]*100001
odd = [0]*100001
for v in V[1::2]:
even[v] += 1
for v in V[::2]:
odd[v] += 1
me = max(even)
mo = max(odd)
if(even.index(me) != odd.index(mo)):
print(N - me - mo)
else:
even.sort()
odd.sort()
print(min(N-even[-1]-odd[-2], N-even[-2]-odd[-1]))
ans()
``` | instruction | 0 | 52,902 | 5 | 105,804 |
Yes | output | 1 | 52,902 | 5 | 105,805 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
from collections import*;n,*v=map(int,open(0).read().split());a,b=[Counter(v[i::2]).most_common()+[(0,0)]for i in(0,1)];i,x=a[0];j,y=b[0];print(n-[x+y,max(x+b[1][1],y+a[1][1])][i==j])
``` | instruction | 0 | 52,903 | 5 | 105,806 |
Yes | output | 1 | 52,903 | 5 | 105,807 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
n = int(input())
V = list(map(int, input().split()))
if len(set(V)) == 1:
print(n//2)
else:
A = V[::2]
B = V[1::2]
for _ in range(N//2):
countA = [A.count(a) for a in set(A)]
countB = [B.count(b) for b in set(B)]
max_countA = max(countA)
max_countB = max(countB)
print(len(A)-max_countA + len(A)-max_countB)
``` | instruction | 0 | 52,904 | 5 | 105,808 |
No | output | 1 | 52,904 | 5 | 105,809 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
l1=[]
l2=[]
n=int(input())
l0=list(map(int,input().split()))
n=0
for x in l0:
if n%2==0:
l1.append(x)
else:
l2.append(x)
n+=1
l1.sort()
l2.sort()
setl1=list(set(l1))
setl2=list(set(l2))
a=setl1[0]
b=setl2[0]
a_c=0
a_c_max=[0,0]
maxa=maxb=0
b=setl2[0]
b_c=0
b_c_max=[0,0]
for x in l1:
if a!=x:
if a_c_max[0]<a_c:
a_c_max[1]=a_c_max[0]
a_c_max[0]=a_c
maxa=a
a=x
a_c=0
else:
a_c+=1
if a_c_max[0]<a_c:
a_c_max[1]=a_c_max[0]
a_c_max[0]=a_c
maxa=a
for x in l2:
if b!=x:
if b_c_max[0]<b_c:
b_c_max[1]=b_c_max[0]
b_c_max[0]=b_c
maxb=b
b=x
b_c=0
else:
b_c+=1
if b_c_max[0]<b_c:
b_c_max[1]=b_c_max[0]
b_c_max[0]=b_c
maxb=b
if a!=b:
print(n-(a_c_max[0]+b_c_max[0]))
else:
print(max(n-(a_c_max[0]+b_c_max[1]),
n-(a_c_max[1]+b_c_max[0])))
``` | instruction | 0 | 52,905 | 5 | 105,810 |
No | output | 1 | 52,905 | 5 | 105,811 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
n=int(input())
N=list(map(int,input().split()))
even=[]
odd=[]
for i in range(len(N)):
if i%2==0:
even.append(N[i])
if i%2==1:
odd.append(N[i])
import collections
c = collections.Counter(even)
x=c.most_common()[0][0]
o=even.count(x)
d= collections.Counter(odd)
y=d.most_common()[0][0]
p=odd.count(y)
s=len(even)-even.count(x)
t=len(odd)-odd.count(y)
if x!=y and o==len(even) and p==len(odd):
print(0)
elif x!=y:
print(s+t)
elif x==y and o==len(even) and p==len(odd):
print(n/2)
elif x==y and (o!=len(even) or p!=len(odd)):
if o>p:
y=d.most_common()[1][0]
s=len(even)-even.count(x)
t=len(odd)-odd.count(y)
print(s+t)
else:
x=d.most_common()[1][0]
s=len(even)-even.count(x)
t=len(odd)-odd.count(y)
print(s+t)
``` | instruction | 0 | 52,906 | 5 | 105,812 |
No | output | 1 | 52,906 | 5 | 105,813 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A sequence a_1,a_2,... ,a_n is said to be /\/\/\/ when the following conditions are satisfied:
* For each i = 1,2,..., n-2, a_i = a_{i+2}.
* Exactly two different numbers appear in the sequence.
You are given a sequence v_1,v_2,...,v_n whose length is even. We would like to make this sequence /\/\/\/ by replacing some of its elements. Find the minimum number of elements that needs to be replaced.
Constraints
* 2 \leq n \leq 10^5
* n is even.
* 1 \leq v_i \leq 10^5
* v_i is an integer.
Input
Input is given from Standard Input in the following format:
n
v_1 v_2 ... v_n
Output
Print the minimum number of elements that needs to be replaced.
Examples
Input
4
3 1 3 2
Output
1
Input
6
105 119 105 119 105 119
Output
0
Input
4
1 1 1 1
Output
2
Submitted Solution:
```
n = int(input())
list = [int(i) for i in input().split()]
list_odd = list[::2]
list_even = list[1::2]
def cnt_element(x):
dict = {}
for i in x:
if i not in dict:
dict[i] = 1
else:
dict[i] += 1
return [(v,k) for k,v in dict.items()]
cnt_odd = sorted(cnt_element(list_odd),reverse=True)
cnt_even = sorted(cnt_element(list_even),reverse=True)
#最頻値が同じの場合
if cnt_odd[0][1] == cnt_even[0][1]:
#リスト内の値が１つの場合
if len(cnt_odd) or len(cnt_even) == 1:
ans = int(n / 2)
#リストが２つ以上の場合
else:
#第２最頻値の出現数が奇数の方が多い
if cnt_odd[1][0] > cnt_even[1][0]:
ans = n - cnt_odd[1][0] - cnt_even[0][0]
#第二２最頻値の出現数が偶数の方が多い
elif cnt_odd[1][0] < cnt_even[1][0]:
ans = n - cnt_odd[0][0] - cnt_even[1][0]
#最頻値が異なる場合
else:
ans = n - cnt_odd[0][0] - cnt_even[0][1]
print(ans)
``` | instruction | 0 | 52,907 | 5 | 105,814 |
No | output | 1 | 52,907 | 5 | 105,815 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,908 | 5 | 105,816 |
"Correct Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def gcd(a,b):
if b==0:return a
if a<b:a,b=b,a
k=a.bit_length()-b.bit_length()
return gcd(b,a^(b<<k))
def main():
md=998244353
n,x=input().split()
x=int(x,2)
aa=[input() for _ in range(int(n))]
aa=[int(a,2) for a in aa]
#bitを多項式の係数と考えて多項式のGCDを求める
g=aa[0]
for a in aa[1:]:
g=gcd(g,a)
#print(bin(g))
#GCDの桁数以上は自由に決められるのでその分を答えに
ans=x>>(g.bit_length()-1)
s=0
# GCDの桁数以上をxと同じにした場合にx以下になるようであればその分も足す
while 1:
k=(x^s).bit_length()-g.bit_length()
#print(k,bin(x^s),bin(x),bin(s))
if k<0:break
s^=g<<k
if s<=x:ans+=1
print(ans%md)
main()
``` | output | 1 | 52,908 | 5 | 105,817 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,909 | 5 | 105,818 |
"Correct Solution:
```
import random
mod=998244353
N,X=input().split()
N=int(N)
A=[]
for i in range(N):
A.append(int(input(),2))
A.sort()
a=A[-1]
M=max(len(X)-1,a.bit_length()-1)
data=[0]*(M+1)
n=a.bit_length()-1
for i in range(M-n,-1,-1):
data[i+n]=a<<i
for i in range(0,N-1):
a=A[i]
flag=True
while flag:
n=a.bit_length()
for j in range(n-1,-1,-1):
a=min(a,a^data[j])
if a!=0:
data[a.bit_length()-1]=a
id=a.bit_length()-1
while data[id+1]==0:
data[id+1]=min((data[id]<<1)^a,(data[id]<<1))
if data[id+1]:
id+=1
else:
flag=False
else:
a=data[id]<<1
else:
break
data2=[0]*(M+1)
for i in range(M+1):
data2[i]=(data[i]!=0)
for i in range(1,M+1):
data2[i]+=data2[i-1]
data2=[0]+data2
#print(data)
#print(data2)
x=0
ans=0
n=len(X)-1
for i in range(len(X)):
if X[i]=="1":
if x>>(n-i)&1==1:
if data[n-i]:
ans+=pow(2,data2[n-i],mod)
ans%=mod
else:
ans+=pow(2,data2[n-i],mod)
ans%=mod
if data[n-i]:
x=x^data[n-i]
else:
break
else:
if x>>(n-i)&1==1:
if data[n-i]:
x=x^data[n-i]
else:
break
else:
continue
else:
ans+=1
ans%=mod
print(ans)
``` | output | 1 | 52,909 | 5 | 105,819 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,910 | 5 | 105,820 |
"Correct Solution:
```
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline
sys.setrecursionlimit(10**5)
n,x = readline().split()
n = int(n)
x = int(x,2)
*a, = map(lambda x:int(x,2), read().split())
def gcd(a,b):
c = 0
while b:
if a < b:
a,b = b,a
continue
a ^= b<<(a.bit_length() - b.bit_length())
return a
v = 0
for ai in a: v = gcd(ai,v)
MOD = 998244353
p2 = [1]
for _ in range(5000): p2.append(p2[-1]*2%MOD)
dv = v.bit_length()
dx = x.bit_length()
def dfs(x,y,d):
if d < dv:
return int(x >= y)
else:
bx = x>>(d-1)&1
by = y>>(d-1)&1
if bx and by:
return (p2[d-dv] + dfs(x,y,d-1)) %MOD
elif not bx and by:
return dfs(x,y^(v<<(d-dv)),d-1)
elif not by and bx:
return (p2[d-dv] + dfs(x,y^(v<<(d-dv)),d-1)) %MOD
else:
return dfs(x,y,d-1)
print(dfs(x,0,dx))
``` | output | 1 | 52,910 | 5 | 105,821 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,911 | 5 | 105,822 |
"Correct Solution:
```
import random
mod=998244353
N,X=input().split()
N=int(N)
A=[]
for i in range(N):
A.append(int(input(),2))
A.sort()
a=A[-1]
M=max(len(X)-1,a.bit_length()-1)
base=[]
n=a.bit_length()-1
for i in range(M-n,-1,-1):
base.append(a<<i)
for i in range(0,N-1):
a=A[i]
for j in range(M):
for b in base:
a=min(a,a^b)
if a==0:
break
else:
base.append(a)
a=a<<1
data=[0]*(M+1)
data2=[0]*(M+1)
for b in base:
data[b.bit_length()-1]=b
data2[b.bit_length()-1]=1
for i in range(1,M+1):
data2[i]+=data2[i-1]
data2=[0]+data2
#print(data)
#print(data2)
x=0
ans=0
n=len(X)-1
for i in range(len(X)):
if X[i]=="1":
if x>>(n-i)&1==1:
if data[n-i]:
ans+=pow(2,data2[n-i],mod)
ans%=mod
else:
ans+=pow(2,data2[n-i],mod)
ans%=mod
if data[n-i]:
x=x^data[n-i]
else:
break
else:
if x>>(n-i)&1==1:
if data[n-i]:
x=x^data[n-i]
else:
break
else:
continue
else:
ans+=1
ans%=mod
print(ans)
``` | output | 1 | 52,911 | 5 | 105,823 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,912 | 5 | 105,824 |
"Correct Solution:
```
import random
mod=998244353
N,X=input().split()
N=int(N)
A=[]
for i in range(N):
A.append(int(input(),2))
A.sort()
a=A[-1]
M=max(len(X)-1,a.bit_length()-1)
data=[0]*(M+1)
n=a.bit_length()-1
for i in range(M-n,-1,-1):
data[i+n]=a<<i
low=n
for i in range(0,N-1):
a=A[i]
flag=True
while flag:
n=a.bit_length()
for j in range(n-1,low-1,-1):
a=min(a,a^data[j])
if a!=0:
data[a.bit_length()-1]=a
id=a.bit_length()-1
low=id
while data[id+1]==0:
data[id+1]=min((data[id]<<1)^a,(data[id]<<1))
id+=1
else:
a=data[id]<<1
else:
break
data2=[0]*(M+1)
for i in range(M+1):
data2[i]=(data[i]!=0)
for i in range(1,M+1):
data2[i]+=data2[i-1]
data2=[0]+data2
#print(data)
#print(data2)
x=0
ans=0
n=len(X)-1
for i in range(len(X)):
if X[i]=="1":
if x>>(n-i)&1==1:
if data[n-i]:
ans+=pow(2,data2[n-i],mod)
ans%=mod
else:
ans+=pow(2,data2[n-i],mod)
ans%=mod
if data[n-i]:
x=x^data[n-i]
else:
break
else:
if x>>(n-i)&1==1:
if data[n-i]:
x=x^data[n-i]
else:
break
else:
continue
else:
ans+=1
ans%=mod
print(ans)
``` | output | 1 | 52,912 | 5 | 105,825 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,913 | 5 | 105,826 |
"Correct Solution:
```
#!/usr/bin/env python3
def divmod(f, g):
assert g
h = 0
for i in reversed(range(f.bit_length() - g.bit_length() + 1)):
if f & (1 << (g.bit_length() + i - 1)):
f ^= g << i
h ^= 1 << i
return h, f
def gcd(f, g):
while g:
q, r = divmod(f, g)
f, g = g, r
return f
import functools
def solve(n, x, a):
# (g) = (a_1, ..., a_n) is a principal ideal since F_2[x] is a PID
g = functools.reduce(gcd, a)
# count h in F_2[x] s.t. h g <= x
cnt = 0
h = 0
for k in reversed(range(x.bit_length() - g.bit_length() + 1)):
bit = 1 << (g.bit_length() + k - 1)
if (x & bit):
cnt += 1 << k
if (x & bit) != (h & bit):
h ^= g << k
cnt += (h <= x)
return cnt % 998244353
def main():
n, x = input().split()
n = int(n)
x = int(x, 2)
a = [ int(input(), 2) for _ in range(n) ]
print(solve(n, x, a))
if __name__ == '__main__':
main()
``` | output | 1 | 52,913 | 5 | 105,827 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,914 | 5 | 105,828 |
"Correct Solution:
```
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
# xor shift（F_2上の多項式）に関する gcd を計算する
from functools import reduce
X = int(readline().split()[1],2)
A = [int(x,2) for x in readlines()]
MOD = 998244353
def gcd(a,b):
if a < b:
a,b = b,a
while b:
LA = a.bit_length()
LB = b.bit_length()
a ^= b << (LA - LB)
if a < b:
a,b = b,a
return a
g = reduce(gcd,A)
# g の "倍数" で、X以下のものを作る方法の数を数える
# 上位の桁を決めると、gの倍数は一意に決まる。
# よって、上位の桁がXに一致するときのみが問題
LX = X.bit_length()
Lg = g.bit_length()
answer = X >> (Lg - 1)
prod = 0
x = X; Lx = LX
while Lx >= Lg:
prod ^= g << (Lx - Lg)
x ^= g << (Lx - Lg)
Lx = x.bit_length()
if prod <= X:
answer += 1
answer %= MOD
print(answer)
``` | output | 1 | 52,914 | 5 | 105,829 |
Provide a correct Python 3 solution for this coding contest problem.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955 | instruction | 0 | 52,915 | 5 | 105,830 |
"Correct Solution:
```
N, X = input().split()
N = int(N); X = int(X, 2)
p = int(input(), 2)
for i in range(N-1):
v = int(input(), 2)
if p > v:
p, v = v, p
while 0 < p:
q = (v ^ (p << (v.bit_length() - p.bit_length())))
if p < q:
p, v = p, q
else:
p, v = q, p
p = v
lx = X.bit_length()
lp = p.bit_length()
MOD = 998244353
ans = (X >> (p.bit_length() - 1)) % MOD
q = p << (lx - lp)
b = 1 << (lx - 1)
x = 0; y = 0
for k in range(lx - lp, -1, -1):
if b & (X ^ y):
y ^= q
b >>= 1; q >>= 1
if y <= X:
ans = (ans + 1) % MOD
print(ans)
``` | output | 1 | 52,915 | 5 | 105,831 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N non-negative integers written on a blackboard. The i-th integer is A_i.
Takahashi can perform the following two kinds of operations any number of times in any order:
* Select one integer written on the board (let this integer be X). Write 2X on the board, without erasing the selected integer.
* Select two integers, possibly the same, written on the board (let these integers be X and Y). Write X XOR Y (XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
How many different integers not exceeding X can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo 998244353.
Constraints
* 1 \leq N \leq 6
* 1 \leq X < 2^{4000}
* 1 \leq A_i < 2^{4000}(1\leq i\leq N)
* All input values are integers.
* X and A_i(1\leq i\leq N) are given in binary notation, with the most significant digit in each of them being 1.
Input
Input is given from Standard Input in the following format:
N X
A_1
:
A_N
Output
Print the number of different integers not exceeding X that can be written on the blackboard.
Examples
Input
3 111
1111
10111
10010
Output
4
Input
4 100100
1011
1110
110101
1010110
Output
37
Input
4 111001100101001
10111110
1001000110
100000101
11110000011
Output
1843
Input
1 111111111111111111111111111111111111111111111111111111111111111
1
Output
466025955
Submitted Solution:
```
#!/usr/bin/env python3
def divmod(f, g):
assert g
h = 0
for i in reversed(range(f.bit_length() - g.bit_length() + 1)):
if f & (1 << (g.bit_length() + i - 1)):
f ^= g << i
h ^= 1 << i
return h, f
def gcd(f, g):
while g:
q, r = divmod(f, g)
f, g = g, r
return f
import functools
def solve(n, x, a):
# (g) = (a_1, ..., a_n) is a principal ideal since F_2[x] is a PID
g = functools.reduce(gcd, a)
# count h in F_2[x] s.t. h g <= x
cnt = 0
h = 0
for k in reversed(range(x.bit_length() - g.bit_length() + 1)):
bit = 1 << (g.bit_length() + k - 1)
if (x & bit):
cnt += 1 << k
if (x & bit) != (h & bit):
h ^= g << k
cnt += 1 # zero
return cnt % 998244353
def main():
n, x = input().split()
n = int(n)
x = int(x, 2)
a = [ int(input(), 2) for _ in range(n) ]
print(solve(n, x, a))
if __name__ == '__main__':
main()
``` | instruction | 0 | 52,916 | 5 | 105,832 |
No | output | 1 | 52,916 | 5 | 105,833 |
Provide a correct Python 3 solution for this coding contest problem.
When Mr. Kay was browsing a certain SNS as usual, the problem that "there are people who can solve IQ150 or more" came to the timeline. Mr. Kay has an IQ of over 150, so he solved the problem in an instant without even looking at it. For him, he doesn't have to work on such a mystery. It is enough to leave it to the computer.
problem
The following mysterious mathematical formula was written in the problem.
* \\ (5 + 3 = 28 \\)
* \\ (9 + 1 = 810 \\)
* \\ (8 + 6 = 214 \\)
* \\ (5 + 4 = 19 \\)
* \\ (2 + 2 = 4 \\)
* \\ (15 + 8 = 723 \\)
* \\ (7 + 9 = -216 \\)
* \\ (3 + 0 = 33 \\)
When thinking about the above operator \\ (+ \\), for a positive integer \\ (a \\) \\ (x \ geq 0, y \ geq 0 \\) and \\ (x + y =) Find the number of integer pairs \\ (x, y \\) such that a \\).
input
A positive integer \\ (a \\) is given on one line.
output
Output the number of pairs \\ ((x, y) \\) that satisfy \\ (a = x + y, x \ geq 0, y \ geq 0 \\) on one line.
Constraint
* \\ (1 \ leq a \ leq 10 ^ 9 (= 1000000000) \\)
Input / output example
Input 1
19
Output 1
1
There is one way of \\ (5 + 4 \\).
Input 2
twenty two
Output 2
2
There are two types: \\ (11 + 11 \\) and \\ (2 + 0 \\).
Input 3
1
Output 3
0
\\ (1 + 0 = 11, 0 + 1 = -11 \\). \\ (1 \\) cannot be generated.
Input 4
101
Output 4
0
Note that \\ (1 --0 \\) is not \\ (101 \\).
Input 5
660233276
Output 5
Four
Example
Input
19
Output
1 | instruction | 0 | 53,019 | 5 | 106,038 |
"Correct Solution:
```
a = input()
ans = 0
for i in range(1, len(a)):
df = a[:i]
sm = a[i:]
if sm[0] == "0":continue
df = int(df)
sm = int(sm)
if (df + sm) % 2 == 0 and sm >= df and (sm - df) % 2 == 0:
ans += 1
if int(a) % 2 == 0:ans += 1
print(ans)
``` | output | 1 | 53,019 | 5 | 106,039 |
Provide a correct Python 3 solution for this coding contest problem.
When Mr. Kay was browsing a certain SNS as usual, the problem that "there are people who can solve IQ150 or more" came to the timeline. Mr. Kay has an IQ of over 150, so he solved the problem in an instant without even looking at it. For him, he doesn't have to work on such a mystery. It is enough to leave it to the computer.
problem
The following mysterious mathematical formula was written in the problem.
* \\ (5 + 3 = 28 \\)
* \\ (9 + 1 = 810 \\)
* \\ (8 + 6 = 214 \\)
* \\ (5 + 4 = 19 \\)
* \\ (2 + 2 = 4 \\)
* \\ (15 + 8 = 723 \\)
* \\ (7 + 9 = -216 \\)
* \\ (3 + 0 = 33 \\)
When thinking about the above operator \\ (+ \\), for a positive integer \\ (a \\) \\ (x \ geq 0, y \ geq 0 \\) and \\ (x + y =) Find the number of integer pairs \\ (x, y \\) such that a \\).
input
A positive integer \\ (a \\) is given on one line.
output
Output the number of pairs \\ ((x, y) \\) that satisfy \\ (a = x + y, x \ geq 0, y \ geq 0 \\) on one line.
Constraint
* \\ (1 \ leq a \ leq 10 ^ 9 (= 1000000000) \\)
Input / output example
Input 1
19
Output 1
1
There is one way of \\ (5 + 4 \\).
Input 2
twenty two
Output 2
2
There are two types: \\ (11 + 11 \\) and \\ (2 + 0 \\).
Input 3
1
Output 3
0
\\ (1 + 0 = 11, 0 + 1 = -11 \\). \\ (1 \\) cannot be generated.
Input 4
101
Output 4
0
Note that \\ (1 --0 \\) is not \\ (101 \\).
Input 5
660233276
Output 5
Four
Example
Input
19
Output
1 | instruction | 0 | 53,020 | 5 | 106,040 |
"Correct Solution:
```
a = list(input())
for i in range(len(a)):
a[i] = int(a[i])
ans = 0
for i in range(len(a)):
if a[i] == 0:
continue
c = 0
for j in range(i):
c *= 10
c += a[j]
d = 0
for j in range(i, len(a)):
d *= 10
d += a[j]
if (c + d) % 2 != 0:
continue
x = (c + d) // 2
y = d - x
if x >= 0 and y >= 0:
ans += 1
print(ans)
``` | output | 1 | 53,020 | 5 | 106,041 |
Provide a correct Python 3 solution for this coding contest problem.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1 | instruction | 0 | 53,048 | 5 | 106,096 |
"Correct Solution:
```
def ascend(a,b):
mini = min(A[a:a+L])
ans[a] = mini
for i in range(a+1,b):
if A[i+L-1] <= mini : mini = A[i+L-1]
elif A[i-1] == mini : mini = min(A[i:i+L])
ans[i] = mini
def descend(a,b):
mini = min(A[b-1:b+L-1])
ans[b-1] = mini
for i in range(b-2,a-1,-1):
if A[i] <= mini : mini = A[i]
elif A[i+L] == mini: mini = min(A[i:i+L])
ans[i] = mini
[N,L] = [int(x) for x in input().split()]
A = [int(x) for x in input().split()]
ans = [None]*(N-L+1)
count = 0;
if N > 10 ** 4:
for i in range(100):
if A[i+1] > A[i] : count += 1
if count > 80 : descend(0, N-L+1)
else : ascend(0,N-L+1)
else :
ascend(0, N-L+1)
for i in ans[:-1] : print(i, end=" ")
print(ans[-1])
``` | output | 1 | 53,048 | 5 | 106,097 |
Provide a correct Python 3 solution for this coding contest problem.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1 | instruction | 0 | 53,053 | 5 | 106,106 |
"Correct Solution:
```
from collections import deque
N, L = map(int, input().split())
A = list(map(int, input().split()))
ans = []
q = deque()
for i, a in enumerate(A):
while q and A[q[-1]] >= a:
q.pop()
q.append(i)
if i - L + 1 >= 0:
ans.append(A[q[0]])
if q[0] == i - L + 1:
q.popleft()
print(*ans)
``` | output | 1 | 53,053 | 5 | 106,107 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1
Submitted Solution:
```
from collections import deque
def slide_min(L:int, li:list):
deq=deque()
ret=[]
for i,x in enumerate(li):
while deq and deq[-1][1]>x:
deq.pop()
deq.append((i,x))
if deq[0][0]+L==i:
deq.popleft()
ret.append(deq[0][1])
return ret[L-1:]
def main():
n,l,*a=map(int,open(0).read().split())
print(*slide_min(l,a))
if __name__=="__main__":
main()
``` | instruction | 0 | 53,055 | 5 | 106,110 |
Yes | output | 1 | 53,055 | 5 | 106,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1
Submitted Solution:
```
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1
class SWAG:
def __init__(self,func,ide):
self.ide = ide
self.func = func
self.front = []
self.back = []
def push(self,x):
# 累積の結果を残す
if self.back: y = self.func(self.back[-1][1],x)
else: y = x
self.back.append((x,y))
def pop(self):
if not self.front:
while self.back:
x,y = self.back.pop()
if self.front: y = self.func(self.front[-1][1],x)
else: y = x
self.front.append((x,y))
return self.front.pop()[1]
def fold_all(self):
y = self.ide
if self.front: y = self.func(self.front[-1][1],y)
if self.back: y = self.func(self.back[-1][1],y)
return y
ans = []
n,l = map(int,input().split())
data = list(map(int,input().split()))
swag = SWAG(min,inf)
for i in range(l-1):
swag.push(data[i])
for i in range(l-1,n):
swag.push(data[i])
ans.append(swag.fold_all())
swag.pop()
print(*ans)
``` | instruction | 0 | 53,057 | 5 | 106,114 |
Yes | output | 1 | 53,057 | 5 | 106,115 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1
Submitted Solution:
```
# -*- coding: utf-8 -*-
N,L = list(map(int, input().split()))
alist = list(map(int, input().split()))
arr = []
for i in range(L):
while arr and alist[i] <= alist[arr[-1]]:
arr.pop()
arr.append(i)
for i in range(L, N):
print(alist[arr[0]], end=' ')
while arr and arr[0] <= i-L:
arr.pop(0)
while arr and alist[i] <= alist[arr[-1]]:
arr.pop()
arr.append(i)
print(alist[arr[0]])
``` | instruction | 0 | 53,058 | 5 | 106,116 |
Yes | output | 1 | 53,058 | 5 | 106,117 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1
Submitted Solution:
```
def binaryinsertion(A,x):
left=0;right=len(A)-1;centre = len(A)//2
while(True):
if(left == right):
if(x[0]<A[left][0]):
A.insert(left,x)
break
else :
A.insert(left+1,x)
break
else:
if(x[0] < A[centre][0]) :
right = centre - 1
elif(A[centre][0] < x[0]) :
left = centre
else :
A.insert(centre,x)
break
centre = left + (right-left)//2
[N,L] = [int(x) for x in input().split()]
A = [[int(x),int(i)] for i,x in enumerate(input().split())]
sweep = A[:L]
sorted(sweep)
ans = [str(sweep[0][0])]
for i in range(L,N) :
sweep.remove(A[i-L])
binaryinsertion(sweep,A[i])
ans.append(str(sweep[0][0]))
print(" ".join(ans))
``` | instruction | 0 | 53,061 | 5 | 106,122 |
No | output | 1 | 53,061 | 5 | 106,123 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.
Constraints
* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$
Input
The input is given in the following format.
$N$ $L$
$a_1$ $a_2$ ... $a_N$
Output
Print a sequence of the minimum in a line. Print a space character between adjacent elements.
Example
Input
7 3
1 7 7 4 8 1 6
Output
1 4 4 1 1
Submitted Solution:
```
answer=[]
element=[]
D=[]
def initRMQ(nn):
global n
n = 1
while n < nn:
n*=2
for i in range(2*n-1):
D.append(2147483647)
def update(k,a):
k += n-1
D[k] = a
while k>0:
k = (k-1)//2
D[k] = min(D[k*2+1] , D[k*2+2])
def findMin(a,b):
return query(a,b,0,0,n)
def query(a,b,k,l,r):
if r <= a or b <= l:
return 2147483647
if a <= l and r <= b:
return D[k]
vl = query(a, b, (k*2)+1, l, (l+r)//2)
vr = query(a, b, (k*2)+2, (l+r)//2, r)
return min(vl,vr)
N,L = map(int,input().split())
initRMQ(N)
element = input().split()
for i in range(len(element)):
update(i,int(element[i]))
for i in range(N-L+1):
answer.append(findMin(i,i+L))
print('')
x = 0
for i in range(len(answer)):
print(answer[i],end='')
x+=1
if x == len(answer):
break
#print(' ',end='')
``` | instruction | 0 | 53,062 | 5 | 106,124 |
No | output | 1 | 53,062 | 5 | 106,125 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = sorted(list(map(int, input().split())))
if 2048 in a:
print("YES")
else:
b = [0] * 11
for i in range(0, 11):
b[i] += a.count(2**i)
if b[i] > 1 and i < 10:
if b[i] % 2 == 0:
b[i+1] += b[i] // 2
b[i] = 0
else:
b[i+1] += (b[i] - 1) // 2
b[i] = 1
temp = 2
out = False
for i in b[::-1]:
if i >= temp:
out = True
break
if i == 0 or i == 1:
break
temp *= 2
print("YES" if out else "NO")
``` | instruction | 0 | 53,163 | 5 | 106,326 |
Yes | output | 1 | 53,163 | 5 | 106,327 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
def proA(arr):
n=len(arr)
arr.sort()
ind=-1
for i in range(len(arr)):
if(arr[n-1-i]>2048):
continue
ind=n-1-i
break
if(ind==-1):
print('NO')
return
if(sum(arr[:ind+1])>=2048):
print('YES')
else:
print('NO')
t=int(input())
for i in range(t):
n=int(input())
arr=list(map(int,input().split()))
proA(arr)
``` | instruction | 0 | 53,164 | 5 | 106,328 |
Yes | output | 1 | 53,164 | 5 | 106,329 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
import math
q=int(input())
for _ in range(q):
n=int(input())
s=[int(x) for x in input().split()]
arr=s
flag=0
kk=dict()
while(flag==0):
flag=1
h=[]
for i in range(0,len(arr)):
kk[arr[i]]=1
d=dict()
for i in range(0,len(arr)):
if(d.get(arr[i])==None):
d[arr[i]]=1
h.append(arr[i])
else:
d[arr[i]]+=1
flag=0
g=[]
for i in range(0,len(h)):
temp=d[h[i]]
for j in range(temp//2):
g.append(h[i]*2)
if(temp%2!=0):
g.append(h[i])
arr=g
if(kk.get(2048)==None):
print('NO')
else:
print('YES')
``` | instruction | 0 | 53,165 | 5 | 106,330 |
Yes | output | 1 | 53,165 | 5 | 106,331 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
# bsdk idhar kya dekhne ko aaya hai, khud kr!!!
# import math
# from itertools import *
# import random
# import calendar
import datetime
# import webbrowser
t = int(input())
for _ in range(t):
n = int(input())
arr = list(map(int, input().split()))
if 2048 in arr:
print("YES")
else:
arr.sort()
while True:
flag = 0
for i in range(0, len(arr) - 1):
if arr[i] == arr[i+1]:
arr[i] += arr[i+1]
flag = 1
arr.pop(i+1)
break
arr.sort()
if flag == 0:
if 2048 in arr:
print("YES")
break
else:
print("NO")
break
else:
if 2048 in arr:
print("YES")
break
``` | instruction | 0 | 53,166 | 5 | 106,332 |
Yes | output | 1 | 53,166 | 5 | 106,333 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
import math
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
pow2=[0]*12
for i in l:
if int(math.log(i,2)) < 12:
pow2[int(math.log(i,2))]+=1
for i in range(len(pow2)-1):
if pow2[i]>=2:
pow2[i+1]+=(pow2[i]//2)
print(pow2)
if pow2[-1]>=1:
print('YES')
else:
print("NO")
``` | instruction | 0 | 53,167 | 5 | 106,334 |
No | output | 1 | 53,167 | 5 | 106,335 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
def main():
a = int(input())
for i in range(a):
temp = int(input())
values = list(filter(lambda x: x <= 2048, map(int, input().split())))
if len(values) is 0:
print('NO')
return
values = sorted(values, reverse=True)
decide = True
while(True):
if values[0] == 2048:
print('YES')
break
elif decide == False:
print('NO')
break
decide = False
while i < len(values) - 1:
if values[i] == values[i+1]:
decide = True
values[i] = values[i] + values[i+1]
del values[i+1]
i += 1
if __name__ == '__main__':
main()
``` | instruction | 0 | 53,168 | 5 | 106,336 |
No | output | 1 | 53,168 | 5 | 106,337 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
times=int(input())
for num in range(0,times):
number=int(input())
p=0
i=0
q=input()
list0=q.split(" ")
for x in range(0,number):
a=int(list0[x])
if a>2048:
if i==number:
print("NO")
break
else:
p=p+a
if p>=2048:
print("YES")
break
``` | instruction | 0 | 53,169 | 5 | 106,338 |
No | output | 1 | 53,169 | 5 | 106,339 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are playing a variation of game 2048. Initially you have a multiset s of n integers. Every integer in this multiset is a power of two.
You may perform any number (possibly, zero) operations with this multiset.
During each operation you choose two equal integers from s, remove them from s and insert the number equal to their sum into s.
For example, if s = \{1, 2, 1, 1, 4, 2, 2\} and you choose integers 2 and 2, then the multiset becomes \{1, 1, 1, 4, 4, 2\}.
You win if the number 2048 belongs to your multiset. For example, if s = \{1024, 512, 512, 4\} you can win as follows: choose 512 and 512, your multiset turns into \{1024, 1024, 4\}. Then choose 1024 and 1024, your multiset turns into \{2048, 4\} and you win.
You have to determine if you can win this game.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 100) – the number of queries.
The first line of each query contains one integer n (1 ≤ n ≤ 100) — the number of elements in multiset.
The second line of each query contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 2^{29}) — the description of the multiset. It is guaranteed that all elements of the multiset are powers of two.
Output
For each query print YES if it is possible to obtain the number 2048 in your multiset, 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
6
4
1024 512 64 512
1
2048
3
64 512 2
2
4096 4
7
2048 2 2048 2048 2048 2048 2048
2
2048 4096
Output
YES
YES
NO
NO
YES
YES
Note
In the first query you can win as follows: choose 512 and 512, and s turns into \{1024, 64, 1024\}. Then choose 1024 and 1024, and s turns into \{2048, 64\} and you win.
In the second query s contains 2048 initially.
Submitted Solution:
```
x = int(input())
sum = 0
for i in range(x):
uniques = []
m = input()
y = input()
z = y.split()
lit = [int(d) for d in z]
lit.sort()
for dum in lit:
if lit.count(dum) > 1 or dum == sum:
sum = sum + dum
else:
continue
if sum% 2048 == 0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 53,170 | 5 | 106,340 |
No | output | 1 | 53,170 | 5 | 106,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
def main():
# Seems like a[i] must have its most significant bit to be 1 more than that
# of a[i-1].
t=int(input())
allans=[]
for _ in range(t):
d,m=readIntArr()
dMSB=0
d2=d
while d2>0:
dMSB+=1
d2=d2>>1
nWaysAtThisMSB=[0 for _ in range(dMSB+1)]
for msb in range(1,dMSB):
nWaysAtThisMSB[msb]=pow(2,msb-1,m)
#last msb only has d-(2**(dMSB-1)-1) ways
nWaysAtThisMSB[dMSB]=(d-(2**(dMSB-1)-1))%m
#Sum up product of all subsequences in nWaysAtThisMSB
dp=[0 for _ in range(dMSB+1)]
for i in range(1,dMSB+1):
dp[i]+=dp[i-1] #don't take current MSB
dp[i]%=m
dp[i]+=nWaysAtThisMSB[i]#take current MSB alone
dp[i]%=m
dp[i]+=dp[i-1]*nWaysAtThisMSB[i]#take current MSB with previous items
dp[i]%=m
allans.append(dp[dMSB])
multiLineArrayPrint(allans)
return
#import sys
#input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
import sys
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
def oneLineArrayPrint(arr):
print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
def readIntArr():
return [int(x) for x in input().split()]
inf=float('inf')
MOD=10**9+7
main()
``` | instruction | 0 | 53,227 | 5 | 106,454 |
Yes | output | 1 | 53,227 | 5 | 106,455 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
def func(a):
b=1
c=1
d=1
for i in range(1,a+1):
c=2*b+1
d=2**(i)-1
if i!=a:
b=c+(b+1)*d
return b,c
for _ in range(int(input())):
d,m=list(map(int,input().split()))
s=1
while 1>0:
if 2**s>d:
break
s=s+1
s=s-1
b,c=func(s)
print(((d-(2**s))*(b+1)+c)%m)
``` | instruction | 0 | 53,228 | 5 | 106,456 |
Yes | output | 1 | 53,228 | 5 | 106,457 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
def log(x):
p = 0
v = 1
while v <= x:
p += 1
v *= 2
return p
ans = []
def ps(arr, m):
n = len(arr)
ans = 1;
for i in range(0,n):
ans = (ans * ((arr[i] + 1) % m)) % m
return ans-1
for _ in range(int(input())):
[d, m] = [int(i) for i in input().split()]
s = log(d)
pt = 0
vals = [0 for i in range(s)]
while (pt < (s-1)):
vals[pt] = pow(2, pt, m)
pt += 1
vals[s-1] = d - pow(2, s-1, m) + 1
a = ps(vals, m)
if a >= 0:
ans.append(str(a))
else:
ans.append(str(m+a))
print('\n'.join(ans))
``` | instruction | 0 | 53,229 | 5 | 106,458 |
Yes | output | 1 | 53,229 | 5 | 106,459 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
import math
for j in range(int(input())):
d,m=map(int,input().split())
#the next has got to have atleast the next bit more
power=math.floor(math.log2(d))+1
binrep=bin(d)[2:]
if len(binrep)>=2:
ones=int(binrep[1:],2)+1
else:
ones=1
ans=0
#watch out for the last number
normal=[]
for s in range(power):
if s==power-1:
normal.append((1+ones)%m)
else:
normal.append((1+pow(2,s,m))%m)
for s in range(power):
if s!=power-1:
a1=pow(2,s,m)
else:
a1=(ones)%m
a2=1
for b in range(s+1,power):
a2*=(normal[b]%m)
a2=a2%m
ans+=(a1*a2)%m
ans=ans%m
print(ans)
``` | instruction | 0 | 53,230 | 5 | 106,460 |
Yes | output | 1 | 53,230 | 5 | 106,461 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
import io
import os
from collections import Counter, defaultdict, deque
from itertools import combinations
def brute(D):
count = 0
for r in range(1, D + 1):
for combo in combinations(range(1, D + 1), r):
xor = [0]
for x in combo:
xor.append(xor[-1] ^ x)
if all(x < y for x, y in zip(xor, xor[1:])):
count += 1
return count
from functools import lru_cache
def solve(D, M):
@lru_cache(maxsize=None)
def dp(D):
if D == 0:
return 0
if D == 1:
return 1
ans = 0
hiBit = D.bit_length() - 1
assert D >= (1 << hiBit)
usingHiBit = D - (1 << hiBit) + 1
ans = usingHiBit + usingHiBit * dp((1 << hiBit) - 1) + dp((1 << hiBit) - 1)
return ans % M
return dp(D)
if __name__ == "__main__":
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
T = int(input())
for t in range(T):
D, M = [int(x) for x in input().split()]
ans = solve(D, M)
print(ans)
``` | instruction | 0 | 53,231 | 5 | 106,462 |
No | output | 1 | 53,231 | 5 | 106,463 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS:
You are given two integers d, m, find the number of arrays a, satisfying the following constraints:
* The length of a is n, n ≥ 1
* 1 ≤ a_1 < a_2 < ... < a_n ≤ d
* Define an array b of length n as follows: b_1 = a_1, ∀ i > 1, b_i = b_{i - 1} ⊕ a_i, where ⊕ is the bitwise exclusive-or (xor). After constructing an array b, the constraint b_1 < b_2 < ... < b_{n - 1} < b_n should hold.
Since the number of possible arrays may be too large, you need to find the answer modulo m.
Input
The first line contains an integer t (1 ≤ t ≤ 100) denoting the number of test cases in the input.
Each of the next t lines contains two integers d, m (1 ≤ d, m ≤ 10^9).
Note that m is not necessary the prime!
Output
For each test case, print the number of arrays a, satisfying all given constrains, modulo m.
Example
Input
10
1 1000000000
2 999999999
3 99999998
4 9999997
5 999996
6 99995
7 9994
8 993
9 92
10 1
Output
1
3
5
11
17
23
29
59
89
0
Submitted Solution:
```
def log(x):
p = 0
v = 1
while v <= x:
p += 1
v *= 2
return p
ans = []
def ps(arr, m):
n = len(arr)
ans = 1;
for i in range(0,n):
ans = ans * (arr[i] + 1)
ans %= m
return ans-1
for _ in range(int(input())):
[d, m] = [int(i) for i in input().split()]
s = log(d)
pt = 0
vals = [0 for i in range(s)]
while (pt < (s-1)):
vals[pt] = pow(2, pt, m)
pt += 1
vals[s-1] = d - pow(2, s-1, m) + 1
a = ps(vals, m)
if a >= 0:
ans.append(str(a))
else:
ans.append("0")
print('\n'.join(ans))
``` | instruction | 0 | 53,232 | 5 | 106,464 |
No | output | 1 | 53,232 | 5 | 106,465 |
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