Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout
import collections
import math

#N = int(input())

N,K = [int(x) for x in stdin.readline().split()]   

b = "{0:b}".format(N)

ones = 0
for bit in b:
    if bit=='1':
        ones += 1

if K<ones or K>N:
    print('NO')
    quit()
else:
    b = [int(x) for x in list(b)]
    
    cur = ones
    for i in range(len(b)-1):
        if b[i]+cur<K:
            cur += b[i]
            b[i+1] += b[i]*2
            b[i] = 0
        else:
            d = K - cur
            b[i+1] += 2*d
            b[i] -= d
            break
        #print(cur,b)
        
    print('YES')  
    b = b[::-1]
    for i in range(len(b)):
        for j in range(b[i]):
            print(2**i,end=' ')