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:
from collections import deque as dq
from heapq import heappop, heappush, heapify
import heapq
def ans(arr):
    return ' '.join([str(-i) for i in arr])
n,k =  map(int,input().split())
s = bin(n)[2:]
ones = s.count('1')
if(ones<=k and n>=k):
    print("YES")
    arr = []
    heapify(arr)
    i = -1
    m = 0
    while(i>=-len(s)):
        if(s[i]=='1'):

            heappush(arr,-1*(pow(2,m)))
        m+=1
        i-=1
    mm = len(arr)
    
    
    
    while(mm!=k):
        w = heappop(arr)
        heappush(arr,(w//2))
        heappush(arr,(w//2))
        mm+=1
    
    print(ans(arr))
    
        
else:
    print("NO")