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 = map(int, input().split())
if n < k:
    print('NO')
    exit()

b = format(n, 'b')
b = list(b)
b.reverse()
c = 0
ans = []
for i in range(len(b)):
    if b[i] == '1':
        c += 1
        ans.append(2**i)

#print(ans)
from collections import deque
ans = deque(ans)
if len(ans) > k:
    print('NO')
else:
    while len(ans) < k:
        x = ans.pop()
        if x%2 == 0:
            ans.appendleft(x//2)
            ans.appendleft(x//2)
        else:
            ans.appendleft(x)
    ans = list(ans)
    ans.sort()
    print('YES')
    print(*ans)