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 math
from collections import deque


def main():
    n, k = [int(x) for x in input().strip().split(" ")]
    is_possible, power_list = solve(n, k)
    if not is_possible:
        print("NO")
    else:
        print("YES")
        print(" ".join(str(x) for x in power_list))


def solve(n, k):
    factors = factorize(n)
    is_possible = len(factors) <= k and sum(factors) >= k
    if not is_possible:
        return False, []
    num_splits_needed = k - len(factors)
    while num_splits_needed > 0:
        f = factors.popleft()
        if f == 1:
            factors.append(f)
            continue
        factors.appendleft(f // 2)
        factors.appendleft(f // 2)
        num_splits_needed -= 1
    return True, factors


def factorize(n):
    fs = deque()
    maybe_factor = 2 ** int(math.floor(math.log2(n)))
    while n > 0:
        if n - maybe_factor >= 0:
            fs.append(maybe_factor)
            n -= maybe_factor
        maybe_factor //= 2
    return fs


main()