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 sys import stdin
from collections import *

n, k = map(int, stdin.readline().split())
bits = bin(n)[2:]
l = bits.count('1')

if k > n or l > k:
    print('NO')
else:
    ans = deque([2 ** i for i in range(len(bits)) if int(bits[-1 - i])])

    while l < k:
        if ans[0] != 1:
            ans.append(ans[0] // 2)
            ans[0] //= 2
            l += 1
        else:
            ans.rotate(-1)
    print('YES')
    print(' '.join(str(x) for x in ans))