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())

if n<k:
    print("NO")
else:
    jog=n-k
    a=k*[0]
    
    for i in range(k-1,-1,-1):
        jog+=2**a[i]
        power=int(math.log(jog)/math.log(2))
        a[i]=power
        jog-=2**power
        if jog<=0:
            break
        
    if jog==0:
        print("YES")
        for i in range(k):
            a[i]=2**a[i]
        print(*a)
    else:
        print("NO")