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:
import math

n, k = list(map(int, input().split()))
t = n-k
sm = 0

ost = []
pos = []

i = 0
ln = n
lk = k

if t==0:
  rs = [1]*k
  print('YES')
  print(*rs)

else:
 
  while(t!=0):
    k = min(n//2, t)
    t-=k
    e = n-k*2
    n = n//2
    ost.append(e)
    pos.append(k)
    i+=1
    if i>int(math.log(ln, 2)):
      print('NO')
      exit()

  res = []
  for i in range(len(ost)):
    res+=[2**i]*ost[i]

  x = len(pos)
  if x!=0:
    res+=pos[-1]*[2**x]


  if lk>ln:
    print('NO')
  else:
    print('YES')
    print(*res)