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(i) for i in input().split(' ')]
ans = []
if n<k:
    print('NO')
    exit()
i = 0
while i < k:
    temp = int(math.log2(n))
    if i == k-1 and 2**temp - n:
        print('NO')
        exit()
    while n - (2**temp + k - (i + 1)) < 0 and temp:
        temp -= 1
    curr = 2**temp
    n -= curr
    ans.append(curr)
    i += 1
print('YES')
print(*ans)