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:
import heapq
h,m=list(map(int,input().split()))
if h<m:
    print('NO')
else:
    
    a=[]
    for i in range(len(bin(h))-2):
        if (h>>i)&1==1:
            a.append((-1)*2**i)
    if len(a)>m:
        print('NO')
    else:
        print('YES')
        k=len(a)
        while m-k>0:
            heapq.heapify(a)
            l=heapq.heappop(a)
            z=1
            while k-1+z*2<=m and abs(l)>1:
                l//=2
                z*=2
            a.extend(z*[l])
            k+=z-1
        
        for i in range(len(a)):
            a[i]*=(-1)
        print(*a)