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 collections import Counter

n, k = [int(i) for i in input().split()]

cnt = 0
cnt2 = 0
C = Counter()

for i in range(30):
    if (n >> i) & 1:
        cnt += 1
        cnt2 += 1 << i
        C[i] += 1

if k < cnt or k > cnt2:
    print('NO')
    exit()

print('YES')
k -= cnt
i = 30

while k > 0:
    if C[i] == 0:
        i -= 1
        continue
    C[i] -= 1
    C[i-1] += 2
    k -= 1

ans = []

for k, v in sorted(C.items()):
    ans += [1 << k] * v

print(*ans)