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:
from math import log

n, k = map(int, input().split())

ans, n0, ones = {}, n, 0

while n0 > 0:
    ans[int(log(n0, 2))] = 1
    n0 -= 2 ** int(log(n0, 2))
    ones += 1

l = int(log(n, 2))

if ones <= k <= n:
    print("YES")
    while ones < k:
        ans[l] -= 1
        if l - 1 not in ans:
            ans[l - 1] = 0
        ans[l - 1] += 2
        if ans[l] == 0:
            l -= 1
        ones += 1
    for i in sorted(ans):
        for _ in range(ans[i]):
            print(2 ** i, end=" ")
else:
    print("NO")