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 PYTHON):

Solution:
R = lambda: map(int, raw_input().split())

n, k = R()
if k > n:
  print 'NO'
else:
  a = []
  while n:
    a += n & -n,
    n -= a[-1]
  if k < len(a):
    print 'NO'
  else:
    o = 0
    while len(a) + o < k:
      b = a.pop() / 2
      if b > 1:
        a += b,
        a += b,
      else:
        o += 2
    print 'YES'
    print ' '.join(map(str, sorted([1] * o + a)))