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 = tuple(map(int, input().split()))

pow2 = []
m = n
p = 1
while m > 0:
    if m % 2 == 1:
        pow2.append(p)
    m >>= 1
    p *= 2

if n < k or len(pow2) > k:
    print('NO')
else:
    print('YES')
    i = 0 if pow2[0] > 1 else 1
    while len(pow2) < k:
        pow2[i] //= 2
        pow2.insert(i, pow2[i])
        if pow2[i] == 1:
            i += 2

    print(' '.join([str(a) for a in pow2]))