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())
a = []
p = n
while n > 0:
    a.append(n % 2)
    n //= 2
i = len(a) - 1
if sum(a) <= k <= p:
    while sum(a) < k:
        if a[i] == 0:
            i-=1
        else:
            a[i - 1]+=2
            a[i]-=1
    print('YES')
    for i in range(len(a)):
        print((str(2**i) + ' ') * a[i],end='')
else:
    print('NO')