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:
from math import log2
n , k = map(int,input().split())

binary = bin(n)[2:]
lbin = binary.count('1')
if n < k or ( (k is 1) and (n is not 1) and (n%2 is 1)):
    print('NO')
elif lbin > k:
    print('NO')
else:
    l = []
   
    print('YES')
    lbin = len(binary)
    for i  in range(lbin):
        if binary[lbin-i-1] == '1':
            l.append(pow(2,i))

    i = 0
    while len(l) < k:
        if l[i]%2 is 0:
            l[i] //= 2
            l.append(l[i])
        else:
            i += 1
            
    print(*l)