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 PYTHON):

Solution:
from math import log

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

def solve():
    nums = [1 << i for i in xrange(int(log(n, 2)), -1, -1) if (n >> i) & 1 == 1]
    size = len(nums)
    if size > k:
        print 'NO'
        return
    need = k - size
    while size > 0 and need > 0:
        size -= 1
        if nums[0] == 1:
            continue
        q = [nums.pop(0)]
        while q[0] > 1 and need > 0:
            cur = q.pop(0)
            cur >>= 1
            q.extend([cur, cur])
            need -= 1
        nums.extend(q)
    if need == 0:
        print 'YES\n', ' '.join(map(str, nums))
    else:
        print 'NO'

solve()