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:
n,k = map(int,input().split())

if n<k:
    print("NO")
elif bin(n).count('1')>k:
    print("NO")
else:
    print("YES")
    ans = []
    t1 = 0
    while n:
        b = n&(-n)
        if b==1:
            t1+=1
        else:
            ans.append(b)
        n-=b
    while len(ans)+t1<k:
        p = ans.pop()
        if p==2:
            t1+=2
        else:
            ans.append(p//2)
            ans.append(p//2)
    print(*([1]*t1+sorted(ans)))