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
import bisect
from random import randint
input=lambda: sys.stdin.readline().strip("\r\n")
from math import gcd
sa=lambda :input()
sb=lambda:int(input())
sc=lambda:input().split()
sd=lambda:list(map(int,input().split()))
se=lambda:float(input())
sf=lambda:list(input())
flsh=lambda: sys.stdout.flush()
mod=10**9+7
def hnbhai():
    n,k=sd()
    ans=[1]*k
    n=n-k
    i=0
    while(i<k and n):
        while(ans[i]<=n):
            n-=ans[i]
            ans[i]*=2
        i+=1
    if n:
        print("NO")
        return
    print("YES")
    print(*ans)
for _ in range(1):
    hnbhai()