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 sys,math
from collections import defaultdict
#n = int(input())
n,k = [int(__) for __ in input().split()]
#arr = [int(__) for __ in input().split()]
#st = input()
#lines = sys.stdin.readlines()
lr = list()
#print(n,k,math.log(n,2))
nn = n
while nn:
    l = math.floor(math.log(nn,2))
    nn -= 2 ** l
    lr.append(l)
    #print(lr,nn)
#print(l)

if k < len(lr) or k > n:
    print('NO')
    exit()
else:
    numz = 0
    while len(lr) + numz < k:
        x = lr.pop()
        if x == 0:
            numz += 1
        elif x == 1:
            numz += 2
        else:
            lr.append(x-1)
            lr.append(x-1)
print('YES')
print(' '.join([str(2**x) for x in lr] + ['1']*numz))