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:
# -*- coding: utf-8 -*-
"""
Created on Sun Jul 26 05:03:49 2020

@author: Dark Soul
"""
from heapq import heappop, heappush, heapify 
  
# Creating empty heap 
heap = [] 
heapify(heap) 
  
# Adding items to the heap using heappush 
# function by multiplying them with -1 


[n,m]=list(map(int, input().split()))
s=bin(n)
s=s[2:]
cnt=0
for i in range(len(s)):
    if s[i]=='1':
        cnt+=1
        heappush(heap, -1 * (2**(len(s)-i-1)))
if n==m:
    print('YES')
    print(*([1]*m))
elif cnt>m:
    print('NO')
elif len(heap)==m:
    print('YES')
    for i in heap: 
        print(-1 * i, end = ' ')
else:
    z=len(heap)
    flag=0
    while z!=m:
        
        x=heap[0]
        if x==-1:
            flag=1
            break
        heappop(heap)
        heappush(heap, 1 * int(x/2))
        heappush(heap, 1 * int(x/2))
        z=len(heap)
        if z>m:
            break
    if flag:
        print('NO')
    else:
        print('YES')
        for i in heap: 
            print(-1 * i, end = ' ')