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 math import log2

def main():
  n,k = map(int, input().strip().split())
  nb = bin(n)[2:]
  if (nb.count('1') > k):
    print('NO')
    return
  if (n < k):
    print('NO')
    return
  
  n += 1
  ans = []
  while k > 0:
    d = n - k # >= 0
    b = 1
    while d >= (b << 1):
      b = b << 1
    ans.append(b)
    n -= b
    k -= 1
  
  print('YES')
  for x in ans:
    print(x, end=' ')
  print()

if __name__ == "__main__":
  main()