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:
# powers of two

def main():
    n,k = map(int,input().split())
    n = bin(n)[2:]
    n = [int(x) for x in n]
    vetor = []
    soma = 0
    for d in n:
        vetor.append(d)
        soma += d
    p = 0    
    while p < len(n)-1 and soma < k:
        if vetor[p]>0:
            vetor[p] -= 1
            vetor[p+1] += 2
            soma += 1
        else:
            p += 1
    if soma ==k :
        print("YES")            
        vetor.reverse() 
        for i in range(len(vetor)):
            for j in range(vetor[i]):
                print(2**i,end = " ")
        print()
    else:
        print("NO")    

main()