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 math
a,k=map(int,input().split())
l=[]
while(True):
    x=math.log2(a)
    l.append(pow(2,int(x)))
    if(int(x)==x):
        break
    else:
        a=a-pow(2,int(x))
if(len(l)>k):
    print("NO")
else:
    l.sort()
    x=0
    while(len(l)!=k and x<len(l)):
       if(l[x]==1):
           x+=1
       else:
           l[x]=l[x]//2
           l.insert(x+1,l[x])
    if(len(l)==k):
        print("YES")
        print(*l)
    else:
        print("NO")