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:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Apr 20 19:17:23 2019

@author: umang
"""

n, k = map(int, input().split())
sum2 = {}
p2 = 1
while n:
    if n%2 :
        sum2[p2] = 1
    p2 *= 2
    n //= 2

if k < sum(sum2.values()):
    print("NO")
else:
    while sum(sum2.values()) < k and list(sum2.keys()) != [1]:
        for i in sum2.keys():
            if i == 1:
                continue
            else:
                sum2[i] -= 1
                try:
                    sum2[i//2] += 2
                except:
                    sum2[i//2] = 2
                if sum2[i] == 0:
                    sum2.pop(i)
                break
                    
    
    if sum(sum2.values()) == k:
        print("YES")
        for i in sum2.keys():
            for j in range(sum2[i]):
                print(i, end = ' ')
    
    else:
        print("NO")