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.
The solution of $ x ^ 3 = q $ is to calculate the recurrence formula $ x_ {n + 1} = x_n-\ frac {x_ {n} ^ 3 --q} {3x_ {n} ^ 2} $ It can be calculated approximately with.
Put a positive number $ \ frac {q} {2} $ in $ x_1 $
$ x_2 = x_1-\ frac {x_ {1} ^ 3 --q} {3x_ {1} ^ 2} $, $ x_3 = x_2-\ frac {x_ {2} ^ 3 --q} {3x_ {2} ^ Calculate as 2} $,….
While doing this calculation
When the value of $ | x ^ 3 --q | $ becomes small enough, stop the calculation and use the last calculated $ x_n $ as an approximate solution of $ x ^ 3 = q $.
Follow this method to create a program that outputs an approximation of the cube root of $ q $ for the input positive integer $ q $. However, use $ | x ^ 3-q | <0.00001 q $ to determine that it is "small enough".
input
Multiple datasets are given. For each dataset, $ q $ ($ 1 \ leq q <2 ^ {31} $) (integer) is given on one line. The end of the input is -1.
The number of datasets does not exceed 50.
output
Print $ x $ (real number) on one line for each dataset. The output result may contain an error of 0.00001 or less.
Example
Input
15
15
-1
Output
2.466212
2.466212
Submitted Solution:
```
def third_root(q):
x=q/2.0
while abs(x**3-q)>=q*10**(-5):
x=x-(x**3-q)/(3*x**2)
return x
while 1:
q=input()
if q==-1:break
ans=third_root(q)
print(ans)
``` | instruction | 0 | 13,218 | 5 | 26,436 |
No | output | 1 | 13,218 | 5 | 26,437 |
Provide a correct Python 3 solution for this coding contest problem.
Example
Input
5
1 2
1 3
1 4
1 5
Output
6 | instruction | 0 | 13,258 | 5 | 26,516 |
"Correct Solution:
```
from collections import deque, defaultdict
import sys
def main():
readline = sys.stdin.readline
write = sys.stdout.write
N = int(readline())
G = [[] for i in range(N)]
for i in range(N-1):
a, b = map(int, readline().split()); a -= 1; b -= 1
G[a].append(b)
G[b].append(a)
H = [-1]*N
MOD = 10**9 + 9
X1 = [0]*N; v1 = 13
X2 = [0]*N; v2 = 17
U = [0]*N
que = deque([0])
U[0] = 1
D = [0]
while que:
v = que.popleft()
for w in G[v]:
if U[w]:
continue
U[w] = 1
que.append(w)
D.append(w)
M = defaultdict(int)
for v in reversed(D):
h = 0
su1 = su2 = 0
for w in G[v]:
if H[w] == -1:
continue
h = max(h, H[w])
su1 += X1[w]; su2 += X2[w]
H[v] = k = h+1
X1[v] = w1 = (su1*v1 + 1) % MOD
X2[v] = w2 = (su2*v2 + 1) % MOD
M[k, w1, w2] += 1
ans = 0
for v in M.values():
ans += v*(v-1)//2
write("%d\n" % ans)
main()
``` | output | 1 | 13,258 | 5 | 26,517 |
Provide a correct Python 3 solution for this coding contest problem.
G: Working
Kou decided to do the same number of jobs every day for the next $ N $.
$ A_i $ jobs are added on the $ i $ day of the $ N $ day.
Mr. Kou has no work to do now, and he doesn't have to finish all the work by the $ N $ day.
How many jobs can you do in a day?
However, Mr. Kou is excellent, so he can do as many jobs as he has.
input
$ N $ is given on the first line.
On the second line, $ N $ integers $ A_1, A_2, A_3, \ dots, A_N $ are given, separated by blanks.
output
Output the maximum number of jobs you can do in a day. Insert a line break at the end.
Constraint
* $ N $ is an integer greater than or equal to $ 1 $ and less than or equal to $ 100 $
* $ A_1, A_2, A_3, \ dots, A_N $ are integers between $ 1 $ and $ 100 $
Input example 1
Five
4 2 5 3 1
Output example 1
3
If you decide to work more than $ 4 $ a day, you'll run out of work on the second day.
Input example 2
Five
9 9 1 9 9
Output example 2
6
Example
Input
5
4 2 5 3 1
Output
3 | instruction | 0 | 13,264 | 5 | 26,528 |
"Correct Solution:
```
n=int(input())
a=[int(x) for x in input().split()]
x=100
for i in range(n):
x=min(x,sum(a[:i+1])//(i+1))
print(x)
``` | output | 1 | 13,264 | 5 | 26,529 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
It seems that a magician with a smoky smell will show off his magic.
"Now, think of one favorite integer."
You decide to think of your counting years in your head.
The magician has thrown the query $ N $ times.
Each query is one of the following:
1. "Multiply the number you have in mind by $ x $."
2. "Add $ x $ to the number you have in mind."
3. "Subtract $ x $ from the number you have in mind."
For each query, process the query against the number you have in mind and think of the resulting value in your head.
"Now, let's guess the number you think of first."
Such magicians are trying to say something.
However, he seems to have forgotten what to say.
A smoky magician is staring at you with sweat.
It can't be helped, so let me tell you what to say.
It seems that the magician intended to say the following at the end.
"If you add $ A $ to the integer you have in mind and divide by $ B $, that is the first integer you have in mind."
Due to constraints, only one set of integers, $ (A, B) $, satisfies the above conditions no matter how many integers you think of.
Find the set of integers $ (A, B) $.
However, $ B $ cannot be $ 0 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 15 $
* $ 1 \ leq q \ leq 3 $
* $ 1 \ leq x \ leq 10 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ q_1 $ $ x_1 $
$ \ vdots $
$ q_n $ $ x_n $
The number of queries given on the $ 1 $ line $ N $ is given.
Query information is given in the $ N $ line that continues from the $ 2 $ line.
$ q $ represents the type of query and corresponds to the number in the list in the question text.
Output
Output the integers $ A and B $ that satisfy the condition on the $ 1 $ line, separated by blanks.
Examples
Input
3
1 2
2 10
3 8
Output
-2 2
Input
10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
Output
0 10000000000 | instruction | 0 | 13,271 | 5 | 26,542 |
"Correct Solution:
```
n = int(input())
a, b = 1, 0
for i in range(n) :
q, x = map(int, input().split())
if q == 1 :
a *= x
b *= x
elif q == 2 :
b += x
elif q == 3 :
b -= x
print(-b, a)
``` | output | 1 | 13,271 | 5 | 26,543 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
It seems that a magician with a smoky smell will show off his magic.
"Now, think of one favorite integer."
You decide to think of your counting years in your head.
The magician has thrown the query $ N $ times.
Each query is one of the following:
1. "Multiply the number you have in mind by $ x $."
2. "Add $ x $ to the number you have in mind."
3. "Subtract $ x $ from the number you have in mind."
For each query, process the query against the number you have in mind and think of the resulting value in your head.
"Now, let's guess the number you think of first."
Such magicians are trying to say something.
However, he seems to have forgotten what to say.
A smoky magician is staring at you with sweat.
It can't be helped, so let me tell you what to say.
It seems that the magician intended to say the following at the end.
"If you add $ A $ to the integer you have in mind and divide by $ B $, that is the first integer you have in mind."
Due to constraints, only one set of integers, $ (A, B) $, satisfies the above conditions no matter how many integers you think of.
Find the set of integers $ (A, B) $.
However, $ B $ cannot be $ 0 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 15 $
* $ 1 \ leq q \ leq 3 $
* $ 1 \ leq x \ leq 10 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ q_1 $ $ x_1 $
$ \ vdots $
$ q_n $ $ x_n $
The number of queries given on the $ 1 $ line $ N $ is given.
Query information is given in the $ N $ line that continues from the $ 2 $ line.
$ q $ represents the type of query and corresponds to the number in the list in the question text.
Output
Output the integers $ A and B $ that satisfy the condition on the $ 1 $ line, separated by blanks.
Examples
Input
3
1 2
2 10
3 8
Output
-2 2
Input
10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
Output
0 10000000000 | instruction | 0 | 13,272 | 5 | 26,544 |
"Correct Solution:
```
n = int(input())
queries = [list(map(int, input().split())) for i in range(n)]
s, t = 1, 0
for q in queries:
if q[0] == 1:
s *= q[1]
t *= q[1]
elif q[0] == 2:
t += q[1]
else:
t -= q[1]
print(-t, s)
``` | output | 1 | 13,272 | 5 | 26,545 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
It seems that a magician with a smoky smell will show off his magic.
"Now, think of one favorite integer."
You decide to think of your counting years in your head.
The magician has thrown the query $ N $ times.
Each query is one of the following:
1. "Multiply the number you have in mind by $ x $."
2. "Add $ x $ to the number you have in mind."
3. "Subtract $ x $ from the number you have in mind."
For each query, process the query against the number you have in mind and think of the resulting value in your head.
"Now, let's guess the number you think of first."
Such magicians are trying to say something.
However, he seems to have forgotten what to say.
A smoky magician is staring at you with sweat.
It can't be helped, so let me tell you what to say.
It seems that the magician intended to say the following at the end.
"If you add $ A $ to the integer you have in mind and divide by $ B $, that is the first integer you have in mind."
Due to constraints, only one set of integers, $ (A, B) $, satisfies the above conditions no matter how many integers you think of.
Find the set of integers $ (A, B) $.
However, $ B $ cannot be $ 0 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 15 $
* $ 1 \ leq q \ leq 3 $
* $ 1 \ leq x \ leq 10 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ q_1 $ $ x_1 $
$ \ vdots $
$ q_n $ $ x_n $
The number of queries given on the $ 1 $ line $ N $ is given.
Query information is given in the $ N $ line that continues from the $ 2 $ line.
$ q $ represents the type of query and corresponds to the number in the list in the question text.
Output
Output the integers $ A and B $ that satisfy the condition on the $ 1 $ line, separated by blanks.
Examples
Input
3
1 2
2 10
3 8
Output
-2 2
Input
10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
Output
0 10000000000 | instruction | 0 | 13,273 | 5 | 26,546 |
"Correct Solution:
```
#!usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
res = list(sys.stdin.readline())
if res[-1] == "\n":
return res[:-1]
return res
def IR(n):
return [I() for i in range(n)]
def LIR(n):
return [LI() for i in range(n)]
def SR(n):
return [S() for i in range(n)]
def LSR(n):
return [LS() for i in range(n)]
sys.setrecursionlimit(1000000)
mod = 1000000007
def solve():
n = I()
a,b = 0,1
for i in range(n):
q,x = LI()
if q == 1:
a *= x
b *= x
elif q == 2:
a += x
b += x
else:
a -= x
b -= x
B = b-a
print(B-b,B)
return
if __name__ == "__main__":
solve()
``` | output | 1 | 13,273 | 5 | 26,547 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
It seems that a magician with a smoky smell will show off his magic.
"Now, think of one favorite integer."
You decide to think of your counting years in your head.
The magician has thrown the query $ N $ times.
Each query is one of the following:
1. "Multiply the number you have in mind by $ x $."
2. "Add $ x $ to the number you have in mind."
3. "Subtract $ x $ from the number you have in mind."
For each query, process the query against the number you have in mind and think of the resulting value in your head.
"Now, let's guess the number you think of first."
Such magicians are trying to say something.
However, he seems to have forgotten what to say.
A smoky magician is staring at you with sweat.
It can't be helped, so let me tell you what to say.
It seems that the magician intended to say the following at the end.
"If you add $ A $ to the integer you have in mind and divide by $ B $, that is the first integer you have in mind."
Due to constraints, only one set of integers, $ (A, B) $, satisfies the above conditions no matter how many integers you think of.
Find the set of integers $ (A, B) $.
However, $ B $ cannot be $ 0 $.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 15 $
* $ 1 \ leq q \ leq 3 $
* $ 1 \ leq x \ leq 10 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ q_1 $ $ x_1 $
$ \ vdots $
$ q_n $ $ x_n $
The number of queries given on the $ 1 $ line $ N $ is given.
Query information is given in the $ N $ line that continues from the $ 2 $ line.
$ q $ represents the type of query and corresponds to the number in the list in the question text.
Output
Output the integers $ A and B $ that satisfy the condition on the $ 1 $ line, separated by blanks.
Examples
Input
3
1 2
2 10
3 8
Output
-2 2
Input
10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
Output
0 10000000000 | instruction | 0 | 13,274 | 5 | 26,548 |
"Correct Solution:
```
N = int(input())
a, b = 1, 0
for _ in range(N):
q, x = map(int, input().split())
if q == 1:
a *= x; b *= x
elif q == 2:
b += x
else:
b -= x
print(-b, a)
``` | output | 1 | 13,274 | 5 | 26,549 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,291 | 5 | 26,582 |
"Correct Solution:
```
import heapq
from collections import deque
from enum import Enum
import sys
import math
from _heapq import heappush, heappop
import copy
BIG_NUM = 2000000000
MOD = 1000000007
EPS = 0.000000001
N = int(input())
table = list(map(int,input().split()))
num_query = int(input())
for _ in range(num_query):
tmp = int(input())
L = 0
R = len(table)-1
mid = (L+R)//2
loc = BIG_NUM
while L <= R:
if table[mid] == tmp:
loc = mid
break
elif table[mid] > tmp:
R = mid-1
else:
L = mid+1
mid = (L+R)//2
if loc == BIG_NUM:
print("0")
else:
print("1")
``` | output | 1 | 13,291 | 5 | 26,583 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,292 | 5 | 26,584 |
"Correct Solution:
```
import bisect
n = int(input())
a = list(map(int, input().split( )))
a.sort()
q = int(input())
for _ in range(q):
k = int(input())
i = bisect.bisect_left(a,k)
if (i == n) or (i == 0 and a[0] > k):
print(0)
elif a[i] > k and k > a[i-1]:
print(0)
else:
print(1)
``` | output | 1 | 13,292 | 5 | 26,585 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,293 | 5 | 26,586 |
"Correct Solution:
```
n = int(input())
A = list(map(int, input().split()))
q = int(input())
for i in range(q):
a = int(input())
left = 0
right = n
flag = 0
mid = (right - left) // 2
while left < right:
if A[mid] == a:
flag = 1
break
if a > A[mid]:
left = mid+1
else:
right = mid
mid = (left + right) //2
print(flag)
``` | output | 1 | 13,293 | 5 | 26,587 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,294 | 5 | 26,588 |
"Correct Solution:
```
import sys
n = int(input())
# a = tuple(input().split())
a = tuple(map(int,sys.stdin.readline().split()))
q = int(input())
# for _ in range(q):
# if input() in a:print('1')
# else:print('0')
for k in sys.stdin:
k = int(k.strip())
if k < a[0] or a[-1] < k:
print('0')
else:
j1 = 0
j2 = len(a)
for _ in range(len(a)):
j = (j1 + j2) // 2
if k == a[j]:
print('1')
break
else:
if a[j] < k:j1 = j
else:j2 = j
if j1 + 1 == j2:
if k == a[j1] or k == a[j2]:
print('1')
break
else:
print('0')
break
if _ == len(a)-1:print('0')
``` | output | 1 | 13,294 | 5 | 26,589 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,295 | 5 | 26,590 |
"Correct Solution:
```
#!/usr/bin/env python3
# ITP2_6_A: Binary Search
from bisect import bisect
def search(li, x):
"""Returns True if x exists in li else False.
Assumes li is sorted in ascending order.
>>> search([1, 2, 3], 2)
True
>>> search([1, 2, 3], 4)
False
>>> search([1, 2, 3], 3)
True
>>> search([1, 2, 3], 0)
False
>>> search([1, 2, 3], 1)
True
"""
i = bisect(li, x)
return 0 < i <= len(li) and li[i-1] == x
def run():
n = int(input())
a = [int(x) for x in input().split()]
assert(n == len(a))
q = int(input())
for _ in range(q):
k = int(input())
if search(a, k):
print(1)
else:
print(0)
if __name__ == '__main__':
run()
``` | output | 1 | 13,295 | 5 | 26,591 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,296 | 5 | 26,592 |
"Correct Solution:
```
n = int(input())
a = set(map(int, input().split()))
q = int(input())
while q:
q -= 1
k = int(input())
print(+(k in a))
``` | output | 1 | 13,296 | 5 | 26,593 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,297 | 5 | 26,594 |
"Correct Solution:
```
import bisect
n = int(input())
a = sorted(list(map(int,input().split())))
a.append(1e20)
for i in range(int(input())):
k = int(input())
place = bisect.bisect_left(a,k)
print(1 if a[place] == k else 0)
``` | output | 1 | 13,297 | 5 | 26,595 |
Provide a correct Python 3 solution for this coding contest problem.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0 | instruction | 0 | 13,298 | 5 | 26,596 |
"Correct Solution:
```
input()
a = set(map(int, input().split()))
[print(1 if int(input()) in a else 0) for _ in range(int(input()))]
``` | output | 1 | 13,298 | 5 | 26,597 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
from bisect import bisect
readline = open(0).readline
N = int(readline())
*A, = map(int, readline().split())
Q = int(readline())
ans = []
for q in range(Q):
k = int(readline())
ans.append("%d\n" % (A[bisect(A, k)-1] == k))
open(1, 'w').writelines(ans)
``` | instruction | 0 | 13,299 | 5 | 26,598 |
Yes | output | 1 | 13,299 | 5 | 26,599 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
# http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP2_6_A&lang=jp
# Binary Search : python3
# 2018.11.26 yonezawa
import sys
input = sys.stdin.readline
def main():
n = int(input())
l = list(map(int,input().split()))
for i in range(int(input())):
max = n -1
min = 0
mid = max // 2
d = int(input())
while True:
if (l[mid] > d ):
max = mid
elif (l[mid] == d ):
print ("1")
break
else:
min = mid
mid = (max + min ) // 2
if ( mid == max or mid == min ):
if ( l[mid] == d or l[max] == d):
print ("1")
break
#print ("debug:",min,mid,max,l[mid])
print ("0")
break
if __name__ == '__main__':
main()
``` | instruction | 0 | 13,300 | 5 | 26,600 |
Yes | output | 1 | 13,300 | 5 | 26,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
import math
n=int(input())
a=list(map(int,input().split()))
q=int(input())
for i in range(q):
k=int(input())
t=0
max=n-1
min=0
while max-min>1:
nn=math.floor((max+min)/2)
if a[nn]==k:
t=1
print("1")
break
elif a[nn]<=k:
min=nn
elif a[nn]>=k:
max=nn
if t==0:
if a[max]==k or a[min]==k:
t=1
print("1")
else:
print("0")
``` | instruction | 0 | 13,301 | 5 | 26,602 |
Yes | output | 1 | 13,301 | 5 | 26,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
def solve():
from sys import stdin
f_i = stdin
n = int(f_i.readline())
A = list(map(int, f_i.readline().split()))
A.append(1000000001)
q = int(f_i.readline())
from bisect import bisect_left
ans = []
for i in range(q):
k = int(f_i.readline())
if k == A[bisect_left(A, k)]:
ans.append('1')
else:
ans.append('0')
print('\n'.join(ans))
solve()
``` | instruction | 0 | 13,302 | 5 | 26,604 |
Yes | output | 1 | 13,302 | 5 | 26,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split(' ')))
def binary_search(val):
left, right = 0, n-1
while right - left > 1:
mid = (right+left)//2
if a[mid] == val: return 1
if a[mid] < val:
left = mid
elif val < a[mid]:
right = mid
return 0
q = int(input())
for i in range(q):
k = int(input())
print(binary_search(k))
``` | instruction | 0 | 13,303 | 5 | 26,606 |
No | output | 1 | 13,303 | 5 | 26,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
n = int(input())
a = list(map(int, input().split(' ')))
def binary_search(val):
left, right = 0, n-1
while right - left >= 1:
mid = (right+left)//2
if a[mid] == val: return 1
if a[mid] < val:
left = mid
elif val < a[mid]:
right = mid
return 0
q = int(input())
for i in range(q):
k = int(input())
print(binary_search(k))
``` | instruction | 0 | 13,304 | 5 | 26,608 |
No | output | 1 | 13,304 | 5 | 26,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
input()
b = list(map(int,input().split()))
def nibu(low,high,i):
middle = (low+high)//2
if b[middle] <= i:
low = middle
else:
high = middle
if low == high:
if i == b[low]:
return 1
else:
return 0
a = int(input())
for i in range(a):
k = int(input())
print(nibu(0,len(b)-1,k))
``` | instruction | 0 | 13,305 | 5 | 26,610 |
No | output | 1 | 13,305 | 5 | 26,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence $A = \\{a_0, a_1, ..., a_{n-1}\\}$ which is sorted by ascending order, find a specific value $k$ given as a query.
Constraints
* $1 \leq n \leq 100,000$
* $1 \leq q \leq 200,000$
* $0 \leq a_0 \leq a_1 \leq ... \leq a_{n-1} \leq 1,000,000,000$
* $0 \leq k_i \leq 1,000,000,000$
Input
The input is given in the following format.
$n$
$a_0 \; a_1 \; ,..., \; a_{n-1}$
$q$
$k_1$
$k_2$
:
$k_q$
The number of elements $n$ and each element $a_i$ are given in the first line and the second line respectively. In the third line, the number of queries $q$ is given and the following $q$ lines, $q$ integers $k_i$ are given as queries.
Output
For each query, print 1 if any element in $A$ is equivalent to $k$, and 0 otherwise.
Example
Input
4
1 2 2 4
3
2
3
5
Output
1
0
0
Submitted Solution:
```
a = int(input())
b = list(map(int,input().split()))
def nibu(low,high,i):
middle = (low+high)//2
if b[middle] <= i:
low = middle
else:
high = middle
if low == high:
if i == b[low]:
return 1
else:
return 0
for i in range(a):
k = int(input())
print(nibu(0,len(b),k))
``` | instruction | 0 | 13,306 | 5 | 26,612 |
No | output | 1 | 13,306 | 5 | 26,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
Submitted Solution:
```
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
dct={}
import math
def simple_fraction(a,b):
x=math.gcd(a,b)
a//=x
b//=x
if a==0:
return (0,1)
if (a<0 and b>0) or (a>0 and b<0):
return (-abs(a),abs(b))
return (abs(a),abs(b))
allcase=0
ans=0
for i in range(n):
if a[i]==0:
if b[i]==0:
allcase+=1
continue
d=simple_fraction(-b[i],a[i])
if d in dct:
dct[d]+=1
ans=max(ans,dct[d])
else:
dct[d]=1
ans=max(ans,1)
print(allcase+ans)
``` | instruction | 0 | 13,367 | 5 | 26,734 |
Yes | output | 1 | 13,367 | 5 | 26,735 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
Submitted Solution:
```
from sys import stdin,stdout
from itertools import combinations
from collections import defaultdict
from decimal import *
getcontext().prec = 50
def listIn():
return list((map(int,stdin.readline().strip().split())))
def stringListIn():
return([x for x in stdin.readline().split()])
def intIn():
return (int(stdin.readline()))
def stringIn():
return (stdin.readline().strip())
def solve(a,b,n):
d=[0]*n
li={}
cnt=0
for i in range(n):
if a[i]!=0:
d[i]=-(Decimal(b[i])/Decimal(a[i]))
else:
if b[i]==0:
cnt+=1
continue
ele=d[i]
if ele not in li:
li[ele]=1
else:
li[ele]+=1
#print(li)
if len(li)>0:
return (max(li.values())+cnt)
else:
return cnt
if __name__=="__main__":
n=intIn()
a=listIn()
b=listIn()
ans=solve(a,b,n)
print(ans)
``` | instruction | 0 | 13,369 | 5 | 26,738 |
Yes | output | 1 | 13,369 | 5 | 26,739 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
Submitted Solution:
```
#!/usr/bin/env python
# coding: utf-8
# In[17]:
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
from collections import defaultdict
def lcd(a, b):
while b:
a, b = b, a % b
return a
c = [0] * n
nums = defaultdict(int)
res_max = 0
res_zero = 0
for i in range(n):
if a[i] == 0:
if not b[i]:
res_zero += 1
continue
r = -b[i] * 1e10 / a[i]
nums[r] += 1
res_max = max(res_max, nums[r])
print(res_max + res_zero)
``` | instruction | 0 | 13,370 | 5 | 26,740 |
Yes | output | 1 | 13,370 | 5 | 26,741 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
Submitted Solution:
```
n = int(input())
b = list(map(int, input(). split()))
c = list(map(int, input(). split()))
k = {}
mx = 0
q = 0
br = 0
for i in range(n):
if b[i] == 0 and c[i] == 0:
q += 1
continue
if b[i] == 0:
br = 1
break
s = -c[i] / b[i]
if s in k:
k[s] += 1
if k[s] > mx:
mx = k[s]
else:
k[s] = 1
if k[s] > mx:
mx = k[s]
if br == 1:
print(0)
else:
print(mx + q)
``` | instruction | 0 | 13,371 | 5 | 26,742 |
No | output | 1 | 13,371 | 5 | 26,743 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
D={'':0}
count = 0
for a,b in zip(A,B):
if a !=0:
x=b/a
if x in D:
D[x] += 1
else:
D[x] = 1
else:
count += 1
print(max(list(D.values()))+count)
``` | instruction | 0 | 13,373 | 5 | 26,746 |
No | output | 1 | 13,373 | 5 | 26,747 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Sereja has got an array, consisting of n integers, a1, a2, ..., an. Sereja is an active boy, so he is now going to complete m operations. Each operation will have one of the three forms:
1. Make vi-th array element equal to xi. In other words, perform the assignment avi = xi.
2. Increase each array element by yi. In other words, perform n assignments ai = ai + yi (1 ≤ i ≤ n).
3. Take a piece of paper and write out the qi-th array element. That is, the element aqi.
Help Sereja, complete all his operations.
Input
The first line contains integers n, m (1 ≤ n, m ≤ 105). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the original array.
Next m lines describe operations, the i-th line describes the i-th operation. The first number in the i-th line is integer ti (1 ≤ ti ≤ 3) that represents the operation type. If ti = 1, then it is followed by two integers vi and xi, (1 ≤ vi ≤ n, 1 ≤ xi ≤ 109). If ti = 2, then it is followed by integer yi (1 ≤ yi ≤ 104). And if ti = 3, then it is followed by integer qi (1 ≤ qi ≤ n).
Output
For each third type operation print value aqi. Print the values in the order, in which the corresponding queries follow in the input.
Examples
Input
10 11
1 2 3 4 5 6 7 8 9 10
3 2
3 9
2 10
3 1
3 10
1 1 10
2 10
2 10
3 1
3 10
3 9
Output
2
9
11
20
30
40
39
Submitted Solution:
```
n,m = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
soma = 0
for mm in range(m):
entrada = [int(x) for x in input().split()]
op = entrada[0]
b = int(entrada[1])
if op == "1":
a[b-1] = int(entrada[2]) - soma
elif op == "2":
soma += b
else:
print(a[b-1] + soma)
``` | instruction | 0 | 13,611 | 5 | 27,222 |
No | output | 1 | 13,611 | 5 | 27,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
import sys
INF = 10**20
MOD = 10**9 + 7
I = lambda:list(map(int,input().split()))
from math import gcd
from math import ceil
from collections import defaultdict as dd, Counter
from bisect import bisect_left as bl, bisect_right as br
"""
Facts and Data representation
Constructive? Top bottom up down
"""
n, k = I()
ans = [[1, 2, 3, 5]]
cur = 4
add = 7
for i in range(1, n):
ok = [add, add + 2, add + 4]
while True:
r = True
for i in ok:
if gcd(i, cur) > 1:
r = False
if r:
break
cur += 2
ok.append(cur)
add += 6
cur += 2
ans.append(ok)
print((add - 2) * k)
for i in ans:
print(*[j * k for j in i])
``` | instruction | 0 | 13,679 | 5 | 27,358 |
Yes | output | 1 | 13,679 | 5 | 27,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
n, k = [int(x) for x in input().split()]
print(k*((n-1)*6+5))
for i in range(n):
print(k*(6*i+1),k*(6*i+3),k*(6*i+5),k*(6*i+2))
``` | instruction | 0 | 13,680 | 5 | 27,360 |
Yes | output | 1 | 13,680 | 5 | 27,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dreamoon likes to play with sets, integers and <image>. <image> is defined as the largest positive integer that divides both a and b.
Let S be a set of exactly four distinct integers greater than 0. Define S to be of rank k if and only if for all pairs of distinct elements si, sj from S, <image>.
Given k and n, Dreamoon wants to make up n sets of rank k using integers from 1 to m such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum m that makes it possible and print one possible solution.
Input
The single line of the input contains two space separated integers n, k (1 ≤ n ≤ 10 000, 1 ≤ k ≤ 100).
Output
On the first line print a single integer — the minimal possible m.
On each of the next n lines print four space separated integers representing the i-th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal m, print any one of them.
Examples
Input
1 1
Output
5
1 2 3 5
Input
2 2
Output
22
2 4 6 22
14 18 10 16
Note
For the first example it's easy to see that set {1, 2, 3, 4} isn't a valid set of rank 1 since <image>.
Submitted Solution:
```
l = input().split(" ")
n = int(l[0])
k = int(l[1])
print((6*n-1)*k)
for i in range(n):
print(str((6*i+1)*k)+" "+str((6*i+2)*k)+" "+str((6*i+3)*k)+" "+str((6*i+5)*k))
``` | instruction | 0 | 13,681 | 5 | 27,362 |
Yes | output | 1 | 13,681 | 5 | 27,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
data = [int(n) for n in input().split()]
n = data[0]
x = data[1]
ans = 0
for i in range(2, n + 1):
if x % i == 0 and x <= i * n:
ans += 1
if (n >= x):
ans += 1
print(ans)
``` | instruction | 0 | 13,697 | 5 | 27,394 |
Yes | output | 1 | 13,697 | 5 | 27,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
if __name__ == '__main__':
n, x = [int(__) for __ in input().strip().split()]
ans = 0
for i in range(1, n + 1):
if x % i == 0 and i * n >= x:
ans += 1
print(ans)
``` | instruction | 0 | 13,698 | 5 | 27,396 |
Yes | output | 1 | 13,698 | 5 | 27,397 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
def multiplication_table(number1, number2):
count = 0
value = 1
while value <= number2 ** 0.5:
if number2 % value == 0 and value <= n and number2 // value <= n:
if value != number2 // value:
count += 2
else:
count += 1
value += 1
return count
n, x = map(int, input().split())
print(multiplication_table(n, x))
``` | instruction | 0 | 13,700 | 5 | 27,400 |
Yes | output | 1 | 13,700 | 5 | 27,401 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
n, x = tuple(map(int, input().split()))
d = 1
res = 0
while d * d < x:
if d > n or x / d > n:
d += 1
continue
if x % d == 0:
res += 1
d+=1
res *= 2
if d * d == x:
res += 1
print(res)
``` | instruction | 0 | 13,701 | 5 | 27,402 |
No | output | 1 | 13,701 | 5 | 27,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
z=list(map(int,input().split()))
s=[]
c=1
for i in range(1,z[1]+1):
for o in range(1,+z[1]+1):
sd=i*o
if sd== z[1] :
s.append(sd)
print(len(s))
``` | instruction | 0 | 13,703 | 5 | 27,406 |
No | output | 1 | 13,703 | 5 | 27,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.
You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.
Input
The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.
Output
Print a single number: the number of times x occurs in the table.
Examples
Input
10 5
Output
2
Input
6 12
Output
4
Input
5 13
Output
0
Note
A table for the second sample test is given below. The occurrences of number 12 are marked bold.
<image>
Submitted Solution:
```
from __future__ import division, print_function
from collections import *
from math import *
from itertools import *
from time import time
import os
import sys
from io import BytesIO, IOBase
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from future_builtins import ascii, filter, hex, map, oct, zip
'''
Notes:
n = size of the table
x = number
'''
def main():
n, x = map(int, input().split())
count = 0
if n >= x:
count = 2
else:
count = 0
for i in range(2, min(x, n)+1):
if x % i == 0:
count += 1
if floor(sqrt(x)) ** 2 == x:
count -= 1
print(count)
# region fastio
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")
def print(*args, **kwargs):
"""Prints the values to a stream, or to sys.stdout by default."""
sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
at_start = True
for x in args:
if not at_start:
file.write(sep)
file.write(str(x))
at_start = False
file.write(kwargs.pop("end", "\n"))
if kwargs.pop("flush", False):
file.flush()
if sys.version_info[0] < 3:
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | instruction | 0 | 13,704 | 5 | 27,408 |
No | output | 1 | 13,704 | 5 | 27,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are n pearls in a row. Let's enumerate them with integers from 1 to n from the left to the right. The pearl number i has the type ai.
Let's call a sequence of consecutive pearls a segment. Let's call a segment good if it contains two pearls of the same type.
Split the row of the pearls to the maximal number of good segments. Note that each pearl should appear in exactly one segment of the partition.
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use scanf/printf instead of cin/cout in C++, prefer to use BufferedReader/PrintWriter instead of Scanner/System.out in Java.
Input
The first line contains integer n (1 ≤ n ≤ 3·105) — the number of pearls in a row.
The second line contains n integers ai (1 ≤ ai ≤ 109) – the type of the i-th pearl.
Output
On the first line print integer k — the maximal number of segments in a partition of the row.
Each of the next k lines should contain two integers lj, rj (1 ≤ lj ≤ rj ≤ n) — the number of the leftmost and the rightmost pearls in the j-th segment.
Note you should print the correct partition of the row of the pearls, so each pearl should be in exactly one segment and all segments should contain two pearls of the same type.
If there are several optimal solutions print any of them. You can print the segments in any order.
If there are no correct partitions of the row print the number "-1".
Examples
Input
5
1 2 3 4 1
Output
1
1 5
Input
5
1 2 3 4 5
Output
-1
Input
7
1 2 1 3 1 2 1
Output
2
1 3
4 7
Submitted Solution:
```
#!/bin/python3
import sys
n = int(input())
a = list(map(int, input().split()))
ans = [];
sa = sorted(a);
cmpr = {};
for i in range(0, len(a)):
cmpr[a[i]] = i;
cid = [0 for i in range(0,n)];
id = 1;
pi = 0
for i in range(0,n):
if cid[cmpr[a[i]]] == id:
ans.append(i + 1)
id+=1
continue;
cid[cmpr[a[i]]] = id
if len(ans) == 0:
print(-1)
else:
print(len(ans))
ans = [0] + ans
for i in range(0, len(ans) - 1):
print(ans[i] + 1 , ans[i + 1] )
``` | instruction | 0 | 13,737 | 5 | 27,474 |
No | output | 1 | 13,737 | 5 | 27,475 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,921 | 5 | 27,842 |
"Correct Solution:
```
from bisect import bisect
def main():
n,k,*a=map(int,open(0).read().split())
a.sort()
i=bisect(a,0)
a,b=a[i:],a[i-1::-1]
n,m=len(a),len(b)
ok=10**18
ng=-ok
while ok-ng>1:
x=(ok+ng)//2
s=0
if x>=0:
s+=n*m
t=0
i=n
for y in a:
while i and a[i-1]*y>x:
i-=1
t+=i
if y*y<=x:
t-=1
s+=t//2
t=0
i=m
for y in b:
while i and b[i-1]*y>x:
i-=1
t+=i
if y*y<=x:
t-=1
s+=t//2
else:
i=m
for y in a:
while i and b[i-1]*y<=x:
i-=1
s+=m-i
if s>=k:
ok=x
else:
ng=x
print(ok)
main()
``` | output | 1 | 13,921 | 5 | 27,843 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,922 | 5 | 27,844 |
"Correct Solution:
```
import sys
input=sys.stdin.readline
n,k=map(int,input().split())
a=list(map(int,input().split()))
ap,an=[],[]
zeronum=0
for i in range(n):
if a[i]>0:
ap.append(a[i])
elif a[i]<0:
an.append(-a[i])
else:
zeronum+=1
np,nn=len(ap),len(an)
def fminus(x):
j=0
cnt=0
for i in range(np):
cnt+=j
while j<nn and an[j]*ap[i]>=x:
j+=1
cnt+=1
return cnt
def fplus(x,length,lis):
r=length-1
cnt=0
for l in range(length):
while lis[r]*lis[l]>x:
if r==l:
break
r-=1
if r==l:
break
elif lis[r]*lis[l]<=x:
cnt+=r-l
return cnt
if np*nn<k<=np*nn+zeronum*(zeronum-1)//2+zeronum*(np+nn):
print(0)
else:
#print(ap)
#print(an)
if k<=np*nn:
an.sort(reverse=True)
ap.sort()
ng=10**18
ok=0
while ng-ok>1:
mid=(ok+ng)//2
if fminus(mid)>=k:
ok=mid
else:
ng=mid
print(-ok)
else:
an.sort()
ap.sort()
k-=np*nn+zeronum*(zeronum-1)//2+zeronum*(np+nn)
#print(k)
ok=10**18
ng=0
#print(ok,ng)
while ok-ng>1:
mid=(ok+ng)//2
if fplus(mid,nn,an)+fplus(mid,np,ap)>=k:
ok=mid
else:
ng=mid
print(ok)
``` | output | 1 | 13,922 | 5 | 27,845 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,923 | 5 | 27,846 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
def count(A, B, x):
N = len(A)
M = len(B)
res = 0
r = -1
for l in range(N):
a = A[l]
while r < M-1 and B[r+1]*a <= x:
r += 1
res += r+1
return res
def count2(A, x):
res = 0
for a in A:
if a*a <= x:
res += 1
return res
N, K = map(int, readline().split())
A = list(map(int, readline().split()))
Am = []
Ap = []
minus = 0
zero = 0
plus = 0
for a in A:
if a < 0:
minus += 1
Am.append(-a)
elif a == 0:
zero += 1
else:
plus += 1
Ap.append(a)
ms = minus*plus
zs = ms + zero*(minus+plus) + zero*(zero-1)//2
Am.sort()
Ap.sort()
Amr = Am[::-1]
Apr = Ap[::-1]
if K <= ms:
K = ms+1-K
ok = max(max(Am+[0]), max(Ap+[0]))**2
ng = 0
while abs(ok-ng)>1:
med = (ok+ng)//2
if count(Amr, Ap, med) >= K:
ok = med
else:
ng = med
ans = -ok
elif K <= zs:
ans = 0
else:
K -= zs
ok = max(max(Am+[0]), max(Ap+[0]))**2
ng = 0
while abs(ok-ng)>1:
med = (ok+ng)//2
if (count(Amr, Am, med) + count(Apr, Ap, med) - count2(Am, med) - count2(Ap, med))//2 >= K:
ok = med
else:
ng = med
ans = ok
print(ans)
``` | output | 1 | 13,923 | 5 | 27,847 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,924 | 5 | 27,848 |
"Correct Solution:
```
n,k=list(map(int,input().split()))
a=list(map(int,input().split()))
am=[]
ap=[]
zc=0
for i in a:
if i<0:
am.append(i)
elif i>0:
ap.append(i)
else:
zc+=1
am.sort()
ap.sort()
#print(am,ap)
def count(n,m,p,z):
mx=-10**20
lm=len(m)
lp=len(p)
if n==0:
if z or (lm and lp):
return (lm*lp+(lm+lp)*z+(z*(z-1))//2,0 if z else m[-1]*p[0])
else:
return (0,0)
elif n<0:
r=0
j=0
for i in m:
while j<len(p) and i*p[j]>n:
j+=1
if j<len(p) and mx<i*p[j]:
mx=i*p[j]
r+=len(p)-j
return (r,mx)
else:
if z or (lm and lp):
mx=0 if z else m[-1]*p[0]
r=lm*lp+(lm+lp)*z+(z*(z-1))//2
j=lp-1
for i in range(lp):
while j>i and p[i]*p[j]>n:
j-=1
if j>i and p[i]*p[j]>mx:
mx=p[i]*p[j]
r+=j-i
if i==j:
break
j=lm-1
for i in range(lm):
while j>i and m[i]*m[j]<=n:
j-=1
if i>j:
j=i
if j<lm-1 and m[i]*m[j+1]>mx:
mx=m[i]*m[j+1]
r+=lm-j-1
return (r,mx)
r=10**18
t=0
s=set()
while True:
ret=count(t,am,ap,zc)
#if r<100:
# print(t,ret)
if ret[0]<k:
s.add(t)
t+=r
r=(r+1)//2
elif ret[0]==k:
print(ret[1])
break
else:
if t in s:
print(ret[1])
break
s.add(t)
t-=r
r=(r+1)//2
``` | output | 1 | 13,924 | 5 | 27,849 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,925 | 5 | 27,850 |
"Correct Solution:
```
import bisect
n, k = map(int, input().split())
a = sorted(map(int, input().split()))
def count(t):
c = 0
for x in a:
if x == 0:
c += len(a) - 1 if t >= 0 else 0
elif x > 0:
c += bisect.bisect_left(a, (t // x) + 1) - (x * x <= t)
else:
c += len(a) - bisect.bisect_left(a, -(t // -x)) - (x * x <= t)
return c
lo = -1000000000000000001
hi = 1000000000000000001
while hi - lo > 1:
mid = (lo + hi) // 2
if count(mid) < k * 2:
lo = mid
else:
hi = mid
print(hi)
``` | output | 1 | 13,925 | 5 | 27,851 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,926 | 5 | 27,852 |
"Correct Solution:
```
from bisect import *
from math import ceil
N, K = map(int, input().split())
A = list(map(int, input().split()))
Ap = []
Am = []
for a in A:
if a >= 0:
Ap.append(a)
elif a < 0:
Am.append(a)
p = len(Ap)
m = len(Am)
Ap.sort()
Am.sort(reverse=True)
U = 10 ** 18
L = - 10 ** 18
while U - L > 1:
mid = (U+L)//2
cnt = 0
if mid >= 0:
cnt += p*m
i = p
t = 0
for a in Ap:
while i and Ap[i-1] * a > mid:
i -= 1
t += i
if a*a <= mid:
t -= 1
cnt += t//2
i = m
t = 0
for a in Am:
while i and Am[i-1] * a > mid:
i -= 1
t += i
if a*a <= mid:
t -= 1
cnt += t//2
else:
i = m
for a in Ap:
while i and Am[i-1] * a <= mid:
i -= 1
cnt += m - i
if cnt < K:
L = mid
else:
U = mid
print(U)
``` | output | 1 | 13,926 | 5 | 27,853 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,927 | 5 | 27,854 |
"Correct Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
plus, zero, minus = [], [], []
for x in a:
if x > 0:
plus.append(x)
elif x == 0:
zero.append(x)
else:
minus.append(x)
m, z, p = len(minus), len(zero), len(plus)
mm, zz, pp = m * p, z * (m + p) + (z * (z - 1)) // 2, (m * (m-1)) // 2 + (p * (p-1)) // 2
plus.sort()
plus2 = plus[::-1]
minus.sort()
minus2 = minus[::-1]
#print(mm, zz, pp)
if mm + zz >= k and mm < k:
print(0)
elif mm >= k:
ok, ng = -10**19, 0
while ng-ok > 1:
x = (ng+ok)//2
res = 0
l = 0
for c in plus:
if l == m:
res += m
elif minus[l] * c >= x:
res += l
else:
while minus[l] * c < x:
l += 1
if l == m:
break
res += l
if res < k:
ok = x
else:
ng = x
print(ng-1)
else:
ok, ng = 0, 10**19
while ng-ok > 1:
x = (ng+ok)//2
lm, lp = 0, 0
res = 0
for c in minus:
if c*c < x:
res -= 1
if lm == m:
res += m
elif minus2[lm] * c >= x:
res += lm
else:
while minus2[lm] * c < x:
lm += 1
if lm == m:
break
res += lm
for c in plus2:
if c*c < x:
res -= 1
if lp == p:
res += p
elif plus[lp] * c >= x:
res += lp
else:
while plus[lp] * c < x:
lp += 1
if lp == p:
break
res += lp
res //= 2
res += zz + mm
#print(x, res)
if res < k:
ok = x
else:
ng = x
print(ng-1)
``` | output | 1 | 13,927 | 5 | 27,855 |
Provide a correct Python 3 solution for this coding contest problem.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064 | instruction | 0 | 13,928 | 5 | 27,856 |
"Correct Solution:
```
N,K = map(int,input().split())
A_s = list(map(int,input().split()))
minus = [-x for x in A_s if x < 0]
plus = [x for x in A_s if x >= 0]
minus.sort()
plus.sort()
def cnt(x):
ans = 0
if x < 0:
r = 0
x = -x
for num in minus[::-1]:
while r < len(plus) and plus[r] * num < x:
r += 1
ans += len(plus) - r
return ans
r = 0
for num in minus[::-1]:
if num * num <= x: ans -= 1
while r < len(minus) and minus[r] * num <= x:
r += 1
ans += r
r = 0
for num in plus[::-1]:
if num * num <= x: ans -= 1
while r < len(plus) and plus[r] * num <= x:
r += 1
ans += r
ans //= 2
ans += len(minus) * len(plus)
return ans
top = 2 * (10**18) + 2
bottom = 0
while top - bottom > 1:
mid = (top + bottom) // 2
if cnt(mid-10**18-1) < K:
bottom = mid
else:
top = mid
print(int(top-10**18-1))
``` | output | 1 | 13,928 | 5 | 27,857 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
def solve():
from bisect import bisect_left, bisect_right
N, K = map(int, input().split())
As = list(map(int, input().split()))
As.sort()
negAs = [-A for A in As[::-1]]
A2s = [A*A for A in As]
A2s.sort()
pstvBs = []
numB0= 0
ngtvBs = []
for A in As:
if A > 0:
pstvBs.append(A)
elif A == 0:
numB0 += 1
else:
ngtvBs.append(A)
def isOK(x):
if x >= 0:
dire = 1
else:
dire = -1
num = 0
# 正
iA = 0
for B in pstvBs[::-dire]:
key = x//B
while iA < N and As[iA] <= key:
iA += 1
num += iA
# ゼロ
if x >= 0:
num += N*numB0
# 負
iA = 0
for B in ngtvBs[::dire]:
key = x//(-B)
while iA < N and negAs[iA] <= key:
iA += 1
num += iA
i = bisect_right(A2s, x)
num -= i
num //= 2
return num >= K
ng, ok = -(10**18)-1, 10**18+1
while abs(ok-ng) > 1:
mid = (ng+ok) // 2
if isOK(mid):
ok = mid
else:
ng = mid
print(ok)
solve()
``` | instruction | 0 | 13,929 | 5 | 27,858 |
Yes | output | 1 | 13,929 | 5 | 27,859 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
from bisect import bisect_left, bisect_right
N, K = map(int, input().split())
As = sorted(map(int, input().split()))
l = - (10 ** 18 + 10)
r = 10 ** 18 + 10
while True:
mid = (l + r) // 2
count = 0
for i, A in enumerate(As):
if A > 0:
count += bisect_right(As, mid//A, lo = i+1) - (i+1)
elif A < 0:
count += N - bisect_left(As, -((-mid)//A), lo = i+1)
else:
if mid >= 0:
count += N - i - 1
if count < K:
l = mid
else:
r = mid
if r - l == 1:
break
print(r)
``` | instruction | 0 | 13,930 | 5 | 27,860 |
Yes | output | 1 | 13,930 | 5 | 27,861 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have N integers A_1, A_2, ..., A_N.
There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?
Constraints
* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 \dots A_N
Output
Print the answer.
Examples
Input
4 3
3 3 -4 -2
Output
-6
Input
10 40
5 4 3 2 -1 0 0 0 0 0
Output
6
Input
30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0
Output
448283280358331064
Submitted Solution:
```
N,K=map(int,input().split())
A=list(map(int,input().split()))
m,p=[],[]
for a in A:
if a<0:
m.append(a)
elif a>0:
p.append(a)
M,P=len(m),len(p)
Z=N-M-P
m.sort()
p.sort()
if M*P<K<=N*(N-1)//2-M*(M-1)//2-P*(P-1)//2:
print(0)
elif K<=M*P:
l,r=-10**18-1,0
while l+1<r:
t=(l+r)//2
x=0
mi=0
for pi in range(P):
while mi<M and m[mi]*p[pi]<=t:
mi+=1
x+=mi
if K<=x:
r=t
else:
l=t
print(r)
else:
l,r=0,10**18+1
K-=M*P+Z*(Z-1)//2+Z*(M+P)
m.reverse()
while l+1<r:
t=(l+r)//2
x=0
mi,pi=0,0
for mj in range(M-1,-1,-1):
while mi<M and m[mi]*m[mj]<=t:
mi+=1
x+=mi-(1 if mj<mi else 0)
for pj in range(P-1,-1,-1):
while pi<P and p[pi]*p[pj]<=t:
pi+=1
x+=pi-(1 if pj<pi else 0)
if K<=x//2:
r=t
else:
l=t
print(r)
``` | instruction | 0 | 13,931 | 5 | 27,862 |
Yes | output | 1 | 13,931 | 5 | 27,863 |
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