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 math
# print(math.log2(10**9))
n,k=map(int,input().split())
ans=[]
while n>0:
    value=2**int(math.log2(n))
    # print(value,end=" ")
    ans.append(value)
    n-=value
    # ans+=1
if len(ans)==k:
    print('YES')
    print(*ans)
elif len(ans)>k:
    print('NO')
else:
    ans.sort()
    # print(ans)
    maxi=0
    for i in range(len(ans)):
        maxi+=((ans[i]))
    # print(maxi)
    if k>maxi:
        print('NO')
    else:
        print('YES')
        i=0
        kt=len(ans)
        # print(ans)
        while i<len(ans) and kt!=k:
            if ans[i]!=1:
                ans[i]//=2
                kt+=1
                ans.append(ans[i])
            else:
                i+=1
        print(*ans)