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:
n,k = map(int, raw_input().split())
a = []
result = []
b = 0
x = 1

if n >= k :
  while x <= pow(10, 9) :
    x = pow(2, b)
    a.append(x)
    b = b + 1

  a.sort(reverse=True)

  for m in a :
    if (n - m) >= 0:
      n = n - m
      result.append(m)

  result.sort(reverse=True)
  if k < len(result) :
    print 'NO'
  else :
    print 'YES'
    if k == len(result):
      print ' '.join(str(x) for x in result)
    else:
      index = 0
      while index < len(result):
        if k == len(result):
          index += 1
          continue
        else:
          if result[index] == 1 :
            index += 1
            continue
          else :
            aa = result[index] / 2
            result.append(aa)
            result[index] = aa
      print ' '.join(str(x) for x in result)
else :
  print 'NO'