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:
n,k=map(int,input().split())
l1=[]

s=bin(n)
for i in range(len(s)):
    
    if(s[i]=='1'):
        l1.append(2**(len(s)-1-i))
if(k<len(l1) or k>n):
    print("NO")
else:
    i=0
    while(len(l1)!=k):
        if(i>=len(l1)):
            i=0
        if(l1[i]!=1):
            l1[i]=int(l1[i]/2)
            l1.append(int(l1[i]))
        i+=1
    print("YES")
    for i in l1:
        print(i,end="  ")