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 bisect import bisect_left as bl, bisect_right as br, insort
import sys
import heapq
from math import *
from collections import defaultdict as dd, deque
def data(): return sys.stdin.readline().strip()
def mdata(): return map(int, data().split())
#sys.setrecursionlimit(100000)

n,k=mdata()
d=dd(int)
b=bin(n)[2:]
a=0
for i in range(len(b)):
    if b[i]=='1':
        a+=1
        d[len(b)-1-i]+=1
if k<a or k>n:
    print('NO')
else:
    while a<k:
        for i in d:
            if d[i]>0 and i!=0:
                d[i]-=1
                d[i-1]+=2
                a+=1
                break
    print("YES")
    l=[]
    for i in sorted(d.keys()):
        l+=[int(pow(2,i))]*d[i]
    print(*l)