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 |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality:
a + b + c + d = n
For example, for n = 35, we have 4 different combinations of (a, b, c, d): (8, 9, 9, 9), (9, 8, 9, 9), (9, 9, 8, 9), and (9, 9, 9, 8).
Input
The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50.
Output
Print the number of combination in a line.
Example
Input
35
1
Output
4
4 | instruction | 0 | 52,073 | 5 | 104,146 |
"Correct Solution:
```
import sys
for line in sys.stdin:
count = 0
n = int(line)
for a in range(10):
for b in range(10):
for c in range(10):
for d in range(10):
if a+b+c+d==n:
count += 1
print(count)
``` | output | 1 | 52,073 | 5 | 104,147 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality:
a + b + c + d = n
For example, for n = 35, we have 4 different combinations of (a, b, c, d): (8, 9, 9, 9), (9, 8, 9, 9), (9, 9, 8, 9), and (9, 9, 9, 8).
Input
The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50.
Output
Print the number of combination in a line.
Example
Input
35
1
Output
4
4
Submitted Solution:
```
import sys
try:
while True:
n = int(input())
res = 0
for i in range(10):
for j in range(10):
for k in range(10):
for m in range(10):
if i + j + k + m == n:
res += 1
print(res)
except Exception:
sys.exit()
``` | instruction | 0 | 52,075 | 5 | 104,150 |
Yes | output | 1 | 52,075 | 5 | 104,151 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality:
a + b + c + d = n
For example, for n = 35, we have 4 different combinations of (a, b, c, d): (8, 9, 9, 9), (9, 8, 9, 9), (9, 9, 8, 9), and (9, 9, 9, 8).
Input
The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50.
Output
Print the number of combination in a line.
Example
Input
35
1
Output
4
4
Submitted Solution:
```
import itertools, sys
d = {i: 0 for i in range(51)}
for i in itertools.combinations_with_replacement(range(0,10), 4):
d[sum(i)] += 1
print(d)
for i in map(int, sys.stdin):
print(d[i]*4)
``` | instruction | 0 | 52,078 | 5 | 104,156 |
No | output | 1 | 52,078 | 5 | 104,157 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality:
a + b + c + d = n
For example, for n = 35, we have 4 different combinations of (a, b, c, d): (8, 9, 9, 9), (9, 8, 9, 9), (9, 9, 8, 9), and (9, 9, 9, 8).
Input
The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50.
Output
Print the number of combination in a line.
Example
Input
35
1
Output
4
4
Submitted Solution:
```
import sys
sum = [0] * 51
for i in range(10):
for j in range(10):
for k in range(min(10,18-i-j)):
for l in range(min(10,18-i-j-k)):
sum[i+j+k+l] += 1
sum[36-i-j-k-l] += 1
for i in sys.stdin:
print(sum[int(i)])
``` | instruction | 0 | 52,080 | 5 | 104,160 |
No | output | 1 | 52,080 | 5 | 104,161 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Write a program which reads an integer n and identifies the number of combinations of a, b, c and d (0 ≤ a, b, c, d ≤ 9) which meet the following equality:
a + b + c + d = n
For example, for n = 35, we have 4 different combinations of (a, b, c, d): (8, 9, 9, 9), (9, 8, 9, 9), (9, 9, 8, 9), and (9, 9, 9, 8).
Input
The input consists of several datasets. Each dataset consists of n (1 ≤ n ≤ 50) in a line. The number of datasets is less than or equal to 50.
Output
Print the number of combination in a line.
Example
Input
35
1
Output
4
4
Submitted Solution:
```
import sys
values = []
for line in sys.stdin:
values.append(int(line))
ans = [1 for i in range(10) for j in range(10) for k in range(10) for l in range(10) if n == i + j + k + l]
print(ans.count(1))
``` | instruction | 0 | 52,081 | 5 | 104,162 |
No | output | 1 | 52,081 | 5 | 104,163 |
Provide a correct Python 3 solution for this coding contest problem.
problem
For the integer n (1 ≤ n), let Pn be a string of n + 1 I's and n O's starting with I and alternating, where I and O are the uppercase Ai and O, respectively. is there.
P1 | IOI
--- | ---
P2 | IOIOI
P3 | IOIOIOI
|. |
|. |
|. |
Pn | IOIOIO ... OI (n O)
Figure 1-1 Character string considered in this question Pn
Given the integer n and the string s consisting only of I and O, write a program that outputs how many Pn's are contained in s.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The integer n (1 ≤ n ≤ 1000000) is written on the first line.
The second line contains the integer m (1 ≤ m ≤ 1000000). M represents the number of characters in s.
The string s is written on the third line. S consists of only I and O.
For all scoring data, 2n + 1 ≤ m. Of the scoring data, 50% of the scoring data satisfies n ≤ 100 and m ≤ 10000.
When n is 0, it indicates the end of input. The number of datasets does not exceed 10.
output
For each dataset, print one integer on one line that indicates how many strings Pn are contained in the string s. If s does not contain Pn, print 0 as an integer.
Examples
Input
1
13
OOIOIOIOIIOII
2
13
OOIOIOIOIIOII
0
Output
4
2
Input
None
Output
None | instruction | 0 | 52,115 | 5 | 104,230 |
"Correct Solution:
```
while True:
n = int(input())
if n==0: break
m = int(input())
s = input()
ar = [0]*m
ans = 0
if m >= 3:
for i in range(2,m):
if s[i-2:i+1] == "IOI":
ar[i] = ar[i-2] + 1
if ar[i] >= n: ans += 1
print(ans)
``` | output | 1 | 52,115 | 5 | 104,231 |
Provide a correct Python 3 solution for this coding contest problem.
problem
For the integer n (1 ≤ n), let Pn be a string of n + 1 I's and n O's starting with I and alternating, where I and O are the uppercase Ai and O, respectively. is there.
P1 | IOI
--- | ---
P2 | IOIOI
P3 | IOIOIOI
|. |
|. |
|. |
Pn | IOIOIO ... OI (n O)
Figure 1-1 Character string considered in this question Pn
Given the integer n and the string s consisting only of I and O, write a program that outputs how many Pn's are contained in s.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The integer n (1 ≤ n ≤ 1000000) is written on the first line.
The second line contains the integer m (1 ≤ m ≤ 1000000). M represents the number of characters in s.
The string s is written on the third line. S consists of only I and O.
For all scoring data, 2n + 1 ≤ m. Of the scoring data, 50% of the scoring data satisfies n ≤ 100 and m ≤ 10000.
When n is 0, it indicates the end of input. The number of datasets does not exceed 10.
output
For each dataset, print one integer on one line that indicates how many strings Pn are contained in the string s. If s does not contain Pn, print 0 as an integer.
Examples
Input
1
13
OOIOIOIOIIOII
2
13
OOIOIOIOIIOII
0
Output
4
2
Input
None
Output
None | instruction | 0 | 52,118 | 5 | 104,236 |
"Correct Solution:
```
base = 2000003
mask = (1 << 32) - 1
while True:
n = int(input())
if not n:
break
m = int(input())
s = [int(c == 'I') for c in input().strip()]
l = 2 * n + 1
key, i, t = 0, 0, 1
while i < l:
key = (key + t) & mask
t = (t * base ** 2) & mask
i += 2
cnt = 0
t1 = 1
for _ in range(l):
t1 = (t1 * base) & mask
e = 0
for i in range(l):
e = e * base + s[i]
for i in range(m - l):
if e == key:
cnt += 1
e = (e * base - t1 * s[i] + s[i + l]) & mask
if e == key:
cnt += 1
print(cnt)
``` | output | 1 | 52,118 | 5 | 104,237 |
Provide a correct Python 3 solution for this coding contest problem.
problem
For the integer n (1 ≤ n), let Pn be a string of n + 1 I's and n O's starting with I and alternating, where I and O are the uppercase Ai and O, respectively. is there.
P1 | IOI
--- | ---
P2 | IOIOI
P3 | IOIOIOI
|. |
|. |
|. |
Pn | IOIOIO ... OI (n O)
Figure 1-1 Character string considered in this question Pn
Given the integer n and the string s consisting only of I and O, write a program that outputs how many Pn's are contained in s.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The integer n (1 ≤ n ≤ 1000000) is written on the first line.
The second line contains the integer m (1 ≤ m ≤ 1000000). M represents the number of characters in s.
The string s is written on the third line. S consists of only I and O.
For all scoring data, 2n + 1 ≤ m. Of the scoring data, 50% of the scoring data satisfies n ≤ 100 and m ≤ 10000.
When n is 0, it indicates the end of input. The number of datasets does not exceed 10.
output
For each dataset, print one integer on one line that indicates how many strings Pn are contained in the string s. If s does not contain Pn, print 0 as an integer.
Examples
Input
1
13
OOIOIOIOIIOII
2
13
OOIOIOIOIIOII
0
Output
4
2
Input
None
Output
None | instruction | 0 | 52,119 | 5 | 104,238 |
"Correct Solution:
```
while True:
n= int(input())
if n== 0: break
m, s= int(input()), input()
ioi= "IOI" if n==3 else "IOI"+"OI"*(n-1)
n= 2*n+1
print(sum(1 for i in range(m-n+1) if s[i:i+n]==ioi))
``` | output | 1 | 52,119 | 5 | 104,239 |
Provide a correct Python 3 solution for this coding contest problem.
problem
For the integer n (1 ≤ n), let Pn be a string of n + 1 I's and n O's starting with I and alternating, where I and O are the uppercase Ai and O, respectively. is there.
P1 | IOI
--- | ---
P2 | IOIOI
P3 | IOIOIOI
|. |
|. |
|. |
Pn | IOIOIO ... OI (n O)
Figure 1-1 Character string considered in this question Pn
Given the integer n and the string s consisting only of I and O, write a program that outputs how many Pn's are contained in s.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The integer n (1 ≤ n ≤ 1000000) is written on the first line.
The second line contains the integer m (1 ≤ m ≤ 1000000). M represents the number of characters in s.
The string s is written on the third line. S consists of only I and O.
For all scoring data, 2n + 1 ≤ m. Of the scoring data, 50% of the scoring data satisfies n ≤ 100 and m ≤ 10000.
When n is 0, it indicates the end of input. The number of datasets does not exceed 10.
output
For each dataset, print one integer on one line that indicates how many strings Pn are contained in the string s. If s does not contain Pn, print 0 as an integer.
Examples
Input
1
13
OOIOIOIOIIOII
2
13
OOIOIOIOIIOII
0
Output
4
2
Input
None
Output
None | instruction | 0 | 52,120 | 5 | 104,240 |
"Correct Solution:
```
def solve():
while True:
n = int(input())
if not n: break
m = int(input())
s = input()
ind = 0
ans = 0
while ind < m:
if s[ind] == "I":
count = 0
while ind + 2 < m:
if s[ind + 1] == "O" and s[ind + 2] == "I":
count += 1
ind += 2
else:
break
if count - n + 1 >= 0:
ans += (count - n + 1)
ind += 1
print(ans)
solve()
``` | output | 1 | 52,120 | 5 | 104,241 |
Provide a correct Python 3 solution for this coding contest problem.
problem
For the integer n (1 ≤ n), let Pn be a string of n + 1 I's and n O's starting with I and alternating, where I and O are the uppercase Ai and O, respectively. is there.
P1 | IOI
--- | ---
P2 | IOIOI
P3 | IOIOIOI
|. |
|. |
|. |
Pn | IOIOIO ... OI (n O)
Figure 1-1 Character string considered in this question Pn
Given the integer n and the string s consisting only of I and O, write a program that outputs how many Pn's are contained in s.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The integer n (1 ≤ n ≤ 1000000) is written on the first line.
The second line contains the integer m (1 ≤ m ≤ 1000000). M represents the number of characters in s.
The string s is written on the third line. S consists of only I and O.
For all scoring data, 2n + 1 ≤ m. Of the scoring data, 50% of the scoring data satisfies n ≤ 100 and m ≤ 10000.
When n is 0, it indicates the end of input. The number of datasets does not exceed 10.
output
For each dataset, print one integer on one line that indicates how many strings Pn are contained in the string s. If s does not contain Pn, print 0 as an integer.
Examples
Input
1
13
OOIOIOIOIIOII
2
13
OOIOIOIOIIOII
0
Output
4
2
Input
None
Output
None | instruction | 0 | 52,121 | 5 | 104,242 |
"Correct Solution:
```
while 1:
n=int(input())
if n==0:break
a='I'+'OI'*n
b,s=int(input()),input()
print(sum(1 for i in range(b-len(a)) if s[i:i+len(a)]==a))
``` | output | 1 | 52,121 | 5 | 104,243 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
100 1 0
50 100
Output
14.57738 | instruction | 0 | 52,128 | 5 | 104,256 |
"Correct Solution:
```
import math
d, n, b = map(int, input().split())
O = [list(map(int, input().split())) for i in range(n)]
def solve(b):
l = d / (b+1)
idx = 0
vx2 = 10**9
for i in range(b+1):
while idx < n and O[idx][0]*(b+1) <= d*(i+1):
p, h = O[idx]
p -= l*i
vx2 = min(vx2, p*(l-p)/(2*h))
idx += 1
if vx2 == 0:
return 10**9
return l if l <= vx2 * 2 else vx2 + l**2 / (4*vx2)
print(math.sqrt(min(map(solve, range(b+1)))))
``` | output | 1 | 52,128 | 5 | 104,257 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
100 1 0
50 100
Output
14.57738 | instruction | 0 | 52,129 | 5 | 104,258 |
"Correct Solution:
```
d, n, b = map(int, input().split())
O = [list(map(int, input().split())) for i in range(n)]
def solve(b):
l = d / (b + 1)
idx = 0
vx2 = 10**9
for i in range(b + 1):
while idx < n and O[idx][0]*(b+1) <= d*(i+1):
p, h = O[idx]
p -= l*i
vx2 = min(vx2, p*(l - p) / (2 * h))
idx += 1
if vx2 == 0:
return 10**9
if l <= vx2 * 2:
return l
return vx2 + l**2 / (4*vx2)
ans = 10**9
for i in range(0, b+1):
ans = min(ans, solve(i))
import math
print(math.sqrt(ans))
``` | output | 1 | 52,129 | 5 | 104,259 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,138 | 5 | 104,276 |
"Correct Solution:
```
n, k = map(int,input().split())
now = 0
while n > 1:
n -= 1
now = (now * k) // (k - 1) + 1
print(now)
``` | output | 1 | 52,138 | 5 | 104,277 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,139 | 5 | 104,278 |
"Correct Solution:
```
#!/usr/bin/env python3
n, k = map(int, input().split())
a = 0
for i in range(n-1):
a = a * k // (k - 1) + 1
print(a)
``` | output | 1 | 52,139 | 5 | 104,279 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,140 | 5 | 104,280 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n,k = LI()
t = 0
for _ in range(n-1):
t = t * k // (k-1) + 1
return t
print(main())
``` | output | 1 | 52,140 | 5 | 104,281 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,141 | 5 | 104,282 |
"Correct Solution:
```
N, k = [int(i) for i in input().split()]
ans = 0
for i in range(N - 1):
ans = (ans * k + k - 1) // (k - 1)
print(ans)
``` | output | 1 | 52,141 | 5 | 104,283 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,142 | 5 | 104,284 |
"Correct Solution:
```
# coding: utf-8
# Here your code !
def main(N,k):
p = 0
p2 = 0
memo = 0
for i in range(N-1):
p, p2 = p2, k*(p2+1)//(k-1) - 2
while p2-1-p2//k != p:
p2+=1
return p2
if __name__ == '__main__':
N,k=input().split()
print(main(int(N),int(k)))
``` | output | 1 | 52,142 | 5 | 104,285 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,143 | 5 | 104,286 |
"Correct Solution:
```
# def test(k):
# res = [0]*20
# l = [i for i in range(20)]
# t = 1
# while l:
# i = 0
# while i < len(l):
# res[l.pop(i)] = t
# i += k-1
# t += 1
# return res
# for k in range(2,11):
# print(k,":",test(k))
from math import floor
N, k = map(int, input().split())
l, r = -1, 10**18
while l+1 < r:
m = (l+r) >> 1
x = m
for i in range(1, N):
x -= x // k + 1
if 0 <= x:
r = m
else:
l = m
print(r)
``` | output | 1 | 52,143 | 5 | 104,287 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,144 | 5 | 104,288 |
"Correct Solution:
```
def horizontal_input(T=str):
return list(map(T,input().split()))
def vertical_input(n,T=str,sep=False,septype=tuple):
data=[]
if sep:
for i in range(n):
data.append(septype(map(T,input().split())))
else:
for i in range(n):
data.append(T(input()))
return data
n,k=horizontal_input(int)
prisoner=0
for i in range(n-1):
prisoner+=1
prisoner+=(prisoner-1)//(k-1)
print(prisoner)
``` | output | 1 | 52,144 | 5 | 104,289 |
Provide a correct Python 3 solution for this coding contest problem.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7 | instruction | 0 | 52,145 | 5 | 104,290 |
"Correct Solution:
```
N,K = map(int, input().split())
ans = 1
for _ in range(N-1):
ans += (ans+K-2)//(K-1)
print(ans-1)
``` | output | 1 | 52,145 | 5 | 104,291 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7
Submitted Solution:
```
n,k=map(int,input().split())
a=0
for _ in range(n-1):a+=a//(k-1)+1
print(a)
``` | instruction | 0 | 52,146 | 5 | 104,292 |
Yes | output | 1 | 52,146 | 5 | 104,293 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
prison
There are an infinite number of prisoners. Initially, the prisoners are numbered 0, 1, 2, ....
Do the following N times:
* Release the 0th prisoner and execute the k, 2k, 3k, ... th prisoners.
* Then renumber the remaining prisoners. At this time, the prisoners with the smallest original numbers are numbered 0, 1, 2, ... in order.
Find the number that was originally assigned to the prisoner released in the Nth operation.
Constraints
* 1 ≤ N ≤ 10 ^ 5
* 2 ≤ k ≤ 10 ^ 5
* The answer is less than 10 ^ {18}.
Input Format
Input is given from standard input in the following format.
N k
Output Format
Print the answer in one line.
Sample Input 1
4 2
Sample Output 1
7
Sample Input 2
13
Sample Output 2
0
Sample Input 3
100000 100000
Sample Output 3
99999
Example
Input
4 2
Output
7
Submitted Solution:
```
# coding: utf-8
# Here your code !
def main(N,k):
p = 0
for i in range(N-1):
p2 = p
while p2-1-p2//k != p:
p2+=1
p=p2
return p
if __name__ == '__main__':
N,k=input().split()
print(main(int(N),int(k)))
``` | instruction | 0 | 52,147 | 5 | 104,294 |
No | output | 1 | 52,147 | 5 | 104,295 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....
You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.
Input
The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).
Output
If it is impossible to represent n as the sum of k powers of two, print NO.
Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.
Examples
Input
9 4
Output
YES
1 2 2 4
Input
8 1
Output
YES
8
Input
5 1
Output
NO
Input
3 7
Output
NO
Submitted Solution:
```
import sys
def input(): return sys.stdin.readline().rstrip("\r\n")
def List(): return list(map(int, input().split()))
def Num(): return int(input())
def solve():
n, k = List()
tot, i = k, k - 1
a = [1 for i in range(k)]
while i >= 0:
while tot + a[i] <= n:
tot += a[i]
a[i] *= 2
i -= 1
if tot == n:
print('YES')
print(*a)
else:
print('NO')
solve()
``` | instruction | 0 | 52,244 | 5 | 104,488 |
Yes | output | 1 | 52,244 | 5 | 104,489 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a bag of size n. Also you have m boxes. The size of i-th box is a_i, where each a_i is an integer non-negative power of two.
You can divide boxes into two parts of equal size. Your goal is to fill the bag completely.
For example, if n = 10 and a = [1, 1, 32] then you have to divide the box of size 32 into two parts of size 16, and then divide the box of size 16. So you can fill the bag with boxes of size 1, 1 and 8.
Calculate the minimum number of divisions required to fill the bag of size n.
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains two integers n and m (1 ≤ n ≤ 10^{18}, 1 ≤ m ≤ 10^5) — the size of bag and the number of boxes, respectively.
The second line of each test case contains m integers a_1, a_2, ... , a_m (1 ≤ a_i ≤ 10^9) — the sizes of boxes. It is guaranteed that each a_i is a power of two.
It is also guaranteed that sum of all m over all test cases does not exceed 10^5.
Output
For each test case print one integer — the minimum number of divisions required to fill the bag of size n (or -1, if it is impossible).
Example
Input
3
10 3
1 32 1
23 4
16 1 4 1
20 5
2 1 16 1 8
Output
2
-1
0
Submitted Solution:
```
from collections import defaultdict
def cal(n, xs):
i = 0
remain = set()
for i, x in enumerate(reversed(bin(n)[2:])):
if x == '1':
remain.add(i)
bcnt = defaultdict(int)
xs.sort()
ans = 0
for x in xs:
if not remain:
break
b = x.bit_length() - 1
if b in remain:
remain.remove(b)
continue
r = min(remain)
if r < b:
remain.remove(r)
ans += b - r
continue
while True:
bcnt[b] += 1
if bcnt[b] == 2:
bcnt[b] = 0
if b + 1 in remain:
remain.remove(b + 1)
else:
b += 1
continue
break
bs = []
for b, cnt in bcnt.items():
for _ in range(cnt):
bs.append(b)
bs.sort()
ib = 0
for r in sorted(remain):
while ib < len(bs):
b = bs[ib]
ib += 1
if b >= r:
ans += b - r
break
else:
return -1
return ans
T = int(input())
for _ in range(T):
n, m = map(int, input().split())
xs = list(map(int, input().split()))
print(cal(n, xs))
``` | instruction | 0 | 52,373 | 5 | 104,746 |
No | output | 1 | 52,373 | 5 | 104,747 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
n=int(input())
z=998244353
if n==1:
print(10)
elif n==2:
x=180
y=10
print(x,y)
else:
ans=[]
for i in range(1,n):
ans.append(20+(9*(n-i-1)))
ans.append(10)
arr=[1]*(n)
arr[-2]=9
for i in range(n-3,-1,-1):
arr[i]=arr[i]*(10*arr[i+1])
arr[i]%=z
for i in range(n):
ans[i]*=arr[i]
ans[i]%=z
print(" ".join(str(x) for x in ans))
``` | instruction | 0 | 52,384 | 5 | 104,768 |
Yes | output | 1 | 52,384 | 5 | 104,769 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
from time import time
power = [1] * 200002
for i in range(1,200002):
power[i] = power[i-1] * 10 % 998244353
n = int(input())
if n == 1:
print(10)
else:
m = [0] * n
m[n-1] = 10
shag = 2
for i in range(n-2,-1,-1):
ans = 2 * 10 * (9 * power[shag - 2])
ans %= 998244353
ans += 10 * 9 * 9 * power[shag - 3] * (shag - 2)
m[i] = int(ans % 998244353)
shag += 1
print(*m)
``` | instruction | 0 | 52,385 | 5 | 104,770 |
Yes | output | 1 | 52,385 | 5 | 104,771 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
mod=998244353
n = int(input())
for i in range(n-1):
num = pow(10,n-i-2,mod)
num *= 180+(n-i-2)*81
num %= mod
print(num)
print(10)
``` | instruction | 0 | 52,386 | 5 | 104,772 |
Yes | output | 1 | 52,386 | 5 | 104,773 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
MOD = 998244353
p10 = [1] * 200001
for i in range(1, 200001):
p10[i] = (p10[i - 1] * 10) % MOD
x = int(input())
for i in range(1,x):
ret = 2 * 10 * 9 * p10[x - i - 1]
ret += (x - i - 1) * 10 * 9 * 9 * p10[x - i - 2]
print(ret % MOD, end = ' ')
print(10)
``` | instruction | 0 | 52,387 | 5 | 104,774 |
Yes | output | 1 | 52,387 | 5 | 104,775 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
n=int(input())
a=[]
a.append(10)
for i in range(n-1):
k=0
for g in range(i+1):
k+=(g+2)*a[-g-1]
a.append(2*(pow(10,i+2)*(i+2)-k))
a[-1]=a[-1]//2
q=''
for i in range(len(a)-1):
q+=str(a[-1-i])
q+=' '
print(q+'10')
``` | instruction | 0 | 52,388 | 5 | 104,776 |
No | output | 1 | 52,388 | 5 | 104,777 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
n=int(input())
m=0
block=[]
for i in range(1,n):
block.append(10*i%998244353)
m+=10*i*(n-i+1)
block.append((n*10**n-m)%998244353)
block=block[::-1]
print(*block,sep=' ')
``` | instruction | 0 | 52,389 | 5 | 104,778 |
No | output | 1 | 52,389 | 5 | 104,779 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
n = int(input())
for i in range(n - 1):
s = ((n - i)* 10 * 9) % 998244353
print(s, sep=' ', end=' ')
print(10)
``` | instruction | 0 | 52,390 | 5 | 104,780 |
No | output | 1 | 52,390 | 5 | 104,781 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You wrote down all integers from 0 to 10^n - 1, padding them with leading zeroes so their lengths are exactly n. For example, if n = 3 then you wrote out 000, 001, ..., 998, 999.
A block in an integer x is a consecutive segment of equal digits that cannot be extended to the left or to the right.
For example, in the integer 00027734000 there are three blocks of length 1, one block of length 2 and two blocks of length 3.
For all integers i from 1 to n count the number of blocks of length i among the written down integers.
Since these integers may be too large, print them modulo 998244353.
Input
The only line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).
Output
In the only line print n integers. The i-th integer is equal to the number of blocks of length i.
Since these integers may be too large, print them modulo 998244353.
Examples
Input
1
Output
10
Input
2
Output
180 10
Submitted Solution:
```
n = int(input())
mod = 998244353
for i in range(1, n - 1):
print(10 * 9 * 9 * (n - i - 1) % mod)
if n >= 2:
print(180, )
print(10)
``` | instruction | 0 | 52,391 | 5 | 104,782 |
No | output | 1 | 52,391 | 5 | 104,783 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
import sys
#input=sys.stdin.readline
from collections import defaultdict as dc
from collections import Counter
from bisect import bisect_right, bisect_left
import math
from operator import itemgetter
from heapq import heapify, heappop, heappush
for _ in range(int(input())):
n=int(input())
l=[]
m=1
l=[n]
i=2
while(i<=int(math.sqrt(n))+1):
p=n
c=0
while(p%i==0):
c+=1
p=p//i
if c>m:
m=c
l=[i]*(c-1)+[p*i]
i+=1
print(m)
print(*l)
``` | instruction | 0 | 52,431 | 5 | 104,862 |
Yes | output | 1 | 52,431 | 5 | 104,863 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
t=int(input())
for _ in range(t):
n=int(input())
d={}
while not n%2:
try:
d[2]+=1
except:
d[2]=1
n=n//2
for i in range(3,int(pow(n,0.5))+1,2):
while not n%i:
try:
d[i]+=1
except:
d[i]=1
n=n//i
if n>1:
try:
d[n]+=1
except:
d[n]=1
l = []
for i in d:
l.append([d[i],i])
l.sort(reverse=True)
ans=[l[0][1]]*l[0][0]
for i in range(1,len(l)):
for b in range(l[i][0]):
ans[-1]*=l[i][1]
print(len(ans))
print(*ans)
``` | instruction | 0 | 52,432 | 5 | 104,864 |
Yes | output | 1 | 52,432 | 5 | 104,865 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
dels = []
ans = []
mxlen = 0
mxans = []
for i in range(2, n//2 + 1):
if i > 10e4:
break
if n % i == 0:
dels.append(i)
for d in dels:
m = n
ans = []
if d != 0:
while True:
if (m//d % d) == 0:
m //= d
ans.append(d)
else:
ans.append(m)
break
if len(ans) > mxlen:
mxans = ans
mxlen = len(ans)
if mxans == []:
mxans.append(n)
print(len(mxans))
print(*mxans)
``` | instruction | 0 | 52,434 | 5 | 104,868 |
Yes | output | 1 | 52,434 | 5 | 104,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
def delitele(number, minimum, sequence):
#print(number, minimum, sequence)
if number == 1:
return sequence[1:]
while True:
if number < minimum:
return None
if number < minimum**2:
minimum = number
if not (number%minimum or minimum%sequence[-1]):
#print(" "*4, number, minimum, sequence)
res = delitele(number//minimum, minimum, sequence+[minimum])
if res:
return res
minimum+=1
res=[]
a = int(input())
#print(a)
for i in range(a):
#print(i)
b = delitele(int(input()), 2, [1])
res+=[[len(b)]]
res+=[b]
for i in res:
print(*i)
#4
#2
#360
#4999999937
#4998207083
``` | instruction | 0 | 52,435 | 5 | 104,870 |
No | output | 1 | 52,435 | 5 | 104,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
from sys import stdin, stdout
import heapq
import cProfile
from collections import Counter, defaultdict, deque
from functools import reduce
import math
import threading
import sys
import time
def get_int(): return int(stdin.readline().strip())
def get_tuple(): return map(int, stdin.readline().split())
def get_list(): return list(map(int, stdin.readline().split()))
def PrimeFactor(n):
count = 0
ans = []
# count the number of
# times 2 divides
while ((n % 2 > 0) == False):
# equivalent to n = n / 2;
n >>= 1
count += 1
# if 2 divides it
if (count > 0):
ans += [2]*count
# check for all the possible
# numbers that can divide it
for i in range(3, int(math.sqrt(n)) + 1):
count = 0
while (n % i == 0):
count += 1
n = int(n / i)
if (count > 0):
ans += [i]*count
i += 2
# if n at the end is a prime number.
if (n > 2):
ans += [n]
return ans
def solve():
n = get_int()
factors = PrimeFactor(n)
factors.sort()
factors = factors[::-1]
stack = [factors[0]]
i = 1
le = len(factors)
while i<le:
if stack[-1]%factors[i]==0:
stack.append(factors[i])
else:
prod = 1
while stack and (prod*stack[-1])%factors[i]!=0:
prod *= stack.pop(-1)
if stack:
prod *= stack.pop(-1)
stack.append(prod)
stack.append(factors[i])
else:
stack.append(prod*factors[i])
i += 1
print(len(stack))
print(*stack[::-1])
testcases = True
if testcases:
t = get_int()
for _ in range(t):
solve()
else:
solve()
``` | instruction | 0 | 52,436 | 5 | 104,872 |
No | output | 1 | 52,436 | 5 | 104,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
import math
from collections import Counter
def fun(n):
arr=[]
while n % 2 == 0:
arr.append(2)
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
arr.append(i)
n = n / i
if n > 2:
arr.append(n)
return(arr)
def mostFrequent(arr):
Hash = Counter()
for i in range(len(arr)):
if Hash[i]==0:
Hash[arr[i]] = 1
else:
Hash[arr[i]] += 1
max_count = 0
res = -1
for i in Hash:
if (max_count < Hash[i]):
res = i
max_count = Hash[i]
return res
for _ in range(int(input())):
n=int(input())
arr=fun(n)
num=mostFrequent(arr)
ans=arr.count(mostFrequent(arr))
print(ans)
for i in range(ans-1):
print(num,end=" ")
print(n//(num**(ans-1)))
``` | instruction | 0 | 52,437 | 5 | 104,874 |
No | output | 1 | 52,437 | 5 | 104,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer n (n > 1).
Your task is to find a sequence of integers a_1, a_2, …, a_k such that:
* each a_i is strictly greater than 1;
* a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n);
* a_{i + 1} is divisible by a_i for each i from 1 to k-1;
* k is the maximum possible (i. e. the length of this sequence is the maximum possible).
If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.
The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).
It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).
Output
For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.
If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.
Example
Input
4
2
360
4999999937
4998207083
Output
1
2
3
2 2 90
1
4999999937
1
4998207083
Submitted Solution:
```
from functools import reduce
import os
import sys
from collections import *
from decimal import *
from math import *
from bisect import *
from heapq import *
from io import BytesIO, IOBase
input = lambda: sys.stdin.readline().rstrip("\r\n")
def value(): return tuple(map(int, input().split())) # multiple values
def arr(): return [int(i) for i in input().split()] # array input
def sarr(): return [int(i) for i in input()] #array from string
def starr(): return [str(x) for x in input().split()] #string array
def inn(): return int(input()) # integer input
def svalue(): return tuple(map(str, input().split())) #multiple string values
def parr(): return [(value()) for i in range(n)] # array of pairs
mo = 1000000007
inf=1e18
div=998244353
#print("Case #{}:".format(_+1),end=" ")
#print("Case #",z+1,":",sep="",end=" ")
# ----------------------------CODE------------------------------#
def factors(n): #return list
return list(set(reduce(list.__add__,
([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
for _ in range(inn()):
n=inn()
if(n%2==0):
c=0
while(n%2==0):
c+=1
n//=2
c-=1
ans=[2]*c+[n*2]
print(len(ans))
print(*ans)
else:
res=factors(n)
#print(res)
ans=n
mx=-inf
for i in res:
c=0
val=n
if(i==1):
continue
while(val%i==0 and val!=1):
c+=1
val//=i
if(val==1 and c>mx):
ans=i
mx=c
res=[ans]*mx
print(mx)
print(*res)
``` | instruction | 0 | 52,438 | 5 | 104,876 |
No | output | 1 | 52,438 | 5 | 104,877 |
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 of positive integers x1, x2, ..., xn and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:
* subtract 1 from the current a;
* subtract a mod xi (1 ≤ i ≤ n) from the current a.
Operation a mod xi means taking the remainder after division of number a by number xi.
Now you want to know the minimum number of moves needed to transform a into b.
Input
The first line contains a single integer n (1 ≤ n ≤ 105). The second line contains n space-separated integers x1, x2, ..., xn (2 ≤ xi ≤ 109). The third line contains two integers a and b (0 ≤ b ≤ a ≤ 109, a - b ≤ 106).
Output
Print a single integer — the required minimum number of moves needed to transform number a into number b.
Examples
Input
3
3 4 5
30 17
Output
6
Input
3
5 6 7
1000 200
Output
206
Submitted Solution:
```
n = int(input())
sez = [int(i) for i in input().split() ]
sez2 = [int(i) for i in input().split() ]
kon = 0
sez.sort()
sez = sez[::-1]
while sez2[1]!=sez2[0]:
pom =[]
for i in range(len(sez)):
mod = sez2[0]%sez[i]
pom = pom + [mod]
if i == len(sez)-1:
break
if mod >= sez[i+1] - 1:
break
if sez2[0]- max(pom) <= sez2[1]:
sez2[0] -=1
kon +=1
continue
if max(pom)==0 or max(pom)==1:
sez2[0] -= 1
kon +=1
else:
sez2[0] -= max(pom)
kon +=1
print(kon)
``` | instruction | 0 | 52,544 | 5 | 105,088 |
No | output | 1 | 52,544 | 5 | 105,089 |
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 of positive integers x1, x2, ..., xn and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:
* subtract 1 from the current a;
* subtract a mod xi (1 ≤ i ≤ n) from the current a.
Operation a mod xi means taking the remainder after division of number a by number xi.
Now you want to know the minimum number of moves needed to transform a into b.
Input
The first line contains a single integer n (1 ≤ n ≤ 105). The second line contains n space-separated integers x1, x2, ..., xn (2 ≤ xi ≤ 109). The third line contains two integers a and b (0 ≤ b ≤ a ≤ 109, a - b ≤ 106).
Output
Print a single integer — the required minimum number of moves needed to transform number a into number b.
Examples
Input
3
3 4 5
30 17
Output
6
Input
3
5 6 7
1000 200
Output
206
Submitted Solution:
```
input()
#x = list(reversed(sorted(set(map(int, input().split())))))
x = list(map(int, input().split()))
a, b = map(int, input().split())
if x[0] == 753088:
print(a, b)
else:
x = list(reversed(sorted(set(x))))
#x = list(range(753088, 853088))
#a = 1234567
#b = 234567
moves = 0
while a > b:
nextA = a - 1
for xi in x:
to = a - a % xi
if nextA > to >= b:
nextA = to
if a - xi + 1 >= nextA:
break
while x and a - a % x[-1] < b:
x.pop()
a = nextA
moves += 1
print(moves)
``` | instruction | 0 | 52,545 | 5 | 105,090 |
No | output | 1 | 52,545 | 5 | 105,091 |
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 of positive integers x1, x2, ..., xn and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:
* subtract 1 from the current a;
* subtract a mod xi (1 ≤ i ≤ n) from the current a.
Operation a mod xi means taking the remainder after division of number a by number xi.
Now you want to know the minimum number of moves needed to transform a into b.
Input
The first line contains a single integer n (1 ≤ n ≤ 105). The second line contains n space-separated integers x1, x2, ..., xn (2 ≤ xi ≤ 109). The third line contains two integers a and b (0 ≤ b ≤ a ≤ 109, a - b ≤ 106).
Output
Print a single integer — the required minimum number of moves needed to transform number a into number b.
Examples
Input
3
3 4 5
30 17
Output
6
Input
3
5 6 7
1000 200
Output
206
Submitted Solution:
```
n = int(input())
sez = [int(i) for i in input().split() ]
sez2 = [int(i) for i in input().split() ]
kon = 0
sez.sort()
sez = sez[::-1]
while sez2[1]!=sez2[0]:
pom =[]
for i in range(len(sez)):
mod = sez2[0]%sez[i]
pom = pom + [mod]
if i == len(sez)-1:
break
if mod >= sez[i+1] - 1:
break
if sez2[0]- max(pom) <= sez2[1]:
sez2[0] -=1
kon +=1
break
if max(pom)==0 or max(pom)==1:
sez2[0] -= 1
kon +=1
else:
sez2[0] -= max(pom)
kon +=1
print(kon)
``` | instruction | 0 | 52,546 | 5 | 105,092 |
No | output | 1 | 52,546 | 5 | 105,093 |
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 of positive integers x1, x2, ..., xn and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:
* subtract 1 from the current a;
* subtract a mod xi (1 ≤ i ≤ n) from the current a.
Operation a mod xi means taking the remainder after division of number a by number xi.
Now you want to know the minimum number of moves needed to transform a into b.
Input
The first line contains a single integer n (1 ≤ n ≤ 105). The second line contains n space-separated integers x1, x2, ..., xn (2 ≤ xi ≤ 109). The third line contains two integers a and b (0 ≤ b ≤ a ≤ 109, a - b ≤ 106).
Output
Print a single integer — the required minimum number of moves needed to transform number a into number b.
Examples
Input
3
3 4 5
30 17
Output
6
Input
3
5 6 7
1000 200
Output
206
Submitted Solution:
```
input()
x = list(sorted(set(map(int, input().split()))))
a, b = map(int, input().split())
moves = 0
while a > b:
nextA = a - 1
for xi in reversed(x):
to = a - a % xi
if nextA > to >= b:
nextA = to
if a - xi + 1 >= nextA:
break
while x and a - a % x[-1] < b:
x.pop()
a = nextA
moves += 1
print(moves)
``` | instruction | 0 | 52,547 | 5 | 105,094 |
No | output | 1 | 52,547 | 5 | 105,095 |
Provide a correct Python 3 solution for this coding contest problem.
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 | instruction | 0 | 52,861 | 5 | 105,722 |
"Correct Solution:
```
S=int(input())
mod=1000000000
x3=(S-1)//mod+1
y3=mod - ((S-1)%mod+1)
print(0,0,1,mod,x3,y3)
``` | output | 1 | 52,861 | 5 | 105,723 |
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:
```
#!/usr/bin/env python3
s = int(input())
y = (10**9 - s % 10**9) % 10**9
x = (s + y) // 10**9
print(0, 0, 1, 10**9, x, y)
``` | instruction | 0 | 52,868 | 5 | 105,736 |
Yes | output | 1 | 52,868 | 5 | 105,737 |
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())
n = 10 ** 9
x = 0--s//n
y = - s % n
print("0 0 {} {} {} {}".format(y, x, n, 1))
``` | instruction | 0 | 52,869 | 5 | 105,738 |
Yes | output | 1 | 52,869 | 5 | 105,739 |
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:
```
import math
s = int(input())
e = math.ceil(s**0.5)
print(0, 0, e, 1, e**2-s, e)
``` | instruction | 0 | 52,870 | 5 | 105,740 |
Yes | output | 1 | 52,870 | 5 | 105,741 |
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())
x1=0
y1=0
x2=10**9
y2=1
y3=-(-s//10**9)
x3=10**9*y3-s
print(x1,y1,x2,y2,x3,y3)
``` | instruction | 0 | 52,871 | 5 | 105,742 |
Yes | output | 1 | 52,871 | 5 | 105,743 |
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:
```
# 2019/07/21
s=int(input())
xy=[s,0,s,1,0,1]
print(xy)
``` | instruction | 0 | 52,872 | 5 | 105,744 |
No | output | 1 | 52,872 | 5 | 105,745 |
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())
# X1, Y1, Y2を0, 0, 0とする
ans = [0, 0, S, 0, 0, 1]
print(*ans)
``` | instruction | 0 | 52,873 | 5 | 105,746 |
No | output | 1 | 52,873 | 5 | 105,747 |
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