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 Fri Dec 28 20:14:56 2018

@author: kasia
"""

ran=input()
ran=ran.split()
n=int(ran[0])
k=int(ran[1])
bin=format(n, 'b')
binary=[int(i) for i in bin]
#print(binary)
if k>n:
    print('NO')
elif sum(binary)>k:
    print('NO')
else:
    print('YES')
    l=[2**i for i in range(0, len(binary)) if binary[len(binary)-i-1]==1]
    #print(' '.join(l))
    #print(len(binary))
    #print(l)
    dl=len(l)
    cur_ind=0
    while dl < k:
        #print(l)
        if l[cur_ind] > 1:
            l[cur_ind]=l[cur_ind]/2
            l.append(l[cur_ind])
            dl=len(l)
        else:
            cur_ind+=1
    l=[str(int(i)) for i in l]
    print(' '.join(l))