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

l1 = input().split()
#l2 = input().split()

l1 = [int(i) for i in l1]
#l2 = [int(i) for i in l2]

n = l1[0]
k = l1[1]

i = 30;
s = 0;
r = []


while(i>=0 and k):
  m = 1 << i;
  if(m>n or n-m < k-1):
    i -= 1;
    continue;
  s+=m;
  r.append(m);
  n-=m;
  k -= 1;

if(r.__len__()==l1[1] and s==l1[0]):
  print("YES");
  for e in r:
    print(str(e) + " ", end='')
else:
    print("NO");