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:
def main():
    n, k= map(int, raw_input().split())
    
    if k > n:
      print "NO"
      return
    
    b = map(int, '{0:b}'.format(n))
    c = sum(b)
    
    if c > k:
      print "NO"
    else:
      rem = k - c
      ind = 0
      while rem > 0:
        if b[ind] > 0:
          b[ind] -= 1
          b[ind+1] += 2
          rem -= 1
        else:
          ind += 1
          
      print "YES"
      b = b[::-1]
      ans = []
      for i in xrange(len(b)):
        ans.extend([2**i for _ in xrange(b[i])])
      print " ".join(map(str, ans))
    

if __name__ == '__main__':
    main()