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:
#!/usr/bin/env python3 
#-*- coding:utf-8 -*-

def my_range(start, end, other_condi):
    while start < end and other_condi:
        yield start
        start += 1

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

ans = [1] * k
n -= k
for i in my_range(0, k, n):
    while ans[i] <= n:
        n -= ans[i]
        ans[i] <<= 1
    i += 1

if n == 0:
    print('YES')
    print(*ans)
else:
    print('NO')