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.
Write a program which reads a sequence and prints it in the reverse order.
Note
解説
Constraints
* n ≤ 100
* 0 ≤ ai < 1000
Input
The input is given in the following format:
n
a1 a2 . . . an
n is the size of the sequence and ai is the ith element of the sequence.
Output
Print the reversed sequence in a line. Print a single space character between adjacent elements (Note that your program should not put a space character after the last element).
Examples
Input
5
1 2 3 4 5
Output
5 4 3 2 1
Input
8
3 3 4 4 5 8 7 9
Output
9 7 8 5 4 4 3 3
Submitted Solution:
```
n =int(input())
a = list(map(int,input().split()))
a.reverse()
for i in range(n):
print(a[i],end=" ")
print()
``` | instruction | 0 | 41,201 | 5 | 82,402 |
No | output | 1 | 41,201 | 5 | 82,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.
There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:
* the number's length does not exceed n;
* the number doesn't have leading zeroes;
* digit i (0 ≤ i ≤ 9) occurs in the number at least a[i] times.
Input
The first line contains integer n (1 ≤ n ≤ 100). The next line contains 10 integers a[0], a[1], ..., a[9] (0 ≤ a[i] ≤ 100) — elements of array a. The numbers are separated by spaces.
Output
On a single line print the remainder of dividing the answer to the problem by 1000000007 (109 + 7).
Examples
Input
1
0 0 0 0 0 0 0 0 0 1
Output
1
Input
2
1 1 0 0 0 0 0 0 0 0
Output
1
Input
3
1 1 0 0 0 0 0 0 0 0
Output
36
Note
In the first sample number 9 meets the requirements.
In the second sample number 10 meets the requirements.
In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total.
Submitted Solution:
```
from math import factorial
dp=[[-1 for i in range (101)] for j in range(101)] # array utilizado para el mamoization donde se guardan las soluciones previamente calculadas
def solve(length,digit,a):
if dp[length][digit] is not -1:
return dp[length][digit] # si la solución ya fue precalculada se devuelve de manera instantanea
elif digit is 9:
if length >= a[9]:
return 1 # si al llegar al análisis del dígito 9 el espacio para ubicarlos
# es menor que la cantidad mínima a ubicar tengo una combinación válida
else:
return 0 # en caso contrario no puedo construir una combinación
elif digit is 0:
ans=0
for i in range(a[0],length):
partial = solve(length-i,1,a) # ubicando i ceros en la combinación comenzando
# en el mínimo que debo ubicar de ceros para obtener una posible combinación válida
partial = combinations(length-1, i) # se calculan cuantas combinaciones se pueden generar a partir de una distribución válida
# sin contar la primera posición (el cero no puede estar ubicado en la primera posición)
ans += partial
dp[length][digit] = ans #se guarda la respuesta calculada en su ubicación correspondiente en el array del memoization
return ans
else:
ans = 0
for i in range(a[digit],length+1):
partial = solve(length-i,digit+1,a) # se determina si ubicando i veces el dígito se puede llegar a una combinación válida
# comenzando i en la cantidad mínima a ubicar
partial = combinations(length, i) # se calculan la cantidad de combinaciones posibles a partir de una distribución válida
ans += partial
dp[length][digit] = ans
return ans
def combinations(n, k):
return factorial(n)//(factorial(k)*factorial(n-k)) # fórmula de combinaciones
max_val = 1000000007
length = int(input())
a = input().rstrip().split(' ')
min_length = 0
for i in range(0, len(a)):
a[i] = int(a[i])
min_length += int(a[i])
ans=0
for i in range(1, length+1):
ans += solve(i,0,a)
ans %= max_val
print(ans)
``` | instruction | 0 | 41,517 | 5 | 83,034 |
No | output | 1 | 41,517 | 5 | 83,035 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.
There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:
* the number's length does not exceed n;
* the number doesn't have leading zeroes;
* digit i (0 ≤ i ≤ 9) occurs in the number at least a[i] times.
Input
The first line contains integer n (1 ≤ n ≤ 100). The next line contains 10 integers a[0], a[1], ..., a[9] (0 ≤ a[i] ≤ 100) — elements of array a. The numbers are separated by spaces.
Output
On a single line print the remainder of dividing the answer to the problem by 1000000007 (109 + 7).
Examples
Input
1
0 0 0 0 0 0 0 0 0 1
Output
1
Input
2
1 1 0 0 0 0 0 0 0 0
Output
1
Input
3
1 1 0 0 0 0 0 0 0 0
Output
36
Note
In the first sample number 9 meets the requirements.
In the second sample number 10 meets the requirements.
In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total.
Submitted Solution:
```
from math import factorial
dp=[[-1 for i in range (101)] for j in range(101)] # array utilizado para el mamoization donde se guardan las soluciones previamente calculadas
def solve(length,digit,a):
if dp[length][digit] is not -1:
return dp[length][digit] # si la solución ya fue precalculada se devuelve de manera instantanea
elif digit is 9:
if length >= a[9]:
return 1 # si al llegar al análisis del dígito 9 el espacio para ubicarlos
# es menor que la cantidad mínima a ubicar tengo una combinación válida
else:
return 0 # en caso contrario no puedo construir una combinación
elif digit is 0:
ans=0
for i in range(a[0],length):
partial = solve(length-i,1,a) # ubicando i ceros en la combinación comenzando
# en el mínimo que debo ubicar de ceros para obtener una posible combinación válida
partial = combinations(length-1, i) # se calculan cuantas combinaciones se pueden generar a partir de una distribución válida
# sin contar la primera posición (el cero no puede estar ubicado en la primera posición)
ans += partial
dp[length][digit] = ans #se guarda la respuesta calculada en su ubicación correspondiente en el array del memoization
return ans
else:
ans = 0
for i in range(a[digit],length+1):
partial = solve(length-i,digit+1,a) # se determina si ubicando i veces el dígito se puede llegar a una combinación válida
# comenzando i en la cantidad mínima a ubicar
partial = combinations(length, i) # se calculan la cantidad de combinaciones posibles a partir de una distribución válida
ans += partial
dp[length][digit] = ans
return ans
def combinations(n, k):
return factorial(n)//(factorial(k)*factorial(n-k)) # fórmula de combinaciones
max_val = 1000000007
length = int(input())
a = input().rstrip().split(' ')
min_length = 0
for i in range(0, len(a)):
a[i] = int(a[i])
min_length += a[i]
ans=0
for i in range(min_length, length+1):
ans += solve(i,0,a)
ans %= max_val
print(ans)
``` | instruction | 0 | 41,518 | 5 | 83,036 |
No | output | 1 | 41,518 | 5 | 83,037 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.
There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:
* the number's length does not exceed n;
* the number doesn't have leading zeroes;
* digit i (0 ≤ i ≤ 9) occurs in the number at least a[i] times.
Input
The first line contains integer n (1 ≤ n ≤ 100). The next line contains 10 integers a[0], a[1], ..., a[9] (0 ≤ a[i] ≤ 100) — elements of array a. The numbers are separated by spaces.
Output
On a single line print the remainder of dividing the answer to the problem by 1000000007 (109 + 7).
Examples
Input
1
0 0 0 0 0 0 0 0 0 1
Output
1
Input
2
1 1 0 0 0 0 0 0 0 0
Output
1
Input
3
1 1 0 0 0 0 0 0 0 0
Output
36
Note
In the first sample number 9 meets the requirements.
In the second sample number 10 meets the requirements.
In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total.
Submitted Solution:
```
def condition3(i,c):
ret=True
s=str(i)
for i in range(10):
if s.count(str(i))<int(c[i]):
ret=False
return ret
def val_min(c):
sum=0
for i in c:
sum+=int(i)
return sum
n=int(input())
s=input()
c=s.split()
contador=0
for i in range(10**val_min(c),10**(n)):
if(condition3(i,c)):
contador+=1
m=10**9+7
print(contador%m)
``` | instruction | 0 | 41,519 | 5 | 83,038 |
No | output | 1 | 41,519 | 5 | 83,039 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
n = int(input())
def composite(n):
i = 2
while i <= n / i:
if n % i == 0:
return True
i += 1
return False
i = 4
while i <= n - i:
if composite(i) and composite(n - i):
break
i += 1
print(i, n - i)
``` | instruction | 0 | 41,602 | 5 | 83,204 |
Yes | output | 1 | 41,602 | 5 | 83,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
n = int(input())
a = [4, 6, 8, 9, 10]
if (n / 2) % 2 == 0:
print(int(n/2), int(n/2))
else:
for i in a:
x = n - i
if x % 2 == 0:
print(i, x)
break
``` | instruction | 0 | 41,604 | 5 | 83,208 |
Yes | output | 1 | 41,604 | 5 | 83,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
n = int(input())
if (n % 2 == 0):
t = n - 8
else:
t = n - 9
print(t)
print(n - t)
``` | instruction | 0 | 41,605 | 5 | 83,210 |
Yes | output | 1 | 41,605 | 5 | 83,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
n=int(input())
d=[4,6,8][n%3]
print(d,n-d)
``` | instruction | 0 | 41,606 | 5 | 83,212 |
No | output | 1 | 41,606 | 5 | 83,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
n = int(input())
if n % 2 == 0:
print(f'{n / 2} {n / 2}')
else:
print(f'9 {n - 9}')
``` | instruction | 0 | 41,607 | 5 | 83,214 |
No | output | 1 | 41,607 | 5 | 83,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
a=int(input())
if(a%2!=0):
b=a-9
f=9
else:
b=f=a//2
print(b,f)
``` | instruction | 0 | 41,608 | 5 | 83,216 |
No | output | 1 | 41,608 | 5 | 83,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One way to create a task is to learn from math. You can generate some random math statement or modify some theorems to get something new and build a new task from that.
For example, there is a statement called the "Goldbach's conjecture". It says: "each even number no less than four can be expressed as the sum of two primes". Let's modify it. How about a statement like that: "each integer no less than 12 can be expressed as the sum of two composite numbers." Not like the Goldbach's conjecture, I can prove this theorem.
You are given an integer n no less than 12, express it as a sum of two composite numbers.
Input
The only line contains an integer n (12 ≤ n ≤ 106).
Output
Output two composite integers x and y (1 < x, y < n) such that x + y = n. If there are multiple solutions, you can output any of them.
Examples
Input
12
Output
4 8
Input
15
Output
6 9
Input
23
Output
8 15
Input
1000000
Output
500000 500000
Note
In the first example, 12 = 4 + 8 and both 4, 8 are composite numbers. You can output "6 6" or "8 4" as well.
In the second example, 15 = 6 + 9. Note that you can't output "1 14" because 1 is not a composite number.
Submitted Solution:
```
def main():
x = int(input())
print(x//2)
if x % 2 == 0:
print(x//2)
else:
print(x//2 + 1)
main()
``` | instruction | 0 | 41,609 | 5 | 83,218 |
No | output | 1 | 41,609 | 5 | 83,219 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,800 | 5 | 83,600 |
Tags: bitmasks, greedy, math
Correct Solution:
```
inp=lambda:map(int,input().split())
n,k=inp()
n2=n
a=[0]*100
i=0
while(n2>0):
a[i]=n2%2
n2//=2
i+=1
cnt=i-1
cnt2=cnt
sum=0
arr=[0]*(10**7+1)
q=[0]*(10**7+1)
for i in range(cnt,-1,-1):
sum+=a[i]
q[i]=a[cnt-i]
if sum>k:
print("No")
quit()
k2=k-sum
beg=0
while k2>0:
if(q[beg]<=k2):
k2-=q[beg]
q[beg+1]+=2*q[beg]
q[beg]=0
beg+=1
else:
break
cnt+=1000
while(q[cnt]==0):
cnt-=1
while k2>0:
q[cnt]-=1
q[cnt+1]+=2
cnt+=1
k2-=1
print("Yes");
for i in range(beg,cnt+1):
for j in range(1,q[i]+1):
print(cnt2-i,'', end='')
``` | output | 1 | 41,800 | 5 | 83,601 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,801 | 5 | 83,602 |
Tags: bitmasks, greedy, math
Correct Solution:
```
from sys import stdin, stdout
from decimal import Decimal
n, k = map(int, stdin.readline().split())
s = list(map(int, list(bin(n)[2:])))
ans = {}
pw = len(s) - 1
for i in range(len(s)):
if s[i]:
ans[len(s) - i - 1] = 1
k -= s.count(1)
if k < 0:
stdout.write('No')
else:
for i in range(pw, -100, -1):
if i in ans and ans[i] <= k:
if i - 1 in ans:
ans[i - 1] += 2 * ans[i]
else:
ans[i - 1] = 2 * ans[i]
k -= ans[i]
ans[i] = 0
elif i in ans and ans[i] > k:
break
if k:
ind = min(list(ans.keys()))
ans[ind] -= 1
ind -= 1
for i in range(k):
if i + 1 == k:
if ind in ans:
ans[ind] += 2
else:
ans[ind] = 2
else:
if ind in ans:
ans[ind] += 1
else:
ans[ind] = 1
ind -= 1
stdout.write('Yes\n')
values = sorted(list(ans.keys()), reverse = True)
for v in values:
if ans[v]:
stdout.write(' '.join(list(map(str, [v for i in range(ans[v])]))) + ' ')
``` | output | 1 | 41,801 | 5 | 83,603 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,802 | 5 | 83,604 |
Tags: bitmasks, greedy, math
Correct Solution:
```
#! /usr/bin/env python3
'''
Author: krishna
Created: Fri Jan 19 20:39:10 2018 IST
File Name: b.py
USAGE:
b.py
Description:
'''
import sys, os
def main():
'''
The Main
'''
n, k = map(int, sys.stdin.readline().split())
x = bin(n)[2:]
if x.count('1') > k:
print("No")
return
ans = [0] * (10 ** 5)
val = len(x) - 1
idx = len(x) - 1
cnt = 0
for i in x:
if (int(i)):
ans[val] = 1
# print(val)
cnt += 1
val -= 1
for i in range(k-cnt):
ans[idx] -= 1
ans[idx-1] += 2
if (ans[idx] == 0):
idx -= 1
# print(ans[18])
# return
maxIdx = idx - 1
minIdx = idx - 1
nonZeroIdx = idx - 1
while (1):
if (minIdx < 0) and (ans[minIdx] == 0):
minIdx += 1
break
if ans[minIdx]:
nonZeroIdx = minIdx
minIdx -= 1
minIdx = nonZeroIdx
# print(ans[0:10])
# print(maxIdx, minIdx)
while (1):
if (
(ans[maxIdx] > 2)
or ((ans[maxIdx] == 2 )and (maxIdx != minIdx))
):
ans[minIdx] -= 1
ans[minIdx - 1] += 2
ans[maxIdx] -= 2
ans[maxIdx + 1] += 1
minIdx -= 1
else:
maxIdx -= 1
if (maxIdx <= minIdx):
break
print("Yes")
x = []
while (1):
for i in range(ans[idx]):
x.append(idx)
idx -= 1
if (idx < 0) and (ans[idx] == 0):
break
# print([(i, ans[i]) for i in range(len(ans)) if ans[i] < 0])
# print(sum(ans))
# print(len(x))
print(" ".join(map(str, x)))
if __name__ == '__main__':
main()
``` | output | 1 | 41,802 | 5 | 83,605 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,803 | 5 | 83,606 |
Tags: bitmasks, greedy, math
Correct Solution:
```
read = lambda: map(int, input().split())
n, k = read()
b = bin(n)[2:]
bl = len(b)
k -= b.count('1')
if k < 0:
print('No')
exit()
print('Yes')
m = -2
a = {}
for _ in range(bl):
if b[_] == '1':
a[bl - _ - 1] = 1
if m is -2:
m = bl - _ - 1
while k > 0:
if k >= a[m]:
k -= a[m]
a[m - 1] = a.get(m - 1, 0) + a[m] * 2
a.pop(m)
m -= 1
else:
break
m = min(a.keys())
while k > 0:
k -= 1
if a[m] is 1:
a.pop(m)
else:
a[m] -= 1
a[m - 1] = a.get(m - 1, 0) + 2
m -= 1
for k in sorted(list(a.keys()), reverse=True):
print(('%d ' % k) * a[k], end='')
``` | output | 1 | 41,803 | 5 | 83,607 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,804 | 5 | 83,608 |
Tags: bitmasks, greedy, math
Correct Solution:
```
inp=lambda:map(int,input().split())
n,k=inp()
n2=n
a=[0]*100
i=0
while(n2>0):
a[i]=n2%2
n2//=2
i+=1
cnt=i-1
cnt2=cnt
sum=0
arr=[0]*(10**7+1)
q=[0]*(10**7+1)
for i in range(cnt,-1,-1):
sum+=a[i]
q[i]=a[cnt-i]
if sum>k:
print("No")
quit()
k2=k-sum
beg=0
while k2>0:
if(q[beg]<=k2):
k2-=q[beg]
q[beg+1]+=2*q[beg]
q[beg]=0
beg+=1
else:
break
cnt+=1000
while(q[cnt]==0):
cnt-=1
while k2>0:
q[cnt]-=1
q[cnt+1]+=2
cnt+=1
k2-=1
print("Yes")
for i in range(beg,cnt+1):
for j in range(1,q[i]+1):
print(cnt2-i,'', end='')
``` | output | 1 | 41,804 | 5 | 83,609 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,805 | 5 | 83,610 |
Tags: bitmasks, greedy, math
Correct Solution:
```
def solve(n, k):
bn = binary(n)
if k < len(bn):
return 'No'
cur_dec = len(bn)
next_dec = cur_dec+1
while True:
if k < next_dec:
dif = k - cur_dec
bn = list(reversed(bn))
for _ in range(dif):
e = bn.pop()
bn += [e-1, e-1]
return 'Yes\n' + ' '.join(map(str,bn))
cur_dec = next_dec
cnt = bn.count(bn[-1])
bn = bn[:-cnt] + [bn[-1]-1]*(cnt*2)
next_dec = cur_dec+bn.count(bn[-1])
def binary(x):
out = []
for i in reversed(range(64+1)):
if x >= 2**i:
x -= 2**i
out.append(i)
return list(reversed(out))
if __name__ == '__main__':
n, k = map(int, input().split())
print(solve(n, k))
``` | output | 1 | 41,805 | 5 | 83,611 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,806 | 5 | 83,612 |
Tags: bitmasks, greedy, math
Correct Solution:
```
ii=lambda:int(input())
kk=lambda:map(int, input().split())
ll=lambda:list(kk())
from math import log
elems = [0]*126
n,k=kk()
c=0
for i in range(63):
if n&(2**i):
elems[i]=1
c+=1
if c > k:
print("No")
exit()
for i in range(63, -63,-1):
if elems[i]:
if elems[i] > k-c:
#stop it, now reverse sweep
break
c+=elems[i]
elems[i-1] += elems[i]*2
elems[i] = 0
prin = []
for i in range(63, -63, -1):
prin.extend([i]*elems[i])
while len(prin)<k:
prin[-1]-=1
prin.append(prin[-1])
print("Yes")
print(" ".join(map(str, prin)))
``` | output | 1 | 41,806 | 5 | 83,613 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ. | instruction | 0 | 41,807 | 5 | 83,614 |
Tags: bitmasks, greedy, math
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
# 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")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0
def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0
def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2)
mod = 998244353
INF = float('inf')
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush
from math import log2
# ------------------------------
def main():
n, k = RL()
# print(bin(n))
ones = bin(n).count('1')
if ones>k:
print('No')
else:
res = []
carr = 0
pt = -60
for i in range(60, 0, -1):
if n>>i & 1:
ones-=1
carr+=1
if carr*2+ones>k:
res.extend([i]*carr)
pt = i-1
for j in range(pt, -1, -1):
if n >> j & 1:
res.append(j)
break
carr*=2
else:
if n&1: carr+=1
now = 0
while carr*2<=k:
carr*=2
now-=1
res.extend([now]*carr)
# print(res)
dif = k-len(res)
if dif>0:
lst = res.pop()
dif+=1
now = 1
pos = lst
res.extend([lst-i for i in range(1, dif-1)])
res.extend([lst-dif+1]*2)
# while now<=dif:
# if now*2>=dif:
# mv = dif-now
# # print(mv, '===', dif, now, pos)
# res.extend([pos]*(now-mv))
# res.extend([pos-1]*(mv*2))
# break
# else:
# res.append(lst-1)
#
# pos-=1
# now*=2
print("Yes")
print(*res)
if __name__ == "__main__":
main()
``` | output | 1 | 41,807 | 5 | 83,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
from heapq import heapify,heappop,heappush
n, k = map(int, input().split())
heap1 = []
heap2 = []
MAX = int(1e5)+10
s = []
heapify(heap1)
heapify(heap2)
i = 0
cnt = 0
while 1 << i <= n:
if 1<<i & n: heappush(heap1,-i);heappush(heap2,-i);cnt += 1
i += 1
if cnt > k: print("NO");exit()
temp = cnt
while temp < k:
x = -1 * heappop(heap1) - 1
heappush(heap1,-x)
heappush(heap1,-x)
temp += 1
temp = heap1[0] * -1
while cnt < k:
if temp == heap2[0] * -1: break
x = heappop(heap2) * -1 - 1
heappush(heap2,-x)
heappush(heap2,-x)
cnt += 1
while heap2:
s.append(heappop(heap2)*-1)
while cnt < k:
s[-1] = s[-1] - 1
s.append(s[-1])
cnt += 1
print("YES")
print(*s)
``` | instruction | 0 | 41,808 | 5 | 83,616 |
Yes | output | 1 | 41,808 | 5 | 83,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
n,k=map(int,input().split())
a=list(bin(n))
a=a[2:]
b=[]
for i in range(100005):
b.append(0)
l=len(a)
c=0
for i in range(l):
if(a[i]=="1"):
b[65-(l-i-1)]=1
c+=1
lini=65-(l-i-1)
if(c<=k):
gfati=0
for i in range(129):
if(gfati==1):
break
if(c==k):
break
if(b[i]==0):
continue
else:
if(i>lini):
lini=i
#print(c,2*b[i])
if(c+b[i]<=k):
#print("why")
b[i+1]+=2*b[i]
c+=b[i]
b[i]=0
else:
gfati=1
#print(c,lini)
if(1):
for i in range(lini,1000005,1):
if(c==k):
break
if(b[i]!=0):
if(c+1<=k):
b[i]-=1
c+=1
b[i+1]+=2
print("Yes")
for i in range(100005):
if(b[i]!=0):
for j in range(b[i]):
print(65-i,end=" ")
else:
print("No")
``` | instruction | 0 | 41,809 | 5 | 83,618 |
Yes | output | 1 | 41,809 | 5 | 83,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
def count1(n):
count = 0
while n > 0:
n &= (n-1)
count+= 1
return count
def find(n, k):
ones = count1(n)
l = list()
if ones > k:
print('No')
else:
tmp = n
pow2 = 1
index = 0
while tmp > 0:
if tmp % 2 == 1:
l.append(index)
tmp //= 2
pow2 *= 2
index += 1
length = len(l)
while length < k:
m = max(l)
c = l.count(m)
rem = [i for i in l if i < m]
if k - length >= c:
rem += [m-1]*(2*c)
l = rem
length = len(l)
else:
# to_add = k - length
# rem += [m] * (c - to_add) + [m-1] * (to_add * 2)
mini = min(l)
to_fill = k - length
l.remove(mini)
for i in range(to_fill):
mini -=1
l.append(mini)
l.append(mini)
break
print('Yes')
l.sort(reverse=True)
# print(len(l))
print(' '.join([str(i) for i in l]))
# find(23,5)
# find(13,2)
# find(1,2)
nn, kk = list(map(int, input().strip().split()))
find(nn, kk)
# find(1000000000000000000, 100000)
``` | instruction | 0 | 41,810 | 5 | 83,620 |
Yes | output | 1 | 41,810 | 5 | 83,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
import math
x, k = map(int, input().split())
kori = k
a = bin(x)
# s = a[2:len(a)]
qtz = 0;
s = []
for i in range(2, len(a)):
if a[i] == "1":
k-=1
s.append(1)
else:
qtz+=1
s.append(0)
v = []
for i in range(len(s)):
if s[i] != 0:
v.append((len(s)-1)-i)
# else:
# v.append("x")
# print(qtz, k)
if k < 0:
print("No")
exit()
else:
tam = len(s)
# print(tam)
print("Yes")
# print(k, s)
if k > 0:
p = 0
#diminui o y máximo
while(1):
# print(p, s[p], len(s))
if tam - 1 <= p:
s.append(0)
if s[p] > k:
break
else:
k-= s[p]
s[p+1] += s[p]*2
s[p] = 0
p+=1
#se k ainda for maior que zero
if k > 0:
j = len(s)-1
while k > 0:
while s[j] == 0:
j-=1
s[j] -= 1
if j == len(s)-1:
s.append(2)
j+=1
else:
s[j+1] += 2
j+=1
k-=1
# print(s)
v = []
for i in range(len(s)):
for j in range(s[i]):
v.append((tam-1) -i)
print(*v)
else:
v = []
for i in range(len(s)):
for j in range(s[i]):
v.append(len(s)-1 -i)
print(*v)
``` | instruction | 0 | 41,811 | 5 | 83,622 |
Yes | output | 1 | 41,811 | 5 | 83,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
n,m = list(map(int,input().split()))
max_pows = -1
temp = n
list_pow = {}
while temp >0:
factor = -1
index = 1
while index <= temp:
index *=2
factor +=1
temp = temp - index//2
if max_pows == -1:
max_pows = factor
list_pow[factor] = 1
min_pows = factor
if len(list_pow) > m:
print("No")
else:
pow_count = len(list_pow)
cur_pow = max_pows
while pow_count + list_pow[cur_pow] <=m:
if list_pow[cur_pow]!=0:
list_pow[cur_pow] -=1
if cur_pow - 1 in list_pow:
list_pow[cur_pow - 1] +=2
else:
list_pow[cur_pow - 1] = 2
pow_count +=1
else:
cur_pow -=1
cur_pow = min_pows
while pow_count!= m:
if list_pow[cur_pow]!=0:
list_pow[cur_pow] -=1
if cur_pow - 1 in list_pow:
list_pow[cur_pow - 1] +=2
else:
list_pow[cur_pow - 1] = 2
pow_count +=1
else:
cur_pow -=1
print("Yes")
cur_count = 0
while cur_count !=m:
if max_pows in list_pow:
for i in range(list_pow[max_pows]):
cur_count +=1
print(max_pows,end = " ")
max_pows -=1
``` | instruction | 0 | 41,812 | 5 | 83,624 |
No | output | 1 | 41,812 | 5 | 83,625 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
n, k = [int(x) for x in input().split()]
s = bin(n).count("1")
found = False
for i in range(s):
v = 2 ** i
v2 = n // v
rest = n % v
rest_length = bin(rest).count("1")
if v2 + rest_length <= k:
found = True
ans = [i] * v2 + [j for j, b in enumerate(bin(rest)[2:][::-1]) if b == '1'][::-1]
while len(ans) < k:
ans = sorted([ans[0] - 1] * 2 + ans[1:])[::-1]
print(" ".join(map(str, ans)))
break
if not found:
print("No")
``` | instruction | 0 | 41,813 | 5 | 83,626 |
No | output | 1 | 41,813 | 5 | 83,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time : 2017/10/20 13:52
# @Author : litianshuang
# @Email : litianshuang@jingdata.com
# @File : test.py
# @Desc :
if __name__== "__main__":
h, k = [int(n) for n in input().split(' ')]
level = 0
ret = []
while h > 0:
if h % 2 == 0:
h //= 2
level += 1
else:
ret.append(level)
h -= 1
ret.sort()
if level >= k:
print('No')
else:
print('Yes')
cntnum = {}
maxn = ret[0]
minn = ret[0]
total_len = len(ret)
for i in ret:
if i not in cntnum:
cntnum[str(i)] = 0
cntnum[str(i)] += 1
if maxn < i:
maxn = i
if minn > i:
minn = i
while total_len <= k:
if total_len + cntnum[str(maxn)] <= k:
if str(maxn - 1) not in cntnum:
cntnum[str(maxn - 1)] = 0
cntnum[str(maxn-1)] += 2 * cntnum[str(maxn)]
total_len += cntnum[str(maxn)]
cntnum[str(maxn)] = 0
maxn -= 1
else:
break
while total_len < k:
cntnum[str(minn - 1)] = 2
cntnum[str(minn)] -= 1
minn -= 1
total_len += 1
ans = []
for num, v in cntnum.items():
for i in range(0, v):
ans.append(int(num))
ans.sort(reverse=True)
print(" ".join([str(x) for x in ans]))
``` | instruction | 0 | 41,814 | 5 | 83,628 |
No | output | 1 | 41,814 | 5 | 83,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:
Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one.
To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.
For definitions of powers and lexicographical order see notes.
Input
The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.
Output
Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.
It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].
Examples
Input
23 5
Output
Yes
3 3 2 1 0
Input
13 2
Output
No
Input
1 2
Output
Yes
-1 -1
Note
Sample 1:
23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23
Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.
Answers like (4, 1, 1, 1, 0) do not have the minimum y value.
Sample 2:
It can be shown there does not exist a sequence with length 2.
Sample 3:
<image>
Powers of 2:
If x > 0, then 2x = 2·2·2·...·2 (x times).
If x = 0, then 2x = 1.
If x < 0, then <image>.
Lexicographical order:
Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
Submitted Solution:
```
import math
n, k = map(int, input().split())
binn=[]
t = n
sb = 0
val=[0]*128
ind = 0
small = 0
one = True
while t > 0:
binn.append(t%2)
if t%2 == 1:
sb += 1
if one:
small = ind
one = False
t = math.trunc(t/2)
ind = ind + 1
#print("small = ", small)
ind = ind - 1
if k < sb:
print("No")
exit(0)
rem = k - sb
#print("k = ", k, " set bits = ", sb)
ans = []
for i in range(0, ind+1):
ans.append([i, binn[i]])
index = len(ans) - 1
isave = index
c=1
one = True
while rem!=0:
shift = 0
#print("at index ", index, " 0 = ", ans[index][0], " 1 = ", ans[index][1])
if ans[index][1] <= rem:
#remove all
shift = ans[index][1]
else:
index = small
one=False
if not one:
shift = 1
if index - 1 < 0:
ans[0][1] -= shift
ans.insert(0, [index - c, 2*shift])
else:
ans[index-1][1] += 2*shift
ans[index][1] -= shift
rem -= shift
#print("rem = ",rem, " shifted = ", shift)
index -= 1
if index < 0:
index = 0
c+=1
print("Yes")
res = ""
aa = 0
count=0
for i in range(len(ans)-1, -1, -1):
if ans[i][1] > 0:
res = res + (str(ans[i][0])+" ")*ans[i][1]
#if ans[i][0]>0:
#print(ans[i][0], " x ", ans[i][1])
#aa += pow(2, (ans[i][0]))*ans[i][1]
#count+=ans[i][1]
print(res)
``` | instruction | 0 | 41,815 | 5 | 83,630 |
No | output | 1 | 41,815 | 5 | 83,631 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,837 | 5 | 83,674 |
"Correct Solution:
```
a = int(input())
print(a*(1+a+a**2))
``` | output | 1 | 41,837 | 5 | 83,675 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,838 | 5 | 83,676 |
"Correct Solution:
```
n=int(input())
#s=input()
print(n+n**2+n**3)
``` | output | 1 | 41,838 | 5 | 83,677 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,839 | 5 | 83,678 |
"Correct Solution:
```
x=input()
X=int(x)
y=X+X**2+X**3
print(y)
``` | output | 1 | 41,839 | 5 | 83,679 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,840 | 5 | 83,680 |
"Correct Solution:
```
a=int(input())
a=a+a**2+a**3
print(a)
``` | output | 1 | 41,840 | 5 | 83,681 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,841 | 5 | 83,682 |
"Correct Solution:
```
x = int(input())
print(str(x**3 + x**2 + x ))
``` | output | 1 | 41,841 | 5 | 83,683 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,842 | 5 | 83,684 |
"Correct Solution:
```
#abc172a
a=int(input())
print(a+a*a+a*a*a)
``` | output | 1 | 41,842 | 5 | 83,685 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,843 | 5 | 83,686 |
"Correct Solution:
```
a=int(input())
t=1+a+a**2
print(t*a)
``` | output | 1 | 41,843 | 5 | 83,687 |
Provide a correct Python 3 solution for this coding contest problem.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110 | instruction | 0 | 41,844 | 5 | 83,688 |
"Correct Solution:
```
n=int(input())
b=n+(n*n)+(n*n*n)
print(b)
``` | output | 1 | 41,844 | 5 | 83,689 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a = int(input())
res = a+a**2+a**3
print(res)
``` | instruction | 0 | 41,845 | 5 | 83,690 |
Yes | output | 1 | 41,845 | 5 | 83,691 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a = int(input())
print(round(a*a*a+a*a+a))
``` | instruction | 0 | 41,846 | 5 | 83,692 |
Yes | output | 1 | 41,846 | 5 | 83,693 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
k = int(input())
print(int(k+k**2+k**3))
``` | instruction | 0 | 41,847 | 5 | 83,694 |
Yes | output | 1 | 41,847 | 5 | 83,695 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a=int(input())
s=a+a*a+a*a*a
print(int(s))
``` | instruction | 0 | 41,848 | 5 | 83,696 |
Yes | output | 1 | 41,848 | 5 | 83,697 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a = int(intput())
print(a+a**2 + a**3)
``` | instruction | 0 | 41,849 | 5 | 83,698 |
No | output | 1 | 41,849 | 5 | 83,699 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a = 2
def calc(a):
step2 = a**2
step3 = a**3
return int(a+step2+step3)
print(calc(a))
``` | instruction | 0 | 41,850 | 5 | 83,700 |
No | output | 1 | 41,850 | 5 | 83,701 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
num = int(input())
print(num + num * mum + num ** 3)
``` | instruction | 0 | 41,851 | 5 | 83,702 |
No | output | 1 | 41,851 | 5 | 83,703 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an integer a as input, print the value a + a^2 + a^3.
Constraints
* 1 \leq a \leq 10
* a is an integer.
Input
Input is given from Standard Input in the following format:
a
Output
Print the value a + a^2 + a^3 as an integer.
Examples
Input
2
Output
14
Input
10
Output
1110
Submitted Solution:
```
a = int(input())
total = a + a**2 + a**3
ptint(total)
``` | instruction | 0 | 41,852 | 5 | 83,704 |
No | output | 1 | 41,852 | 5 | 83,705 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58 | instruction | 0 | 41,910 | 5 | 83,820 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
A = list(map(int, input().split()))
bit = 1
for a in A:
bit |= (bit<<a)
S = sum(A)
for i in range((S+1)//2, S+1):
if bit&(1<<i):
print(i)
break
``` | output | 1 | 41,910 | 5 | 83,821 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58 | instruction | 0 | 41,911 | 5 | 83,822 |
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split()))
S = sum(A)
M = (S+1)//2
dp = 1
for a in A:
dp |= (dp<<a)
ans = M
while 1:
if dp&(1<<ans):
print(ans)
exit()
ans += 1
``` | output | 1 | 41,911 | 5 | 83,823 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58 | instruction | 0 | 41,913 | 5 | 83,826 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
sm = sum(a)
dp = 1
for i in range(N): dp |= (dp << a[i])
#print(dp)
x = 1 << ((sm + 1) // 2)
for i in range((sm + 1) // 2 + 1):
if dp & x:
print((sm + 1) // 2 + i)
break
x <<= 1
``` | output | 1 | 41,913 | 5 | 83,827 |
Provide a correct Python 3 solution for this coding contest problem.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58 | instruction | 0 | 41,914 | 5 | 83,828 |
"Correct Solution:
```
import sys
readline = sys.stdin.readline
N = int(readline())
A = list(map(int, readline().split()))
S = sum(A)
bits = 1
for a in A:
bits |= bits << a
ans = (S + 1) // 2
bits >>= ans
while True:
if bits & 1:
print(ans)
exit()
bits >>= 1
ans += 1
``` | output | 1 | 41,914 | 5 | 83,829 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58
Submitted Solution:
```
import sys
readline = sys.stdin.readline
N = int(readline())
A = list(map(int, readline().split()))
S = sum(A)
dp = 1
for a in A:
dp |= dp<<a
dp ^= dp&((1<<(-(-S//2))) - 1)
print((-dp&dp).bit_length() - 1)
``` | instruction | 0 | 41,917 | 5 | 83,834 |
Yes | output | 1 | 41,917 | 5 | 83,835 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58
Submitted Solution:
```
import sys
input = sys.stdin.readline
n = int(input())
A = list(map(int, input().split()))
M = sum(A)
s = 1 << M
for a in A:
s |= s >> a
ans = bin(s)[2+(M+1)//2:].find("1") + (M+1)//2
print(ans)
``` | instruction | 0 | 41,918 | 5 | 83,836 |
Yes | output | 1 | 41,918 | 5 | 83,837 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.
Constraints
* 1 \leq N \leq 2000
* 1 \leq A_i \leq 2000
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the median of the sorted list of the sums of all non-empty subsequences of A.
Examples
Input
3
1 2 1
Output
2
Input
1
58
Output
58
Submitted Solution:
```
n=int(input())
A=[int(i) for i in input().split()]
dp=1
for i in range(n):
now=A[i]
dp=dp|(dp<<now)
for i in range((sum(A)+1)//2,sum(A)+1):
if dp&(1<<i)>0:
print(i)
break
``` | instruction | 0 | 41,919 | 5 | 83,838 |
Yes | output | 1 | 41,919 | 5 | 83,839 |
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