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 sys

def input(): return sys.stdin.readline().rstrip("\r\n")
def List(): return list(map(int, input().split()))
def Num(): return int(input())


def solve():
    n, k = List()
    tot, i = k, k - 1
    a = [1 for i in range(k)]
    while i >= 0:
        while tot + a[i] <= n:
            tot += a[i]
            a[i] *= 2
        i -= 1
    if tot == n:
        print('YES')
        print(*a)
    else:
        print('NO')


solve()