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:
from sys import stdin, stdout
from math import *
from heapq import *
from collections import *

def main():
    n,k=[int(x) for x in stdin.readline().split()]
    if (k>n):
        stdout.write("NO")
        return 0
    a=[]
    for i in range(34):
        a.append( int(((n>>i)&1)==1))
    k=k-sum(a)
    if (k<0):
        stdout.write("NO")
        return 0
    i=33
    while(k>0):
        while(i>0):
            if (a[i]==0):
                i=i-1
            else:
                break
        if (i<=0):
            stdout.write("NO")
            return 0
        a[i]=a[i]-1
        a[i-1]=a[i-1]+2
        k=k-1
    res=[]
    for i in range(33):
        while(a[i]>0):
            a[i]=a[i]-1
            res.append(str(1<<i))
    stdout.write("\n".join(["YES"]+[" ".join(res)]))
    return 0

if __name__ == "__main__":
    main()