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:
import heapq


def bitcnt(X):
    res = 0
    v = X
    while v:
        res += v & 1
        v >>= 1
    return res


def bits(X):
    res = []
    order = 0
    v = X
    while v:
        if v & 1:
            res.append(1 << order)
        order += 1
        v >>= 1
    return res


def main():
    n, k = map(int, input().split())
    cnt = bitcnt(n)
    if cnt <= k:
        if n < k:
            print("NO")
            return

        print("YES")
        ansque = [-v for v in bits(n)]
        heapq.heapify(ansque)
        for j in range(k-cnt):
            x = heapq.heappop(ansque)
            heapq.heappush(ansque, x//2)
            heapq.heappush(ansque, x//2)
        ansque = list(ansque)
        ans = [-v for v in ansque]
        print(*ans)
        return

    else:
        print("NO")
        return


main()