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:
GI = lambda: int(input()); GIS = lambda: map(int, input().split()); LGIS = lambda: list(GIS())

def main():
    n, k = GIS()
    l = []
    ones = 0
    while n:
        n, m = divmod(n, 2)
        l.append(m)
        ones += m
    if ones > k:
        print("NO")
        return
    i = len(l) - 1
    while ones < k and i > 0:
        if l[i] == 0:
            i -= 1
        else:
            l[i] -= 1
            l[i-1] += 2
            ones += 1

    if ones < k:
        print("NO")
    else:
        print("YES")
        for i, c in enumerate(l):
            if c:
                print(('%i ' % 2 ** i) * c, end='')
        print()

main()