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 main():
    n, k = [int(i) for i in input().split()]

    if n < k:
        print("NO")
        return
    
    res = [1] * k

    if n == k:
        print("YES")
        print(*res)
        return

    n -= k
    i = 0

    while i < k and n:
        while res[i] <= n:
            n -= res[i]
            res[i] *= 2
        i += 1
    
    if n: print("NO")
    else: print("YES", *res)

main()