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 tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,532 | 5 | 97,064 |
Tags: math, number theory
Correct Solution:
```
a,b=map(int,input().split())
while True:
if a==0 or b==0:
break
if a>=2*b:
a=a%(2*b)
elif b>=2*a:
b=b%(2*a)
else:
break
print(a,b)
``` | output | 1 | 48,532 | 5 | 97,065 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,533 | 5 | 97,066 |
Tags: math, number theory
Correct Solution:
```
a,b=map(int,input().split())
while a!=0 and b!=0:
# print(a,b)
if a>2*b or b>2*a:
while a>(2*b) and b!=0:
k=a//(2*b)
a-=(2*b*k)
while b>2*a and a!=0:
k=b//(2*a)
b-=(2*a*k)
elif a==2*b:a=0
elif b==2*a:b=0
else:exit(print(a,b))
print(a,b)
``` | output | 1 | 48,533 | 5 | 97,067 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,534 | 5 | 97,068 |
Tags: math, number theory
Correct Solution:
```
a, b = map(int, input().split())
while a>0 and b>0:
cnt=0
if a>=(b*2):
a%=(b*2)
cnt+=1
elif b>=(a*2):
b%=(a*2)
cnt+=1
if cnt==0:
break
print(a,b)
``` | output | 1 | 48,534 | 5 | 97,069 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,535 | 5 | 97,070 |
Tags: math, number theory
Correct Solution:
```
a = [int(i) for i in input().split()]
while (True):
if a[0] == 0 or a[1] == 0: break
elif a[0] >= a[1] * 2:
e = a[0] // a[1]
if e % 2 != 0: e -= 1
a[0] -= a[1] * e
elif a[1] >= a[0] * 2:
e = a[1] // a[0]
if e % 2 != 0: e -= 1
a[1] -= a[0] * e
else: break
print(a[0], a[1])
``` | output | 1 | 48,535 | 5 | 97,071 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,536 | 5 | 97,072 |
Tags: math, number theory
Correct Solution:
```
x, y = map(int, input().split())
ans = []
k = 0
while True:
if x >= 2 * y:
x %= 2 * y
else:
y %= 2 * x
if x == 0 or y == 0:
break
if ans == [x, y]:
k += 1
else:
ans = [x, y]
k = 0
if k == 5:
break
print(x, y)
``` | output | 1 | 48,536 | 5 | 97,073 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12. | instruction | 0 | 48,537 | 5 | 97,074 |
Tags: math, number theory
Correct Solution:
```
# def f(a,b):
# if a==0 or b==0:
# return (a,b)
# elif a >= 2*b:
# a -= 2*b
# return f(a,b)
# elif b >= 2*a:
# b -= 2*a
# return f(a,b)
# else:
# return (a,b)
a,b = list(map(int, input().split()))
while(a!=0 and b!=0):
if a >= 2*b:
a %= 2*b
continue
elif b >= 2*a:
b %= 2*a
continue
else:
break
print(a,b)
``` | output | 1 | 48,537 | 5 | 97,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
def first(a,b):
if(a==0 or b==0):
print(a,b)
else:
if(a>b*5):
k=a//b
if(k%2==0):
a=a-b*(k-4)
else:
a=a-b*(k-5)
if(b>a*5):
k=b//a
if(k%2==0):
b=b-a*(k-4)
else:
b=b-a*(k-5)
second(a,b)
def second(a,b):
if(a>=2*b):
a=a-2*b
first(a,b)
else:
third(a,b)
def third(a,b):
if(b>=2*a):
b=b-2*a
first(a,b)
else:
print(a,b)
n,m=map(int,input().split())
if(n>m*5):
a=n//m
if(a%2==0):
n=n-m*(a-4)
else:
n=n-m*(a-5)
if(m>>n*5):
a=m//n
if(a%2==0):
m=m-n*(a-4)
else:
m=m-n*(a-5)
first(n,m)
``` | instruction | 0 | 48,538 | 5 | 97,076 |
Yes | output | 1 | 48,538 | 5 | 97,077 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
numbers=input().split(" ")
a=int(numbers[0])
b=int(numbers[1])
con=1
while (a!=0) and (b!=0):
if a>=2*b:
a=a%(2*b)
elif b>=2*a:
b=b%(2*a)
else:
break
print(a,b)
``` | instruction | 0 | 48,539 | 5 | 97,078 |
Yes | output | 1 | 48,539 | 5 | 97,079 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
import re
import sys
from bisect import bisect, bisect_left, insort, insort_left
from collections import Counter, defaultdict, deque
from copy import deepcopy
from decimal import Decimal
from fractions import gcd
from itertools import (
accumulate, combinations, combinations_with_replacement, groupby,
permutations, product)
from math import (
acos, asin, atan, ceil, cos, degrees, factorial, hypot, log2, pi, radians,
sin, sqrt, tan)
from operator import itemgetter, mul
from string import ascii_lowercase, ascii_uppercase, digits
def inp():
return(int(input()))
def inlist():
return(list(map(int, input().split())))
def instr():
s = input()
return(list(s[:len(s)]))
def invr():
return(map(int, input().split()))
def gcd_custom(a, b):
if a == 0 or b == 0:
return a, b
if a >= 2*b:
return gcd_custom(a % (2*b), b)
elif b >= 2*a:
return gcd_custom(a, b % (2*a))
else:
return a, b
a, b = invr()
c, d = gcd_custom(a, b)
print(c, d)
``` | instruction | 0 | 48,540 | 5 | 97,080 |
Yes | output | 1 | 48,540 | 5 | 97,081 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
a, b = [int(v) for v in input().split()]
while a > 0 and b > 0:
if a >= 2 * b:
a %= 2 * b
elif b >= 2 * a:
b %= 2 * a
else:
break
print(a, b)
``` | instruction | 0 | 48,541 | 5 | 97,082 |
Yes | output | 1 | 48,541 | 5 | 97,083 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
def solve(a,b,i):
if a==0 or b==0:
return [a,b]
else:
if a>=2*b and i==False:
a=a-2*b
i=True
return solve(a,b,i)
else:
if b>=2*a and i==True:
b=b-2*a
i=False
return solve(a,b,i)
else:
return [a,b]
if __name__ == '__main__':
m, n = map(int,(input().split(' ')))
print(" ".join(map(str,solve(m,n,False))))
``` | instruction | 0 | 48,542 | 5 | 97,084 |
No | output | 1 | 48,542 | 5 | 97,085 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
import sys
m,n=[int(x) for x in input().split()]
if n==0 or m==0:
print(m,n)
sys.exit();
if n>=2*m and n%m==0 :
print(m,0)
sys.exit()
elif m>=2*n and m%n==0:
print(0,n)
sys.exit()
while (m>=2*n or n>=2*m) and (m>0 and n>0):
if m>=(2*n):
m=m%(2*n)
else:
n=n%(2*m)
print(m,n)
print(m,n)
``` | instruction | 0 | 48,543 | 5 | 97,086 |
No | output | 1 | 48,543 | 5 | 97,087 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
a,b=map(int,input().split())
while 1:
if a==0 or b==0:
break
if a>=2*b:
a-=((a//b)*b)
else:
if b>=2*a:
b-=((b//a)*a)
else:
break
print(a,b)
``` | instruction | 0 | 48,544 | 5 | 97,088 |
No | output | 1 | 48,544 | 5 | 97,089 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have two variables a and b. Consider the following sequence of actions performed with these variables:
1. If a = 0 or b = 0, end the process. Otherwise, go to step 2;
2. If a ≥ 2·b, then set the value of a to a - 2·b, and repeat step 1. Otherwise, go to step 3;
3. If b ≥ 2·a, then set the value of b to b - 2·a, and repeat step 1. Otherwise, end the process.
Initially the values of a and b are positive integers, and so the process will be finite.
You have to determine the values of a and b after the process ends.
Input
The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018). n is the initial value of variable a, and m is the initial value of variable b.
Output
Print two integers — the values of a and b after the end of the process.
Examples
Input
12 5
Output
0 1
Input
31 12
Output
7 12
Note
Explanations to the samples:
1. a = 12, b = 5 <image> a = 2, b = 5 <image> a = 2, b = 1 <image> a = 0, b = 1;
2. a = 31, b = 12 <image> a = 7, b = 12.
Submitted Solution:
```
a = 0
b = 0
def step1(n, m, a, b):
if (n==0 or m==0):
a = n
b = m
n = 0
m = 0
print(a, b)
return n , m , a , b
else:
step2(n, m, a, b)
def step2(n, m, a, b):
if (n >= 2*m):
n = n - 2*m
step1(n, m, a, b)
else:
step3(n, m, a, b)
def step3(n, m, a, b):
if (m >= 2*n):
m = m - 2*n
step1(n, m, a, b)
else:
a = n
b = m
n = 0
m = 0
step1(n, m, a, b)
n, m = map(int, input().split())
step1(n,m,a,b)
``` | instruction | 0 | 48,545 | 5 | 97,090 |
No | output | 1 | 48,545 | 5 | 97,091 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are an integer K and integers a_1,\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.
* Every term in P is an integer between 1 and K (inclusive).
* For each i=1,\dots, K, P contains a_i occurrences of i.
* For each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1,\dots, K.
Constraints
* 1 \leq K \leq 100
* 1 \leq a_i \leq 1000 \quad (1\leq i\leq K)
* a_1 + \dots + a_K\leq 1000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K
a_1 a_2 \dots a_K
Output
If there is no sequence satisfying the conditions, print `-1`. Otherwise, print the lexicographically smallest sequence satisfying the conditions.
Examples
Input
3
2 4 3
Output
2 1 3 2 2 3 1 2 3
Input
4
3 2 3 2
Output
1 2 3 4 1 3 1 2 4 3
Input
5
3 1 4 1 5
Output
-1
Submitted Solution:
```
import numpy as np
K = input()
counts = np.array(list(map(int, input().split())))
def subtract_count(counts: np.ndarray):
if counts.max() == 1: block = np.ones_like(counts)
else: block = (counts == counts.max()).astype(int) + 1
return counts - block, block
def block_to_str(block):
arange = np.arange(1, len(block) + 1)
if block.max() == 1: return " ".join(map(str, arange))
twice = list(arange[block == block.max()])
once = list(arange[block != block.max()])
return " ".join(map(str, twice + once + twice))
def greedy_solution(counts):
blocks = []
while counts.max() > 0:
counts, block = subtract_count(counts)
blocks.append(block)
# print(blocks, counts)
if counts.min() < 0:
return -1
sorted_strs = sorted([block_to_str(block) for block in blocks])
return " ".join(sorted_strs)
def solution(counts):
candidates = []
candidates.append(greedy_solution(counts))
alt = np.ones_like(counts)
alt[0] = 2
alts = [alt]
for alt in alts:
alt = np.array(alt)
sol = greedy_solution(counts - alt)
if sol == -1:
continue
candidates.append(block_to_str(alt) + " " + sol)
return sorted(candidates)[0]
print(solution(counts))
``` | instruction | 0 | 48,554 | 5 | 97,108 |
No | output | 1 | 48,554 | 5 | 97,109 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are an integer K and integers a_1,\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.
* Every term in P is an integer between 1 and K (inclusive).
* For each i=1,\dots, K, P contains a_i occurrences of i.
* For each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1,\dots, K.
Constraints
* 1 \leq K \leq 100
* 1 \leq a_i \leq 1000 \quad (1\leq i\leq K)
* a_1 + \dots + a_K\leq 1000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K
a_1 a_2 \dots a_K
Output
If there is no sequence satisfying the conditions, print `-1`. Otherwise, print the lexicographically smallest sequence satisfying the conditions.
Examples
Input
3
2 4 3
Output
2 1 3 2 2 3 1 2 3
Input
4
3 2 3 2
Output
1 2 3 4 1 3 1 2 4 3
Input
5
3 1 4 1 5
Output
-1
Submitted Solution:
```
k=int(input())
a=list(map(int,input().split()))
sum_a=sum(a)
max_a=max(a)
min_a=min(a)
if max_a>min_a+2:
print(-1)
exit()
p=[None]*sum_a
temp0=[]
temp1=[]
if max_a == min_a+2:
for i in range(k):
if a[i] ==max_a:
temp0.append(i+1)
else:
temp1.append(i+1)
fronts=(temp0+temp1+temp0)
#print(fronts)
len_f=len(fronts)
p[:len_f]=fronts
temp2=[]
temp3=[]
for j in range(k):
if a[j] ==min_a:
temp2.append(j+1)
else:
temp3.append(j+1)
ends=(temp3+temp2+temp3)
#print(ends)
len_e=len(ends)
p[-len_e:]=ends
index_i=len_f-k
if sum(temp1) < sum(temp3):
for l in range(len_f,sum_a-len_e):
p[l]=fronts[index_i]
index_i+=1
if index_i >=len_f:
index_i=len_f-k
else:
index_i=0
for l in range(len_e,sum_a-len_e):
p[l]=ends[index_i]
index_i+=1
if index_i >=len_e:
index_i=0
elif max_a==min_a:
fronts=[i for i in range(1,k+1)]
index_i=0
p=fronts*min_a
else:
fronts=[i for i in range(1,k+1)]
#print(fronts)
p[:k]=fronts
temp2=[i for i in range(1,k//2+1)]
temp3=[]
for j in range(k//2,k):
if a[j] ==min_a:
temp2.append(j+1)
else:
temp3.append(j+1)
ends=(temp3+temp2+temp3)
#print(ends)
len_e=len(ends)
p[-len_e:]=ends
index_i=0
for l in range(k,sum_a-len_e):
p[l]=fronts[index_i]
index_i+=1
if index_i >=k:
index_i=0
print(" ".join((str(x) for x in p)))
``` | instruction | 0 | 48,555 | 5 | 97,110 |
No | output | 1 | 48,555 | 5 | 97,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are an integer K and integers a_1,\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.
* Every term in P is an integer between 1 and K (inclusive).
* For each i=1,\dots, K, P contains a_i occurrences of i.
* For each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1,\dots, K.
Constraints
* 1 \leq K \leq 100
* 1 \leq a_i \leq 1000 \quad (1\leq i\leq K)
* a_1 + \dots + a_K\leq 1000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K
a_1 a_2 \dots a_K
Output
If there is no sequence satisfying the conditions, print `-1`. Otherwise, print the lexicographically smallest sequence satisfying the conditions.
Examples
Input
3
2 4 3
Output
2 1 3 2 2 3 1 2 3
Input
4
3 2 3 2
Output
1 2 3 4 1 3 1 2 4 3
Input
5
3 1 4 1 5
Output
-1
Submitted Solution:
```
import sys
def solve(k, aaa):
if k == 1:
return [1] * aaa[0]
min_a = min(aaa)
max_a = max(aaa)
if min_a * 2 < max_a:
return [-1]
ans = []
while True:
min_a = min(aaa)
max_a1 = max(aaa[1:])
max_a = max(aaa[0], max_a1)
if min_a <= 0:
assert max_a == 0
break
if (min_a - 1) * 2 < max_a - 1:
must_use = [i for i, a in enumerate(aaa) if a - 1 > (min_a - 1) * 2]
next_max = max_a - 2
elif (aaa[0] - 2) * 2 >= max_a1 - 1:
must_use = []
next_max = max(aaa[0] - 2, max_a1 - 1)
else:
ans.extend(range(1, k + 1))
for i in range(k):
aaa[i] -= 1
continue
can_use = []
cant_use = []
for i in range(k):
if i in must_use:
pass
elif (aaa[i] - 2) * 2 >= next_max:
can_use.append(i)
else:
cant_use.append(i)
double = []
if len(must_use) == 0:
double.append(can_use[0] + 1)
else:
max_use = must_use[-1]
use = must_use + can_use
use.sort()
double = [i + 1 for i in use if i <= max_use]
single = [i for i in range(1, k + 1) if i not in double]
for i in double:
aaa[i - 1] -= 2
for i in single:
aaa[i - 1] -= 1
ans.extend(double)
ans.extend(single)
ans.extend(double)
return ans
k, *aaa = map(int, sys.stdin.buffer.read().split())
print(*solve(k, aaa))
``` | instruction | 0 | 48,556 | 5 | 97,112 |
No | output | 1 | 48,556 | 5 | 97,113 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are an integer K and integers a_1,\dots, a_K. Determine whether a sequence P satisfying below exists. If it exists, find the lexicographically smallest such sequence.
* Every term in P is an integer between 1 and K (inclusive).
* For each i=1,\dots, K, P contains a_i occurrences of i.
* For each term in P, there is a contiguous subsequence of length K that contains that term and is a permutation of 1,\dots, K.
Constraints
* 1 \leq K \leq 100
* 1 \leq a_i \leq 1000 \quad (1\leq i\leq K)
* a_1 + \dots + a_K\leq 1000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
K
a_1 a_2 \dots a_K
Output
If there is no sequence satisfying the conditions, print `-1`. Otherwise, print the lexicographically smallest sequence satisfying the conditions.
Examples
Input
3
2 4 3
Output
2 1 3 2 2 3 1 2 3
Input
4
3 2 3 2
Output
1 2 3 4 1 3 1 2 4 3
Input
5
3 1 4 1 5
Output
-1
Submitted Solution:
```
k=int(input())
a=list(map(int,input().split()))
sum_a=sum(a)
max_a=max(a)
min_a=min(a)
if max_a>min_a+2:
print(-1)
exit()
p=[None]*sum_a
temp0=[]
temp1=[]
if max_a == min_a+2:
for i in range(k):
if a[i] ==max_a:
temp0.append(i+1)
else:
temp1.append(i+1)
fronts=(temp0+temp1+temp0)
print(fronts)
len_f=len(fronts)
p[:len_f]=fronts
temp2=[]
temp3=[]
for j in range(k):
if a[j] ==min_a:
temp2.append(j+1)
else:
temp3.append(j+1)
ends=(temp3+temp2+temp3)
#print(ends)
len_e=len(ends)
p[-len_e:]=ends
index_i=len_f-k
for l in range(len_f,sum_a-len_e):
p[l]=fronts[index_i]
index_i+=1
if index_i >=len_f:
index_i=len_f-k
elif max_a==min_a:
fronts=[i for i in range(1,k+1)]
index_i=0
p=fronts*min_a
else:
fronts=[i for i in range(1,k+1)]
#print(fronts)
p[:k]=fronts
temp2=[i for i in range(1,k//2+1)]
temp3=[]
for j in range(k//2,k):
if a[j] ==min_a:
temp2.append(j+1)
else:
temp3.append(j+1)
ends=(temp3+temp2+temp3)
#print(ends)
len_e=len(ends)
p[-len_e:]=ends
index_i=0
for l in range(k,sum_a-len_e):
p[l]=fronts[index_i]
index_i+=1
if index_i >=k:
index_i=0
print(" ".join((str(x) for x in p)))
``` | instruction | 0 | 48,557 | 5 | 97,114 |
No | output | 1 | 48,557 | 5 | 97,115 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,590 | 5 | 97,180 |
"Correct Solution:
```
N, M = map(int, input().split())
A = list(map(int, input().split()))
D = [(A[i], 1) for i in range(N)]
for i in range(M):
B, C = (map(int, input().split()))
D.append((C, B))
D.sort()
D.reverse()
ans, left = 0, N
for (i, j) in D:
use = min(j, left)
ans += use * i
left -= use
print(ans)
``` | output | 1 | 48,590 | 5 | 97,181 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,591 | 5 | 97,182 |
"Correct Solution:
```
N, M = map(int, input().split())
A = list(map(int, input().split()))
D = []
E = []
for i in range(M):
B, C = map(int, input().split())
D.append([C, B])
D = sorted(D, reverse = True)
for j in range(len(D)):
E += [D[j][0]]*D[j][1]
if len(E) >= N:
break
F = sorted(A + E, reverse = True)
print(sum(F[0:N]))
``` | output | 1 | 48,591 | 5 | 97,183 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,592 | 5 | 97,184 |
"Correct Solution:
```
n, m = map(int, input().split())
a = [(1, int(x)) for x in input().split()]
for i in range(m):
x, y = map(int, input().split())
a.append((x, y))
a.sort(key=lambda x:x[1], reverse=True)
res = 0
for j, k in a:
while j > 0 and n > 0:
res += k
j -= 1
n -= 1
print(res)
``` | output | 1 | 48,592 | 5 | 97,185 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,593 | 5 | 97,186 |
"Correct Solution:
```
n, m = (int(_) for _ in input().split())
a = list(map(int, input().split()))
x = [list(int(_) for _ in input().split()) for i in range(m)]
x = sorted(x,key = lambda x:-x[1])
[a.extend(list(i[1] for ii in range(i[0]))) for i in x if len(a) <= n * 2]
a = sorted(a,key = lambda x:-x)
print(sum(a[:n]))
``` | output | 1 | 48,593 | 5 | 97,187 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,594 | 5 | 97,188 |
"Correct Solution:
```
n,m=map(int,input().split())
a=list(map(int,input().split()))
a.sort()
bc=[list(map(int,input().split())) for i in range(m)]
bc.sort(key=lambda x:x[1],reverse=True)
d=[]
i=0
while i<m and len(d)<n:
d+=[bc[i][1]]*bc[i][0]
i+=1
d=d[:n]
s=sum(a)
ans=s
for x in range(min(n,len(d))):
s+=d[x]-a[x]
ans=max(ans,s)
print(ans)
``` | output | 1 | 48,594 | 5 | 97,189 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,595 | 5 | 97,190 |
"Correct Solution:
```
N, M = map(int, input().split())
a = [(1, int(i)) for i in input().split()]
for _ in range(M):
b, c = map(int, input().split())
a.append((b, c))
a = sorted(a, key=lambda x: x[1])
ans = 0
t = 0
while t < N:
b, c = a.pop()
p = min(b, N-t)
ans += p * c
t += p
print(ans)
``` | output | 1 | 48,595 | 5 | 97,191 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,596 | 5 | 97,192 |
"Correct Solution:
```
N,M=map(int,input().split())
A=list(map(int,input().split()))
BC=[list(map(int,input().split())) for _ in range(M)]#リストの表記が違う
BC.sort(key=lambda x: -x[1])#リバースと-1の違い
for b,c in BC:
A.extend([c]*b)
if len(A)>N*2:
break
A.sort(reverse=True)
print(sum(A[:N]))
``` | output | 1 | 48,596 | 5 | 97,193 |
Provide a correct Python 3 solution for this coding contest problem.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001 | instruction | 0 | 48,597 | 5 | 97,194 |
"Correct Solution:
```
n,k = map(int,input().split())
li = list(map(int,input().split()))
rc = [list(map(int,input().split())) for i in range(k)]
rc.sort(key=lambda x:x[1], reverse=True)
tmp = 0
for i in rc:
li += [i[1]]*i[0]
tmp += i[0]
if tmp>n:
break
print(sum(sorted(li, reverse=True)[0:n]))
``` | output | 1 | 48,597 | 5 | 97,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
N, M = map(int, input().split())
A = list(map(int, input().split()))
p = [(A[i], 1) for i in range(N)]
for j in range(M):
B, C = map(int, input().split())
p.append((C, B))
p.sort(reverse=True)
ans, cnt = 0, N
for (v, c) in p:
use = min(c, cnt)
ans += use * v
cnt -= use
print(ans)
``` | instruction | 0 | 48,598 | 5 | 97,196 |
Yes | output | 1 | 48,598 | 5 | 97,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
N,M=map(int,input().split())
A=[]
[A.append([int(i),1]) for i in input().split()]
for i in range(M):
A.append(list(map(int,input().split()))[::-1])
A.sort(reverse=True)
cnt=0
ans=0
for a in A:
if N<=(cnt+a[1]):
ans+=(N-cnt)*a[0]
break
else:
ans+=a[0]*a[1]
cnt+=a[1]
print(ans)
``` | instruction | 0 | 48,599 | 5 | 97,198 |
Yes | output | 1 | 48,599 | 5 | 97,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
n,m = map(int,input().split())
a = list(map(int,input().split()))
bc = [list(map(int,input().split())) for _ in range(m)]
bc = sorted(bc,key=lambda x:(x[1]),reverse=True)
count=0
for b,c in bc:
count += b
a.extend([c]*b)
if count >= n:
break
print(sum(sorted(a,reverse=True)[:n]))
``` | instruction | 0 | 48,600 | 5 | 97,200 |
Yes | output | 1 | 48,600 | 5 | 97,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
I=lambda:list(map(int,input().split()))
n,m=I()
a=I()
a.sort(reverse=True)
qq=[I() for i in range(m)]
qq.sort(key=lambda x:x[1],reverse=True)
ans=0
for x,y in qq:
for j in range(x):
if not a:
break
aa=a.pop()
ans+=max(aa,y)
ans+=sum(a)
print(ans)
``` | instruction | 0 | 48,601 | 5 | 97,202 |
Yes | output | 1 | 48,601 | 5 | 97,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
import heapq
def solve():
N, M = map(int, input().split())
A = list(map(int, input().split()))
BC = [list(map(int, input().split())) for i in range(M)]
A.sort()
BC.sort(key=lambda x: x[1], reverse=True)
BC2 = []
for bc in BC:
for i in range(bc[0]):
BC2.append(bc[1])
BC_idx = 0
for i in range(N):
if BC_idx >= len(BC2):
break
if A[i] < BC2[BC_idx]:
A[i] = BC2[BC_idx]
BC_idx += 1
print(sum(A))
if __name__ == '__main__':
solve()
``` | instruction | 0 | 48,602 | 5 | 97,204 |
No | output | 1 | 48,602 | 5 | 97,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
import numpy as np
N,M=map(int,input().split())
# A=np.array(list(map(int,input().split())))
A=np.array(list(map(int,input().split())),dtype=np.int64)
A=np.sort(A)
EXC=[]
for i in range(M):
exc=list(map(int,input().split()))
EXC.append(exc)
excArry=np.array(EXC,dtype=np.int64)
col_num=1
Arr=excArry[np.argsort(excArry[:,col_num])[::-1]]
# print(A)
# print(Arr)
point=0
for j in range (M):
change_Num=Arr[j][1]
count=np.count_nonzero(A<change_Num)
if count > 0:
m=min(count,Arr[j][0])
A[point:point+m]=change_Num
point+=m
# A=np.sort(A)
else:
break
print(np.sum(A))
# for j in range (B):
# count=np.count_nonzero(A<C)
# if count>0:
# m=min(B,count)
# A[:m]=C
# else:
# continue
# A=np.sort(A)
# print(np.sum(A))
``` | instruction | 0 | 48,603 | 5 | 97,206 |
No | output | 1 | 48,603 | 5 | 97,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
n, m = map(int, input().split())
A = sorted(map(int, input().split()))
info = []
for _ in range(m):
b, c = map(int, input().split())
info.append([b, c])
info.sort(key=lambda x: x[1], reverse=True)
# print(info, A)
index = 0
for i in range(m):
if index == n:
break
for j in range(info[i][0]):
if A[index] < info[i][1]:
A[index] = info[i][1]
index += 1
else:
break
ans = sum(A)
print(ans)
``` | instruction | 0 | 48,604 | 5 | 97,208 |
No | output | 1 | 48,604 | 5 | 97,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have N cards. On the i-th card, an integer A_i is written.
For each j = 1, 2, ..., M in this order, you will perform the following operation once:
Operation: Choose at most B_j cards (possibly zero). Replace the integer written on each chosen card with C_j.
Find the maximum possible sum of the integers written on the N cards after the M operations.
Constraints
* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq A_i, C_i \leq 10^9
* 1 \leq B_i \leq N
Input
Input is given from Standard Input in the following format:
N M
A_1 A_2 ... A_N
B_1 C_1
B_2 C_2
\vdots
B_M C_M
Output
Print the maximum possible sum of the integers written on the N cards after the M operations.
Examples
Input
3 2
5 1 4
2 3
1 5
Output
14
Input
10 3
1 8 5 7 100 4 52 33 13 5
3 10
4 30
1 4
Output
338
Input
3 2
100 100 100
3 99
3 99
Output
300
Input
11 3
1 1 1 1 1 1 1 1 1 1 1
3 1000000000
4 1000000000
3 1000000000
Output
10000000001
Submitted Solution:
```
import sys
fin = sys.stdin.readline
N, M = map(int, fin().split())
As = list(map(int, fin().split()))
BC = [tuple(map(int, fin().split())) for _ in range(M)]
As = sorted(As)
BC = sorted(BC, key=lambda x: x[1], reverse=True)
def f(As, num, val):
count = 0
for i in range(num):
if As[i] < val:
count += 1
else:
break
return val * count, As[count:]
sum__ = 0
for num, val in BC:
sum_, As = f(As, num, val)
sum__ += sum_
print(sum__ + sum(As))
``` | instruction | 0 | 48,605 | 5 | 97,210 |
No | output | 1 | 48,605 | 5 | 97,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
MOD = 10**9+7
n = int(input())
s = input()
dp = [[0] * (n + 1) for _ in range(n + 1)]
# dp[i][j] - the number of ways to put numbers in prefix of size 'i' such that the last number is 'j'
dp[1][1] = 1
for length in range(2, n + 1):
pref = [0] * (length + 1)
for i in range(1, length):
pref[i] = (pref[i - 1] + dp[length - 1][i]) % MOD
for b in range(1, length + 1):
l = r = 0
if s[length - 2] == '<':
l, r = 1, b - 1
else:
l, r = b, length - 1
if l <= r:
dp[length][b] = (dp[length][b] + (pref[r] - pref[l - 1] + MOD) % MOD) % MOD
res = sum(dp[n]) % MOD
print(res)
``` | instruction | 0 | 48,614 | 5 | 97,228 |
Yes | output | 1 | 48,614 | 5 | 97,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
# -*- coding: utf-8 -*-
#############
# Libraries #
#############
import sys
input = sys.stdin.readline
import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache
#############
# Constants #
#############
MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"
#############
# Functions #
#############
######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]
#####Shorten#####
def DD(arg): return defaultdict(arg)
#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)
######Combination######
kaijo_memo = []
def kaijo(n):
if(len(kaijo_memo) > n): return kaijo_memo[n]
if(len(kaijo_memo) == 0): kaijo_memo.append(1)
while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
return kaijo_memo[n]
gyaku_kaijo_memo = []
def gyaku_kaijo(n):
if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
return gyaku_kaijo_memo[n]
def nCr(n,r):
if n == r: return 1
if n < r or r < 0: return 0
ret = 1
ret = ret * kaijo(n) % MOD
ret = ret * gyaku_kaijo(r) % MOD
ret = ret * gyaku_kaijo(n-r) % MOD
return ret
######Factorization######
def factorization(n):
arr = []
temp = n
for i in range(2, int(-(-n**0.5//1))+1):
if temp%i==0:
cnt=0
while temp%i==0:
cnt+=1
temp //= i
arr.append([i, cnt])
if temp!=1: arr.append([temp, 1])
if arr==[]: arr.append([n, 1])
return arr
#####MakeDivisors######
def make_divisors(n):
divisors = []
for i in range(1, int(n**0.5)+1):
if n % i == 0:
divisors.append(i)
if i != n // i:
divisors.append(n//i)
return divisors
#####MakePrimes######
def make_primes(N):
max = int(math.sqrt(N))
seachList = [i for i in range(2,N+1)]
primeNum = []
while seachList[0] <= max:
primeNum.append(seachList[0])
tmp = seachList[0]
seachList = [i for i in seachList if i % tmp != 0]
primeNum.extend(seachList)
return primeNum
#####GCD#####
def gcd(a, b):
while b: a, b = b, a % b
return a
#####LCM#####
def lcm(a, b):
return a * b // gcd (a, b)
#####BitCount#####
def count_bit(n):
count = 0
while n:
n &= n-1
count += 1
return count
#####ChangeBase#####
def base_10_to_n(X, n):
if X//n: return base_10_to_n(X//n, n)+[X%n]
return [X%n]
def base_n_to_10(X, n):
return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))
def base_10_to_n_without_0(X, n):
X -= 1
if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
return [X%n]
#####IntLog#####
def int_log(n, a):
count = 0
while n>=a:
n //= a
count += 1
return count
#############
# Main Code #
#############
N = I()
S = S()
def ACC1(l):
N = len(l)
ret = [0]*(N+1)
for i in range(N):
ret[i+1] = ret[i]+l[i]
ret[i+1] %= MOD
return ret
prev = [1 for j in range(N)]
for i in range(N-1):
now = [0 for j in range(N)]
s = S[i]
for j in range(N):
if s == "<":
if j < N-1-i:
now[j] += prev[j]
now[N-1-i] -= prev[j]
else:
if j:
now[0] += prev[j]
now[j] -= prev[j]
prev = ACC1(now)[1:]
print(prev[0])
``` | instruction | 0 | 48,615 | 5 | 97,230 |
Yes | output | 1 | 48,615 | 5 | 97,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
N = int(input())
s = input()
MOD = 10**9 + 7
# dp[i][j] : 左からi番目の数値まで確定していて、最後に置いた値が未使用の値のうちj番目に小さい値 である場合の数(0-indexed)
dp = [[0]*N for _ in range(N)]
for i in range(N):
dp[0][i] = 1 # 一番左は0からN-1まで1通りずつ
for i in range(1,N):
if s[i-1] == ">": # dp[i-1][j]をdp[i][j-1],...,dp[i][0] に足す
x = dp[i-1][N-i]
for j in reversed(range(N-i)): # jが大きい要素から順に累積和を足す
dp[i][j] += x
dp[i][j] %= MOD
x += dp[i-1][j]
x %= MOD
else: # dp[i-1][j]をdp[i][j],...,dp[i][N-i-1] に足す。dp[i][j]が含まれる点に注意
x = dp[i-1][0]
for j in range(N-i): # jが小さい要素から順に累積和を足す
dp[i][j] += x
dp[i][j] %= MOD
x += dp[i-1][j+1]
x %= MOD
print(dp[N-1][0]) # 最後に置く値は必ず0番目に小さいのでdp[N-1][0]以外のdp[N-1]の要素は0
``` | instruction | 0 | 48,616 | 5 | 97,232 |
Yes | output | 1 | 48,616 | 5 | 97,233 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
n = int(input())
S = input()
p = 10**9 + 7
DP = [[0 for j in range(n + 1)] for i in range(n + 1)]
for j in range(n):
DP[1][j] = 1
for i in range(2, n + 1):
A = [0]
for j in range(n):
A.append(A[-1] + DP[i - 1][j])
for j in range(n - i + 1):
if S[i - 2] == '<':
DP[i][j] = (A[n - i + 1 + 1] - A[j + 1]) % p
else:
DP[i][j] = A[j + 1] % p
print(DP[n][0])
``` | instruction | 0 | 48,617 | 5 | 97,234 |
Yes | output | 1 | 48,617 | 5 | 97,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
n = int(input())
s = input()
# combinationの準備
md = 10 ** 9 + 7
n_max = 3005
fac = [1]
inv = [1] * (n_max + 1)
k_fac_inv = 1
for i in range(1, n_max + 1):
k_fac_inv = k_fac_inv * i % md
fac.append(k_fac_inv)
k_fac_inv = pow(k_fac_inv, md - 2, md)
for i in range(n_max, 1, -1):
inv[i] = k_fac_inv
k_fac_inv = k_fac_inv * i % md
def com(com_n, com_r):
return fac[com_n] * inv[com_r] * inv[com_n - com_r] % md
def way(a):
an = len(a)
if an <= 1: return 1
if a in memo: return memo[a]
res = 0
if a[0]: res += way(a[1:])
if not a[-1]: res += way(a[:-1])
for i in range(an - 1):
if not a[i] and a[i + 1]:
res += way(a[:i]) * way(a[i + 2:]) * com(an, i + 1)
res %= md
memo[a] = res
return res
memo = {}
def main():
a = [c == "<" for c in s]
a=tuple(a)
print(way(a))
main()
``` | instruction | 0 | 48,618 | 5 | 97,236 |
No | output | 1 | 48,618 | 5 | 97,237 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
n = int(input())
S = input()
p = 10**9 + 7
DP = [[0 for j in range(n + 1)] for i in range(n + 1)]
for i in range(2, n + 1):
A = [0]
for j in range(n):
A.append(A[-1] + DP[i - 1][j])
for j in range(n - i + 1):
if S[i - 2] == '<':
DP[i][j] = (A[n - (i - 1) + 1] - A[j + 1]) % p
else:
DP[i][j] = A[j + 1] % p
print(DP[n][0])
``` | instruction | 0 | 48,620 | 5 | 97,240 |
No | output | 1 | 48,620 | 5 | 97,241 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let N be a positive integer. You are given a string s of length N - 1, consisting of `<` and `>`.
Find the number of permutations (p_1, p_2, \ldots, p_N) of (1, 2, \ldots, N) that satisfy the following condition, modulo 10^9 + 7:
* For each i (1 \leq i \leq N - 1), p_i < p_{i + 1} if the i-th character in s is `<`, and p_i > p_{i + 1} if the i-th character in s is `>`.
Constraints
* N is an integer.
* 2 \leq N \leq 3000
* s is a string of length N - 1.
* s consists of `<` and `>`.
Input
Input is given from Standard Input in the following format:
N
s
Output
Print the number of permutations that satisfy the condition, modulo 10^9 + 7.
Examples
Input
4
<><
Output
5
Input
5
<<<<
Output
1
Input
20
>>>><>>><>><>>><<>>
Output
217136290
Submitted Solution:
```
from itertools import accumulate
MOD = 10**9+7
n = int(input())
S = input()
dp = [1]*n
for s in S:
if s == "<":
dp = list(accumulate(dp[::-1][:-1]))[::-1]
else:
dp = list(accumulate(dp[:-1]))
ans = dp[0]%MOD
print(ans)
``` | instruction | 0 | 48,621 | 5 | 97,242 |
No | output | 1 | 48,621 | 5 | 97,243 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,654 | 5 | 97,308 |
"Correct Solution:
```
x = int(input())
if x == 0:
print(4)
print(3, 3, 3, 3)
exit()
x-= 1
phase = x//50
subphase = x%50
pstart = phase*50
left = 99+phase-(x-pstart)
right = 48+phase-(x-pstart)
ans = [left]*(1+subphase)+[right]*(49-subphase)
print(50)
print(*ans)
``` | output | 1 | 48,654 | 5 | 97,309 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,655 | 5 | 97,310 |
"Correct Solution:
```
k = int(input())
n = 50
p = k // n
a = [i + p for i in range(n)]
m = k % n
for i in range(n) :
if i < m : a[i] += n - (m - 1)
else : a[i] -= m
print(n)
print(*a)
``` | output | 1 | 48,655 | 5 | 97,311 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,656 | 5 | 97,312 |
"Correct Solution:
```
# coding: utf-8
INF = 10 ** 20
MOD = 10 ** 9 + 7
def II(): return int(input())
def ILI(): return list(map(int, input().split()))
def read():
K = II()
return (K,)
def solve(K):
N = 50
a = [49] * N
div, mod = divmod(K, N)
for i in range(N):
a[i] += div
if mod != 0:
for i in range(mod):
a[i] += N - (mod - 1)
for i in range(mod, N):
a[i] += -mod
ans = "50\n" + " ".join(map(str, a))
return ans
def main():
params = read()
print(solve(*params))
if __name__ == "__main__":
main()
``` | output | 1 | 48,656 | 5 | 97,313 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,657 | 5 | 97,314 |
"Correct Solution:
```
K=int(input())
Q=K//50
R=K%50
ans=[49+Q]*50
for i in range(50):
if i<50-R:
ans[i]-=R
else:
ans[i]+=50-R+1
print(50)
print(' '.join(map(str,ans)))
``` | output | 1 | 48,657 | 5 | 97,315 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,658 | 5 | 97,316 |
"Correct Solution:
```
k = int(input())
n = 50
print(n)
l = []
for i in range(n):
tmp = [n+1-i]*i + [-i]*(n-i)
l.append(tmp)
res = []
for i in range(n):
res.append(k//n + i + l[k%n][i])
print(*res)
"""
for s in l:
print(*s)
"""
``` | output | 1 | 48,658 | 5 | 97,317 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,659 | 5 | 97,318 |
"Correct Solution:
```
k = int(input())
a,b = k//50, k%50
base = 49+(a if not b else a+1)
print(50)
if b==0:
print(" ".join(map(str, [base]*50)))
else:
i = 50 - b
print(" ".join(map(str, [base-50+i-1]*i + [base+i]*(50-i))))
``` | output | 1 | 48,659 | 5 | 97,319 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,660 | 5 | 97,320 |
"Correct Solution:
```
def ri(): return int(input())
def rli(): return list(map(int, input().split()))
def ris(): return list(input())
def pli(a): return "".join(list(map(str, a)))
def plis(a): return " ".join(list(map(str, a)))
K = ri()
X = K // 50
mod = K % 50
a = [49 - mod + X for i in range(50)]
for i in range(mod):
a[i] += 51
print(50)
print(plis(a))
``` | output | 1 | 48,660 | 5 | 97,321 |
Provide a correct Python 3 solution for this coding contest problem.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425 | instruction | 0 | 48,661 | 5 | 97,322 |
"Correct Solution:
```
from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import *
from bisect import bisect
def read():
return int(input())
def reads():
return [int(x) for x in input().split()]
K = read()
N = 50
print(N)
q, r = divmod(K, N)
ans = [q + 2 * N - r] * r + [q + N-1 - r] * (N - r)
print(' '.join(str(a) for a in ans))
``` | output | 1 | 48,661 | 5 | 97,323 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
* Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.
Constraints
* 0 ≤ K ≤ 50 \times 10^{16}
Input
Input is given from Standard Input in the following format:
K
Output
Print a solution in the following format:
N
a_1 a_2 ... a_N
Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.
Examples
Input
0
Output
4
3 3 3 3
Input
1
Output
3
1 0 3
Input
2
Output
2
2 2
Input
3
Output
7
27 0 0 0 0 0 0
Input
1234567894848
Output
10
1000 193 256 777 0 1 1192 1234567891011 48 425
Submitted Solution:
```
k = int(input())
n = 50
p = k // n
a = [i + p for i in range(n)]
m = k % n
for i in range(m) :
a[i] += n
for j in range(n) :
if i != j :
a[j] -= 1
print(n)
print(*a)
``` | instruction | 0 | 48,662 | 5 | 97,324 |
Yes | output | 1 | 48,662 | 5 | 97,325 |
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