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.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
# RawCoder : https://bit.ly/RCyouTube
# Author : MehulYK
for i in range(int(input())):
a, b = map(int, input().split())
if((a + b) % 3 == 0):
print("yes")
else:
print("no")
``` | instruction | 0 | 963 | 5 | 1,926 |
No | output | 1 | 963 | 5 | 1,927 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. You may perform any number of operations on them (possibly zero).
During each operation you should choose any positive integer x and set a := a - x, b := b - 2x or a := a - 2x, b := b - x. Note that you may choose different values of x in different operations.
Is it possible to make a and b equal to 0 simultaneously?
Your program should answer t independent test cases.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.
Then the test cases follow, each test case is represented by one line containing two integers a and b for this test case (0 ≤ a, b ≤ 10^9).
Output
For each test case print the answer to it — YES if it is possible to make a and b equal to 0 simultaneously, and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
6 9
1 1
1 2
Output
YES
NO
YES
Note
In the first test case of the example two operations can be used to make both a and b equal to zero:
1. choose x = 4 and set a := a - x, b := b - 2x. Then a = 6 - 4 = 2, b = 9 - 8 = 1;
2. choose x = 1 and set a := a - 2x, b := b - x. Then a = 2 - 2 = 0, b = 1 - 1 = 0.
Submitted Solution:
```
for _ in range(int(input())):
x,y =map(int, input().split())
if (x==0 and y) or (y==0 and x):
print('NO')
else:
print('NO' if (x+y)%3 else 'YES')
``` | instruction | 0 | 964 | 5 | 1,928 |
No | output | 1 | 964 | 5 | 1,929 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, …, a_n of non-negative integers.
You need to find the largest number m of triples (i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m) such that:
* 1 ≤ i_p < j_p < k_p ≤ n for each p in 1, 2, …, m;
* a_{i_p} = a_{k_p} = 0, a_{j_p} ≠ 0;
* all a_{j_1}, a_{j_2}, …, a_{j_m} are different;
* all i_1, j_1, k_1, i_2, j_2, k_2, …, i_m, j_m, k_m are different.
Input
The first line of input contains one integer t (1 ≤ t ≤ 500 000): the number of test cases.
The first line of each test case contains one integer n (1 ≤ n ≤ 500 000).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).
The total sum of n is at most 500 000.
Output
For each test case, print one integer m: the largest number of proper triples that you can find.
Example
Input
8
1
1
2
0 0
3
0 1 0
6
0 0 1 2 0 0
6
0 1 0 0 1 0
6
0 1 3 2 0 0
6
0 0 0 0 5 0
12
0 1 0 2 2 2 0 0 3 3 4 0
Output
0
0
1
2
1
1
1
2
Note
In the first two test cases, there are not enough elements even for a single triple, so the answer is 0.
In the third test case we can select one triple (1, 2, 3).
In the fourth test case we can select two triples (1, 3, 5) and (2, 4, 6).
In the fifth test case we can select one triple (1, 2, 3). We can't select two triples (1, 2, 3) and (4, 5, 6), because a_2 = a_5.
Submitted Solution:
```
from sys import stdout,stdin
from collections import defaultdict,deque
import math
t=int(stdin.readline())
for _ in range(t):
n=int(stdin.readline())
#n,e=map(int,stdin.readline().split())
l=list(map(int,stdin.readline().split()))
d=defaultdict(int)
if n<3:
print(0)
else:
for i in l:
d[i]+=1
nl=len(d)
if d[i]>0:
nl-=1
z=d[0]//2
if nl==0:
print(0)
else:
print(min(z,nl))
``` | instruction | 0 | 1,047 | 5 | 2,094 |
No | output | 1 | 1,047 | 5 | 2,095 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, …, a_n of non-negative integers.
You need to find the largest number m of triples (i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m) such that:
* 1 ≤ i_p < j_p < k_p ≤ n for each p in 1, 2, …, m;
* a_{i_p} = a_{k_p} = 0, a_{j_p} ≠ 0;
* all a_{j_1}, a_{j_2}, …, a_{j_m} are different;
* all i_1, j_1, k_1, i_2, j_2, k_2, …, i_m, j_m, k_m are different.
Input
The first line of input contains one integer t (1 ≤ t ≤ 500 000): the number of test cases.
The first line of each test case contains one integer n (1 ≤ n ≤ 500 000).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).
The total sum of n is at most 500 000.
Output
For each test case, print one integer m: the largest number of proper triples that you can find.
Example
Input
8
1
1
2
0 0
3
0 1 0
6
0 0 1 2 0 0
6
0 1 0 0 1 0
6
0 1 3 2 0 0
6
0 0 0 0 5 0
12
0 1 0 2 2 2 0 0 3 3 4 0
Output
0
0
1
2
1
1
1
2
Note
In the first two test cases, there are not enough elements even for a single triple, so the answer is 0.
In the third test case we can select one triple (1, 2, 3).
In the fourth test case we can select two triples (1, 3, 5) and (2, 4, 6).
In the fifth test case we can select one triple (1, 2, 3). We can't select two triples (1, 2, 3) and (4, 5, 6), because a_2 = a_5.
Submitted Solution:
```
t = int(input())
def rainbow(n, arr):
zeros = []
for i in range(n):
if arr[i] == 0: zeros.append(i)
Count, p = 0, 0
start, end = 0, len(zeros) - 1
while start < end:
if zeros[end] - zeros[start] <= end - start + p: break
start, end = start + 1, end - 1
Count += 1
if zeros[start] == zeros[start - 1] + 1 and zeros[end] == zeros[end + 1] - 1:
p += 1
return Count
for i in range(t):
n = int(input())
arr = list(map(int, input().split()))
print(rainbow(n, arr))
``` | instruction | 0 | 1,048 | 5 | 2,096 |
No | output | 1 | 1,048 | 5 | 2,097 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, …, a_n of non-negative integers.
You need to find the largest number m of triples (i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m) such that:
* 1 ≤ i_p < j_p < k_p ≤ n for each p in 1, 2, …, m;
* a_{i_p} = a_{k_p} = 0, a_{j_p} ≠ 0;
* all a_{j_1}, a_{j_2}, …, a_{j_m} are different;
* all i_1, j_1, k_1, i_2, j_2, k_2, …, i_m, j_m, k_m are different.
Input
The first line of input contains one integer t (1 ≤ t ≤ 500 000): the number of test cases.
The first line of each test case contains one integer n (1 ≤ n ≤ 500 000).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).
The total sum of n is at most 500 000.
Output
For each test case, print one integer m: the largest number of proper triples that you can find.
Example
Input
8
1
1
2
0 0
3
0 1 0
6
0 0 1 2 0 0
6
0 1 0 0 1 0
6
0 1 3 2 0 0
6
0 0 0 0 5 0
12
0 1 0 2 2 2 0 0 3 3 4 0
Output
0
0
1
2
1
1
1
2
Note
In the first two test cases, there are not enough elements even for a single triple, so the answer is 0.
In the third test case we can select one triple (1, 2, 3).
In the fourth test case we can select two triples (1, 3, 5) and (2, 4, 6).
In the fifth test case we can select one triple (1, 2, 3). We can't select two triples (1, 2, 3) and (4, 5, 6), because a_2 = a_5.
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
a_reverse = a[::-1]
x = 0
y = 0
m = x
k = n - y - 1
differ_0_list = []
while(True):
if 0 in a[x:] and 0 in a_reverse[y:]:
x = a.index(0,x)
y = a_reverse.index(0,y)
else:
break
m = x
k = n - y - 1
if m >= k:
break
x += 1
y += 1
for differ_0 in a[m:k]:
if differ_0 != 0 and differ_0 not in differ_0_list:
differ_0_list.append(differ_0)
break
print(len(differ_0_list))
``` | instruction | 0 | 1,049 | 5 | 2,098 |
No | output | 1 | 1,049 | 5 | 2,099 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence a_1, a_2, …, a_n of non-negative integers.
You need to find the largest number m of triples (i_1, j_1, k_1), (i_2, j_2, k_2), ..., (i_m, j_m, k_m) such that:
* 1 ≤ i_p < j_p < k_p ≤ n for each p in 1, 2, …, m;
* a_{i_p} = a_{k_p} = 0, a_{j_p} ≠ 0;
* all a_{j_1}, a_{j_2}, …, a_{j_m} are different;
* all i_1, j_1, k_1, i_2, j_2, k_2, …, i_m, j_m, k_m are different.
Input
The first line of input contains one integer t (1 ≤ t ≤ 500 000): the number of test cases.
The first line of each test case contains one integer n (1 ≤ n ≤ 500 000).
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n).
The total sum of n is at most 500 000.
Output
For each test case, print one integer m: the largest number of proper triples that you can find.
Example
Input
8
1
1
2
0 0
3
0 1 0
6
0 0 1 2 0 0
6
0 1 0 0 1 0
6
0 1 3 2 0 0
6
0 0 0 0 5 0
12
0 1 0 2 2 2 0 0 3 3 4 0
Output
0
0
1
2
1
1
1
2
Note
In the first two test cases, there are not enough elements even for a single triple, so the answer is 0.
In the third test case we can select one triple (1, 2, 3).
In the fourth test case we can select two triples (1, 3, 5) and (2, 4, 6).
In the fifth test case we can select one triple (1, 2, 3). We can't select two triples (1, 2, 3) and (4, 5, 6), because a_2 = a_5.
Submitted Solution:
```
t = int(input())
def rainbow(n, arr):
zeros = []
for i in range(n):
if arr[i] == 0: zeros.append(i)
Count = 0
start, end = 0, len(zeros) - 1
while start < end:
if zeros[end] - zeros[start] == end - start: break
start, end = start + 1, end - 1
Count += 1
return Count
for i in range(t):
n = int(input())
arr = list(map(int, input().split()))
print(rainbow(n, arr))
``` | instruction | 0 | 1,050 | 5 | 2,100 |
No | output | 1 | 1,050 | 5 | 2,101 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a multiset of powers of two. More precisely, for each i from 0 to n exclusive you have cnt_i elements equal to 2^i.
In one operation, you can choose any one element 2^l > 1 and divide it into two elements 2^{l - 1}.
You should perform q queries. Each query has one of two types:
* "1 pos val" — assign cnt_{pos} := val;
* "2 x k" — calculate the minimum number of operations you need to make at least k elements with value lower or equal to 2^x.
Note that all queries of the second type don't change the multiset; that is, you just calculate the minimum number of operations, you don't perform them.
Input
The first line contains two integers n and q (1 ≤ n ≤ 30; 1 ≤ q ≤ 2 ⋅ 10^5) — the size of array cnt and the number of queries.
The second line contains n integers cnt_0, cnt_1, ..., cnt_{n - 1} (0 ≤ cnt_i ≤ 10^6).
Next q lines contain queries: one per line. Each query has one of two types:
* "1 pos val" (0 ≤ pos < n; 0 ≤ val ≤ 10^6);
* "2 x k" (0 ≤ x < n; 1 ≤ k ≤ 10^{15}).
It's guaranteed that there is at least one query of the second type.
Output
For each query of the second type, print the minimum number of operations you need to make at least k elements with a value lower or equal to 2^x or -1 if there is no way to do it.
Example
Input
6 11
0 1 0 0 1 0
2 1 5
2 4 18
1 1 0
2 2 5
2 0 17
1 0 3
2 1 2
1 1 4
1 4 0
1 5 1
2 2 8
Output
4
16
4
-1
0
1
Submitted Solution:
```
n, q=list(map(int, input().split()))
cnt=list(map(int, input().split()))
for case in range(0, q):
o, x, y=list(map(int, input().split()))
if(o==1):
cnt[x]=y
else:
maxSplit=0
current=0
for i in range(0, x+1):
maxSplit+=(2**i)*cnt[i]
current+=cnt[i]
if(maxSplit>=y):
print(max(0, y-current))
else:
found=None
ans=0
for i in range(x+1, n):
maxSplit+=(2**i)*cnt[i]
if(maxSplit>=y):
found=i
maxSplit-=(2**i)*cnt[i]
break
else:
ans+=(2**(i-x)-1)*cnt[i]
current+=2**(i-x)*cnt[i]
if(found is None):
ans=-1
else:
for i in range(found, x, -1):
req=y-maxSplit
req=(req-1)//(2**i)+1
maxSplit+=(2**i)*(req-1)
ans+=(2**(i-x)-1)*(req-1)
current+=2**(i-x)*(req-1)
ans+=1
ans+=y-current
print(ans)
``` | instruction | 0 | 1,063 | 5 | 2,126 |
No | output | 1 | 1,063 | 5 | 2,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a multiset of powers of two. More precisely, for each i from 0 to n exclusive you have cnt_i elements equal to 2^i.
In one operation, you can choose any one element 2^l > 1 and divide it into two elements 2^{l - 1}.
You should perform q queries. Each query has one of two types:
* "1 pos val" — assign cnt_{pos} := val;
* "2 x k" — calculate the minimum number of operations you need to make at least k elements with value lower or equal to 2^x.
Note that all queries of the second type don't change the multiset; that is, you just calculate the minimum number of operations, you don't perform them.
Input
The first line contains two integers n and q (1 ≤ n ≤ 30; 1 ≤ q ≤ 2 ⋅ 10^5) — the size of array cnt and the number of queries.
The second line contains n integers cnt_0, cnt_1, ..., cnt_{n - 1} (0 ≤ cnt_i ≤ 10^6).
Next q lines contain queries: one per line. Each query has one of two types:
* "1 pos val" (0 ≤ pos < n; 0 ≤ val ≤ 10^6);
* "2 x k" (0 ≤ x < n; 1 ≤ k ≤ 10^{15}).
It's guaranteed that there is at least one query of the second type.
Output
For each query of the second type, print the minimum number of operations you need to make at least k elements with a value lower or equal to 2^x or -1 if there is no way to do it.
Example
Input
6 11
0 1 0 0 1 0
2 1 5
2 4 18
1 1 0
2 2 5
2 0 17
1 0 3
2 1 2
1 1 4
1 4 0
1 5 1
2 2 8
Output
4
16
4
-1
0
1
Submitted Solution:
```
from math import ceil
class cnt:
def __init__(self, n, a):
self.a = a
self.n = n-1
self.smm = [a[0]]
self.summ = [a[0]]
for i in range(1,n):
self.smm.append(self.smm[i-1] + 2**i * self.a[i])
self.summ.append(self.summ[i-1] + self.a[i])
# print('Created')
# print('c.a:', self.a, 'c.n:', self.n, 'c.smm:', self.smm, 'c.summ:', self.summ)
def f(self, pos, val):
ppos = pos
self.a[pos]=val
if pos == 0:
self.smm[0] = val
self.summ[0] = val
pos += 1
for ii in range(pos,n):
self.smm[ii]=(self.smm[ii-1] + 2**ii * self.a[ii])
self.summ[ii]=(self.summ[ii-1] + self.a[ii])
# print('F: pos:', ppos, 'val:', val, 'self.a:', self.a, 'self.smm:', self.smm, 'self.summ:', self.summ)
def ss(self, x, k):
if x == self.n:
# print('SS: x:', x, 'k:', k, 'res:', -1 if self.a[x] < k else 0)
return -1 if self.a[x] < k else 0
if self.a[x] >= k:
# print('SS: x:', x, 'k:', k, 'res:', 0)
return 0
kk = k
k = (k - self.a[x] + 1)//2
rs = self.ss(x+1, k)
if rs == -1:
# print('SS: x:', x, 'k:', kk, 'res:', -1)
return -1
# print('SS: x:', x, 'k:', kk, 'res:', k+rs)
return k + rs
def s(self, x, k):
if self.smm[self.n] < k:
# print('S: x:', x, 'k:', k, 'res:', -1)
return -1
if self.smm[x] >= k:
# print('S: x:', x, 'k:', k, 'res:', max(0, k-self.summ[x]))
return max(0, k-self.summ[x])
else:
kk = k
k = k - self.smm[x]
nd = ceil(k/(2**x))
rs = self.ss(x+1, nd)
if rs == -1:
# print('S: x:', x, 'k:', kk, 'res:', -1, 'nd:', nd)
return -1
# print('S: x:', x, 'k:', kk, 'res:', k+nd+rs, 'nd:',nd)
return max(0, k-nd*2-self.smm[x]) + nd + rs
n, q = map(int, input().split())
a = list(map(int, input().split()))
c = cnt(n, a)
acts = []
fpr = []
for _ in range(q):
qq, f, s = map(int, input().split())
if qq == 1:
c.f(f, s)
else:
fpr.append(c.s(f, s))
print(*fpr, sep='\n')
``` | instruction | 0 | 1,064 | 5 | 2,128 |
No | output | 1 | 1,064 | 5 | 2,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
# Fast IO Region
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")
"""
# Get out of main function
def main():
pass
# decimal to binary
def binary(n):
return (bin(n).replace("0b", ""))
# binary to decimal
def decimal(s):
return (int(s, 2))
# power of a number base 2
def pow2(n):
p = 0
while n > 1:
n //= 2
p += 1
return (p)
# if number is prime in √n time
def isPrime(n):
if (n == 1):
return (False)
else:
root = int(n ** 0.5)
root += 1
for i in range(2, root):
if (n % i == 0):
return (False)
return (True)
# list to string ,no spaces
def lts(l):
s = ''.join(map(str, l))
return s
# String to list
def stl(s):
# for each character in string to list with no spaces -->
l = list(s)
# for space in string -->
# l=list(s.split(" "))
return l
# Returns list of numbers with a particular sum
def sq(a, target, arr=[]):
s = sum(arr)
if (s == target):
return arr
if (s >= target):
return
for i in range(len(a)):
n = a[i]
remaining = a[i + 1:]
ans = sq(remaining, target, arr + [n])
if (ans):
return ans
# Sieve for prime numbers in a range
def SieveOfEratosthenes(n):
cnt = 0
prime = [True for i in range(n + 1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n + 1, p):
prime[i] = False
p += 1
for p in range(2, n + 1):
if prime[p]:
cnt += 1
# print(p)
return (cnt)
# for positive integerse only
def nCr(n, r):
f = math.factorial
return f(n) // f(r) // f(n - r)
# 1000000007
mod = int(1e9) + 7
def ssinp(): return input()
# s=input()
def iinp(): return int(input())
# n=int(input())
def nninp(): return map(int, input().split())
# a,b,c=map(int,input().split())
def llinp(): return list(map(int, input().split()))
# a=list(map(int,input().split()))
def p(xyz): print(xyz)
def p2(a, b): print(a, b)
import math
# import random
# sys.setrecursionlimit(300000)
# from fractions import Fraction
from collections import OrderedDict
# from collections import deque
######################## mat=[[0 for i in range(n)] for j in range(m)] ########################
######################## list.sort(key=lambda x:x[1]) for sorting a list according to second element in sublist ########################
######################## Speed: STRING < LIST < SET,DICTIONARY ########################
######################## from collections import deque ########################
######################## ASCII of A-Z= 65-90 ########################
######################## ASCII of a-z= 97-122 ########################
######################## d1.setdefault(key, []).append(value) ########################
#for __ in range(iinp()):
n,k=nninp()
l1=[0]
ind=1
length=1
for i in range(n):
l1.append([ind,length+1])
ind=length+1
length=(2*length)+1
for i in range(1,n+1):
if(((k-l1[i][0])/l1[i][1])%1==0):
print(i)
exit()
``` | instruction | 0 | 1,355 | 5 | 2,710 |
Yes | output | 1 | 1,355 | 5 | 2,711 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
n, k = [int(i) for i in input().split()]
p = 2**n
# for k in range(p-1):
num = k
counter = n
while num != 0:
num = abs(num-p//2)
# print(num)
p = p//2
counter-=1
print(counter+1)
# p = 2**n
``` | instruction | 0 | 1,357 | 5 | 2,714 |
Yes | output | 1 | 1,357 | 5 | 2,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
# https://codeforces.com/problemset/problem/743/B
# Problem
# Big O:
# Time complexity: O(n) n-> step
# Space complexity: O(1)
def sequenceLengthAtStep(steps):
if steps == 1:
return 1
return sequenceLengthAtStep(steps - 1) * 2 + 1
def elementAtPos(pos, steps):
sequenceLength = sequenceLengthAtStep(steps)
integer = 1
firstIntegerPos = 1
while firstIntegerPos < sequenceLength:
integerModulus = firstIntegerPos * 2
if (pos - firstIntegerPos) % integerModulus == 0:
return integer
integer += 1
firstIntegerPos *= 2
return integer
# Read input
steps, pos = (int(x) for x in input().split())
print(elementAtPos(pos, steps))
``` | instruction | 0 | 1,358 | 5 | 2,716 |
Yes | output | 1 | 1,358 | 5 | 2,717 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
n,k=map(int,input().split())
from math import log
ans=n
while (k):
k%=2**ans
ans-=1
print(ans+1)
``` | instruction | 0 | 1,359 | 5 | 2,718 |
No | output | 1 | 1,359 | 5 | 2,719 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
from sys import stdin, stdout
def b_e(n):
if n == 0:
return 1
elif n%2 == 0:
return b_e(n//2)*b_e(n//2)
else:
return 2*b_e(n//2)*b_e(n//2)
def give(n):
yield b_e(n-1)
yield b_e(n)
def main():
n, m = map(int, stdin.readline().strip().split())
l, r = 1, n+1
number = -1
while l <= r:
mid = (l+r) // 2
a, d = give(mid)
if m-a < 0:
r = mid - 1
elif m-a>0 and (m-a)%d != 0:
l = mid + 1
else:
number = mid
break
stdout.write(f'{number}')
if __name__ == '__main__':
main()
``` | instruction | 0 | 1,360 | 5 | 2,720 |
No | output | 1 | 1,360 | 5 | 2,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
# -*- coding: utf-8 -*-
"""
Spyder Editor
This is a temporary script file.
"""
def pow_mod(base, exp):
if exp == 0:
return 1
elif exp == 1:
return base
elif (exp & 1) != 0:
return base * pow_mod(base * base, exp // 2)
else:
return pow_mod(base * base, exp // 2)
#n, m = map(int, input().split())
#c = ([int(z) for z in input().split()])
n, k = map(int, input().split())
t1 = pow_mod(2, n-1)
print(t1)
if k==t1:
print(n)
elif k%2!=0:
print('1')
else:
flag = 1
while(flag==1):
if (k!=t1):
n = n - 1
k = max(min(k, t1-k), min(k, k-t1))
t1 = t1//2
else:
flag = 0
print(n)
``` | instruction | 0 | 1,361 | 5 | 2,722 |
No | output | 1 | 1,361 | 5 | 2,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.
Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.
The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.
Please help Chloe to solve the problem!
Input
The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).
Output
Print single integer — the integer at the k-th position in the obtained sequence.
Examples
Input
3 2
Output
2
Input
4 8
Output
4
Note
In the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.
In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4.
Submitted Solution:
```
from copy import deepcopy
n, k = [int(x) for x in input().split()]
if k & 1:
print(1)
else:
x = 1
c = 0
while x < k:
x = x << 1
c += 1
d = min(abs(k - x), abs(k - x // 2))
if d & (d - 1) == 0 and d > 2:
print(d - 1)
else:
if d == 0:
d = k
a = [1]
pp = 2
while True:
cc = deepcopy(a)
a.append(pp)
a = a + cc
pp += 1
if 2 ** (pp - 1) > d:
break
if k > len(a):
if k % (2 ** (c - 1)) - 1 < len(a):
print(a[k % (2 ** (c - 1)) - 1])
else:
print(a[k % len(a)])
else:
print(a[k - 1])
``` | instruction | 0 | 1,362 | 5 | 2,724 |
No | output | 1 | 1,362 | 5 | 2,725 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,428 | 5 | 2,856 |
"Correct Solution:
```
s = int(input())
mod = 10**9 + 7
dp = [0]*(s+1)
dp[0] = 1
x = 0
for i in range(1,s+1):
if i >= 3:
x += dp[i-3]
dp[i] = x
print(dp[s]%mod)
``` | output | 1 | 1,428 | 5 | 2,857 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,429 | 5 | 2,858 |
"Correct Solution:
```
ans = [0]*2001
for i in range(3, 6):
ans[i] = 1
for i in range(6, 2001):
tmp = i - 3
ans[i] = (sum(ans[3:tmp+1])+1)%(10**9+7)
print(ans[int(input())])
``` | output | 1 | 1,429 | 5 | 2,859 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,430 | 5 | 2,860 |
"Correct Solution:
```
s = int(input())
mod = 1000000007
dp = [0]*(s+1)
dp[0] = 1
for i in range(3,s+1):
for j in range(i-2):
dp[i] += dp[j]
dp[i] %= mod
print(dp[s])
``` | output | 1 | 1,430 | 5 | 2,861 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,431 | 5 | 2,862 |
"Correct Solution:
```
s = int(input())
MOD = 10**9+7
dp = [0] * (s+1)
dp[0] = 1
for i in range(s+1):
for j in range(0, i-3+1):
dp[i] += dp[j]
dp[i] %= MOD
print(dp[s])
``` | output | 1 | 1,431 | 5 | 2,863 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,432 | 5 | 2,864 |
"Correct Solution:
```
S=int(input())
f=[1,0,0]
for i in range(S-2):f.append(f[i]+f[i+2])
print(f[S]%(10**9+7))
``` | output | 1 | 1,432 | 5 | 2,865 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,433 | 5 | 2,866 |
"Correct Solution:
```
s = int(input())
dp = [0 for _ in range(s+1)]
MOD = 10**9+7
for i in range(3,s+1):
dp[i] = 1
for j in range(3,i-2):
dp[i] += dp[i-j]
dp[i] %= MOD
print(dp[s])
``` | output | 1 | 1,433 | 5 | 2,867 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,434 | 5 | 2,868 |
"Correct Solution:
```
s = int(input())
m = 10**9+7
a = [1,0,0,1,1,1,2]
if s < 7:
print(a[s])
exit()
for i in range(7,s+1):
a.append((sum(a[3:i-2])+1)%m)
print(a[s])
``` | output | 1 | 1,434 | 5 | 2,869 |
Provide a correct Python 3 solution for this coding contest problem.
Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501 | instruction | 0 | 1,435 | 5 | 2,870 |
"Correct Solution:
```
n=int(input())
M=10**9+7
F=[1]
for i in range(1,2001): F+=[i*F[-1]%M]
c=lambda n,r: F[n]*pow(F[r]*F[n-r],M-2,M)%M
a=0
for i in range(n//3):
n-=3
a=(a+c(n+i,n))%M
print(a)
``` | output | 1 | 1,435 | 5 | 2,871 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
s = int(input())
MOD = 10**9+7
ans = [0 for _ in range(2000)]
for i in range(2, 2000):
ans[i] = (sum(ans[2:i-2]) + 1) % MOD
print(ans[s-1])
``` | instruction | 0 | 1,436 | 5 | 2,872 |
Yes | output | 1 | 1,436 | 5 | 2,873 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
s=int(input())
m=10**9+7
dp=[0]*(s+1)
dp[0]=1
for i in range(1,s+1):
for j in range(0,(i-3)+1):
dp[i]+=dp[j]
dp[i]%=m
print(dp[s])
``` | instruction | 0 | 1,437 | 5 | 2,874 |
Yes | output | 1 | 1,437 | 5 | 2,875 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
S = int(input())
mod = 10 ** 9 + 7
dp = [1, 0, 0]
cnt = 0
for i in range(3, S+1):
cnt = dp[i-1] + dp[i-3]
cnt %= mod
dp.append(cnt)
ans = dp[S]
print(ans)
``` | instruction | 0 | 1,438 | 5 | 2,876 |
Yes | output | 1 | 1,438 | 5 | 2,877 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
N = int(input())
dp=[0]*(N+1)
dp[0]=1
for i in range(1,N+1):
for u in range(i-2):
dp[i]+=dp[u]
print(dp[N]%(10**9+7))
``` | instruction | 0 | 1,439 | 5 | 2,878 |
Yes | output | 1 | 1,439 | 5 | 2,879 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
n = int(input())
ans = [0]*(n+1) #ans[k]:入力値kでの答え
#初期値３、４、５
ans[3] = 1
ans[4] = 1
ans[5] = 1
if n == 1 or n == 2:
print(0)
sys.exit()
if 3<= n <=5:
print(1)
sys.exit()
for i in range(6,n+1):
start = 3
stop = i-3
s = 1
for j in range(start,stop+1):
s = (s+ans[j]) % (10**9+7)
ans[i] = s
print(ans[-1])
``` | instruction | 0 | 1,440 | 5 | 2,880 |
No | output | 1 | 1,440 | 5 | 2,881 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
M = 10**9+7
S = int(input())
num_list = [0]*(S+1)
num_list[-1] = 1
for idx in reversed(range(S+1)):
if idx-9 > -1:
num_list[idx-9] += num_list[idx]
if idx-8 > -1:
num_list[idx-8] += num_list[idx]
if idx-7 > -1:
num_list[idx-7] += num_list[idx]
if idx-6 > -1:
num_list[idx-6] += num_list[idx]
if idx-5 > -1:
num_list[idx-5] += num_list[idx]
if idx-4 > -1:
num_list[idx-4] += num_list[idx]
if idx-3 > -1:
num_list[idx-3] += num_list[idx]
ans = num_list[0]%M
print(ans)
``` | instruction | 0 | 1,441 | 5 | 2,882 |
No | output | 1 | 1,441 | 5 | 2,883 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
input=sys.stdin.readline
s=int(input())
INF=10**9+7
def modcomb(n,k,m):
fac=[0]*(n+1)
finv=[0]*(n+1)
inv=[0]*(n+1)
fac[0]=fac[1]=1
finv[0]=finv[1]=1
inv[1]=1
for i in range(2,n+1):
fac[i]=fac[i-1]*i%m
inv[i]=m-inv[m%i]*(m//i)%m
finv[i]=finv[i-1]*inv[i]%m
return fac[n]*(finv[k]*finv[n-k]%m)%m
ans=0
for n in range(1,667):
if s-3*n>=0:
ans=(ans+modcomb(s-2*n-1,n-1,INF))%INF
print(ans)
``` | instruction | 0 | 1,442 | 5 | 2,884 |
No | output | 1 | 1,442 | 5 | 2,885 |
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 how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.
Constraints
* 1 \leq S \leq 2000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
S
Output
Print the answer.
Examples
Input
7
Output
3
Input
2
Output
0
Input
1729
Output
294867501
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**9)
def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))
INF=10**20
class Counting():
def __init__(self,maxim,mod):
maxim += 1
self.mod = mod
self.fact = [0]*maxim
self.fact[0] = 1
for i in range(1,maxim):
self.fact[i] = self.fact[i-1] * i % mod
self.invfact = [0]*maxim
self.invfact[maxim-1] = pow(self.fact[maxim-1],mod-2,mod)
for i in reversed(range(maxim-1)):
self.invfact[i] = self.invfact[i+1] * (i+1) % mod
def nCk(self,n,r):
if n < 0 or n < r: return 0
return self.fact[n] * self.invfact[r] * self.invfact[n-r] % self.mod
def nPk(self,n,r):
if n < 0 or n < r: return 0
return self.fact[n] * self.invfact[n-r] % self.mod
def main():
S=ii()
MOD = 10**9+7
k = 1
ans = 0
C = Counting(10**6,MOD)
while S-3*k > 0:
ans += C.nCk(S-2*k-1,k-1)
ans %= MOD
k += 1
print(ans%MOD)
if __name__ == "__main__":
main()
``` | instruction | 0 | 1,443 | 5 | 2,886 |
No | output | 1 | 1,443 | 5 | 2,887 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,460 | 5 | 2,920 |
"Correct Solution:
```
n = int(input())
C = list(map(int, input().split()))
mod = 10**9 + 7
if n == 1:
ans = 2 * C[0]
ans %= mod
print(ans)
exit()
ans = 0
pattern = 2 ** (n-1) % mod
d = 2 ** (n-2) % mod
C.sort(reverse=True)
for c in C:
ans += (c * pattern) % mod
pattern += d
pattern %= mod
ans %= mod
print(ans*(2**n) % mod)
``` | output | 1 | 1,460 | 5 | 2,921 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,461 | 5 | 2,922 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
a.sort(reverse = True)
mod = 10 ** 9 + 7
res = 0
if N == 1:
print(a[0] * 2 % mod)
exit(0)
for i in range(N):
res += a[i] * (pow(2, N - 1, mod) % mod + pow(2, N - 2, mod) * i % mod) % mod
res %= mod
print(res * pow(2, N, mod) % mod)
``` | output | 1 | 1,461 | 5 | 2,923 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,462 | 5 | 2,924 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
MOD = 10**9+7
N = int(readline())
C = list(map(int, readline().split()))
C.sort()
ans = 0
for i in range(N):
ans = (ans + pow(2, 2*N-2, MOD)*C[i]*(N-i+1))%MOD
print(ans)
``` | output | 1 | 1,462 | 5 | 2,925 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,463 | 5 | 2,926 |
"Correct Solution:
```
import sys,bisect
input = sys.stdin.readline
n = int(input())
c = list(map(int,input().split()))
c.sort()
mod = 10**9+7
se = pow(2,mod-2,mod)
res = 0
for i,e in enumerate(c):
cnt = (pow(4,n,mod)%mod)*se%mod
res = (res + (e*cnt))%mod
res = (res + (e*pow(4,n-1,mod)%mod)*(n-1-i)%mod)%mod
print(res%mod)
``` | output | 1 | 1,463 | 5 | 2,927 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,464 | 5 | 2,928 |
"Correct Solution:
```
MOD = 10 ** 9 + 7
N = int(input())
C = list(map(int, input().split()))
C.sort()
if N == 1:
print (2 * C[0] % MOD)
exit()
lst = [0] * (N + 3)
lst[0] = 1
for i in range(1, N + 3):
lst[i] = (lst[i - 1] * 2) % MOD
ANS = 0
for i, c in enumerate(C):
ANS += c * (N + 1 - i)
ANS *= lst[N - 2]
ANS %= MOD
ANS *= lst[N]
print (ANS % MOD)
``` | output | 1 | 1,464 | 5 | 2,929 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,465 | 5 | 2,930 |
"Correct Solution:
```
mod=10**9+7
n=int(input())
arr=list(map(int,input().split()))
arr=sorted(arr)
ans=0
if n==1:
print((2*arr[0])%mod)
else:
table=[1]
for _ in range(n):
tmp=table[-1]*2
tmp%=mod
table.append(tmp)
for i in range(n):
if i==n-1:
ans+=(table[i-1]*(n-i+1)*arr[i])%mod
else:
ans+=(table[i]*(n-i+1)*table[n-i-2]*arr[i])%mod
print((ans*table[n])%mod)
``` | output | 1 | 1,465 | 5 | 2,931 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,466 | 5 | 2,932 |
"Correct Solution:
```
N = int(input())
C = [int(c) for c in input().split()]
C.sort()
MOD = 10**9+7
p2 = [1]
for i in range(2*N+10):
p2 += [p2[-1]*2%MOD]
ans = 0
for i in range(N):
m = (p2[N-1-i]+(N-i-1)*p2[N-i-2])*C[i]
# print(m)
m = m*p2[N+i]%MOD
ans += m
print(ans%MOD)
``` | output | 1 | 1,466 | 5 | 2,933 |
Provide a correct Python 3 solution for this coding contest problem.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312 | instruction | 0 | 1,467 | 5 | 2,934 |
"Correct Solution:
```
mod = 10**9+7
n = int(input())
c = [int(x) for x in input().split()]
c = sorted(c)
ans = 0
pow2 = [1]
for i in range(n+1):
tmp = (pow2[-1]*2)%mod
pow2.append(tmp)
for i in range(n):
ans += pow2[n]*pow2[i]*((n-1-i)*pow2[n-2-i] + pow2[n-1-i])*c[i]
ans %= mod
print(ans)
``` | output | 1 | 1,467 | 5 | 2,935 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
N = int(input())
C = sorted(list(map(int,input().split())))[::-1]
ans = 0
MOD = 10**9 + 7
for k in range(N):
ans += pow(2,2*N-2,MOD)*(k+2)*C[k]
print(ans%MOD)
``` | instruction | 0 | 1,468 | 5 | 2,936 |
Yes | output | 1 | 1,468 | 5 | 2,937 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
M=1000000007
N=int(input())
C=sorted(map(int,input().split()),reverse=True)
def pow(x,p):
if(p==0):
return 1;
if(p%2):
a=pow(x,p-1)%M;
return x*a%M
else:
a=pow(x,p//2)%M
return a*a%M
ans=0;
p2=pow(2,2*N-2)%M
for k in range(N):
ans=(ans+(C[k]*((p2*k)%M+2*p2))%M)%M
print(ans)
``` | instruction | 0 | 1,469 | 5 | 2,938 |
Yes | output | 1 | 1,469 | 5 | 2,939 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
MOD=10**9+7
N=int(input())
C=sorted(map(int,input().split()))
p=pow(4,N-1,MOD)
ans=0
for i in range(N):
res=p*C[i]*(N-i+1)
ans=(ans+res)%MOD
print(ans)
``` | instruction | 0 | 1,470 | 5 | 2,940 |
Yes | output | 1 | 1,470 | 5 | 2,941 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
MOD=10**9+7
N=int(input())
if N==1:
C=int(input())
print(2*C%MOD)
exit()
C=list(map(int, input().split()))
C.sort(reverse=True)
out=0
tmp1=pow(2, N-1, MOD)
tmp2=pow(2, N-2, MOD)
for i in range(N):
out+=(tmp1+tmp2*i)*C[i]
out%=MOD
out=out*pow(2, N, MOD)
print(int(out%MOD))
``` | instruction | 0 | 1,471 | 5 | 2,942 |
Yes | output | 1 | 1,471 | 5 | 2,943 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**6)
N = int(input())
C = list(map(int, input().split()))
C.sort()
MOD = 10**9 + 7
ans = 0
# どうも公式ドキュメントによると、組み込み関数のpowの第三引数に値渡すとMODとってくれるらしいので、完全に無駄
def pow_mod(x, n, mod):
if n == 0:
return 1 % mod
elif n % 2 == 0:
y = pow_mod(x, n//2, mod)
return y * y % MOD
else:
return x * pow_mod(x, n-1, mod) % mod
for i in range(N):
# 詳細は開設動画の通りだが、i桁目の右にr個の数字、左にlこの数字がある
l = i
r = N - i - 1
# i桁目の寄与が C[i] * 2**l * (2**r + r * 2**(r-1))で、最後に2**Nをかける（Tのとり方が2**Nこあるので）
# -> C[i] * 2**l * (2**(N+r) + r * 2**(r+N-1))
ans += ((C[i] * pow_mod(2, l, MOD)) % MOD * (pow_mod(2, N+r, MOD) + r * pow_mod(2, N+r-1, MOD))) % MOD
ans %= MOD
print(ans)
``` | instruction | 0 | 1,472 | 5 | 2,944 |
No | output | 1 | 1,472 | 5 | 2,945 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
n = int(input())
c = list(map(int, input().split()))
mod = 10**9 + 7
c.sort()
ans = 0
for i in range(n):
ans += c[i] * pow(2, i, mod) % mod * (pow(2, n-i-1, mod) * (n-i) + pow(2, n-i, mod) ) % mod * pow(2, n, mod) % mod
ans %= mod
print(ans)
``` | instruction | 0 | 1,473 | 5 | 2,946 |
No | output | 1 | 1,473 | 5 | 2,947 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
import sys
import math
import fractions
import bisect
import queue
import heapq
from collections import deque
sys.setrecursionlimit(4100000)
MOD = int(1e9+7)
PI = 3.14159265358979323846264338327950288
INF = 1e18
'''
1行のint
N, K = map(int, input().split())
1行のstring
S, T = input().split()
1行の整数配列
P = list(map(int,input().split()))
改行あり
x = []
y = []
for i in range(N):
x1,y1=[int(i) for i in input().split()]
x.append(x1)
y.append(y1)
N行M列の初期化
dp = [[INF] * M for i in range(N)]
'''
N = int(input())
C = list(map(int,input().split()))
# コストの小さいものから更新していけばいい
C.sort()
# 2のべき乗は先に計算しておく
beki = []
for i in range(3*N+20):
beki.append(int(math.pow(2, i))%MOD)
ans = 0
for i in range(N):
ans += (C[i] * beki[2*N-2] * (N-i+1))%MOD
print(ans % MOD)
``` | instruction | 0 | 1,474 | 5 | 2,948 |
No | output | 1 | 1,474 | 5 | 2,949 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:
* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.
* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.
There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).
Constraints
* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
C_1 C_2 \cdots C_N
Output
Print the sum of f(S, T), modulo (10^9+7).
Examples
Input
1
1000000000
Output
999999993
Input
2
5 8
Output
124
Input
5
52 67 72 25 79
Output
269312
Submitted Solution:
```
number=10**9+7
n=int(input())
c=list(map(int, input().split()))
c.sort(reverse=True)
sum=0
for i in range(1, n+1):
sum=(sum+(4**(n-1))*(i+1)*c[i-1])%number
print(sum)
``` | instruction | 0 | 1,475 | 5 | 2,950 |
No | output | 1 | 1,475 | 5 | 2,951 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0 | instruction | 0 | 1,476 | 5 | 2,952 |
"Correct Solution:
```
a,b,c= map(int,input().split())
t = min(a-b,c)
print(c-t)
``` | output | 1 | 1,476 | 5 | 2,953 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0 | instruction | 0 | 1,477 | 5 | 2,954 |
"Correct Solution:
```
a,b,c=map(int,input().split())
print(b+c-a if b+c-a>=0 else 0)
``` | output | 1 | 1,477 | 5 | 2,955 |
Provide a correct Python 3 solution for this coding contest problem.
We have two bottles for holding water.
Bottle 1 can hold up to A milliliters of water, and now it contains B milliliters of water.
Bottle 2 contains C milliliters of water.
We will transfer water from Bottle 2 to Bottle 1 as much as possible.
How much amount of water will remain in Bottle 2?
Constraints
* All values in input are integers.
* 1 \leq B \leq A \leq 20
* 1 \leq C \leq 20
Input
Input is given from Standard Input in the following format:
A B C
Output
Print the integer representing the amount of water, in milliliters, that will remain in Bottle 2.
Examples
Input
6 4 3
Output
1
Input
8 3 9
Output
4
Input
12 3 7
Output
0 | instruction | 0 | 1,478 | 5 | 2,956 |
"Correct Solution:
```
A,B,C=map(int,input().split());print(max(0,C-A+B))
``` | output | 1 | 1,478 | 5 | 2,957 |
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