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=list(map(int,input().strip().split()))
l=[]
p=0
nn=n
length=0
while(n):
    if n%2==1:
        l.append(2**p)
    p+=1
    n=n//2
if len(l)<=k<=nn:
    print("YES")
    i=0
    while(1):
        if len(l)+length==k:
            print(" ".join(map(str,l)))
            break
        if l[0]!=1:
            toappendat0=l.pop(0)//2
            l=[toappendat0]*2+l
        else:
            length+=1
            print(l.pop(0),end=" ")
else:
    print("NO")