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:
#!/usr/bin/python

from __future__ import print_function
import math
import sys

def pw2(n, k):

    s = k

    A = [1 for x in range(k)]
    i = k - 1

    while i >= 0:
        while s + A[i] <= n:
            s += A[i]
            A[i] *= 2
        i -= 1

    if (s != n):
        print('NO')
        return

    print('YES')
    for i in range(0, k, 1):
        print(A[i], end = ' ')

def main():
    n = list(map(int, raw_input().split()))
    pw2(n[0], n[1])

if __name__ == '__main__':
    main()