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:
def FindAllElements(n, k): 
    sum = k 
    A = [1 for i in range(k)] 
    i = k - 1
    while(i >= 0): 
        while (sum + A[i] <= n): 
            sum += A[i] 
            A[i] *= 2
        i -= 1
      
    
    for i in range(0, k, 1): 
        print(A[i], end = ' ') 
  
n,k=[int(x) for x in input().split()]
temp=n
ans=1
curr=0
c=0
while n>0:
    bit=(n)&1
    if bit:
        c+=1
        ans*=2**curr
    n=n>>1
    curr+=1
#print(c)
if ans>=k and c<=k and temp>=k:
    print('YES')
    FindAllElements(temp,k)
    print()
else:
    print('NO')