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

[n, k] = [int(x) for x in input().split(' ')]

def solve():
    A = [1] * k
    currentSum = k
    
    if sum(A) > n:
        print('NO')
        return
    else:
        for i in range(k):
            A[i] = int(math.pow(2,math.floor(math.log2(n-currentSum+1))))
            currentSum += A[i] - 1
            if currentSum == n:
                print('YES')
                print(' '.join([str(a) for a in A]))
                return    
    print('NO')
    return

solve()