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
input = sys.stdin.readline

'''

'''

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

from collections import deque

def powers_of_two(n):
    b = bin(n)[2::]
    dq = deque()
    for i, c in enumerate(reversed(b)):
        if c == "1":
            dq.append(2**i)
    return dq

def solve(n, k):
    if k > n:
        return []
    elif k == n:
        return [1] * n

    dq = powers_of_two(n)
    length = len(dq)
    while length < k:
        cur = dq.pop()
        a = cur // 2

        if a == 1:
            dq.appendleft(1)
            dq.appendleft(1)
        else:
            dq.append(a)
            dq.append(a)
        
        length += 1
    
    return dq if length == k else []

res = solve(n, k)

if not res:
    print("NO")
else:
    print("YES")
    print(*res)