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
def highestPowerof2(n): 
    return int(math.log(n, 2));   
n,k = map(int,input().split())
if n<k:
    print("NO")
else:
    f=-1
    l=[1]*k
    l[k-1]=n-(k-1)
    s=n
    d=0
    for i in range(k-1,-1,-1):
        l[i]+=d
        w=highestPowerof2(l[i])
        hi=(pow(2, w))
        d=l[i]-hi
        if d==0:
            f=1
            break
        else:
            l[i]=hi
    if f==-1:
        print("NO")
    else:
        print("YES")
        for z in l:
            print(z,end=" ")