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:
t, k = map(int, input().split())

s = str(bin(t))[2:]

if (t < k or k < s.count("1")):
  print("NO")
else:
  l = [int(i) for i in s]
  l.reverse()
  for i in range(len(l)-1, 0, -1):
    if l[i] != 0:
      if sum(l)+l[i] < k:
        l[i-1] += 2*l[i]
        l[i] = 0
      else:
        t = k-sum(l)
        l[i-1] += t*2
        l[i] -= t
  print("YES")
  for i in range(len(l)):
    print((l[i]*(str(2**i) + " ")), end = "")