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
n,k=map(int,input().split())
s=bin(n)
t=s[2:]
l=t[::-1]
c=[]
for j in range(len(l)):
    if l[j] == "1":
        c.append(int(math.pow(2, j)))
a=[]
if k<len(c):
    print("NO")
elif k>n:
    print("NO")
else:
    print("YES")
    n-=k
    a=[1]*(k)
    i=0
    while i<k and n>0:
        while(a[i]<=n):
            n-=a[i]
            a[i]*=2
        i+=1
    print(*a)