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/env python
# -*- coding: utf-8 -*-

from collections import defaultdict
from math import factorial as f
from fractions import gcd as g

N, K = [int (i) for i in raw_input ().split ()]
mx = N
mn = bin (N).count ('1')
if K >= mn and K <= mx:
    print "YES"
    while K:
        K -= 1
        for i in range (32):
            x = 2 ** i
            NN = N - x
            MX = NN
            MN = bin (NN).count ('1')
            if K >= MN and K <= MX:
                print x,
                N -= x
                break
else:
    print "NO"