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:
if __name__ == "__main__":
    n, k = map(int, input().split())
    if n < k:
        print("NO")
        exit(0)

    c = [0] * 32
    for i in range(32):
        if (1<<i) & n:
            c[i] += 1
            k -= 1

    if k < 0:
        print("NO")
        exit(0)

    print("YES")

    for _ in range(k):
        for i in range(1, 32):
            if c[i] > 0:
                c[i] -= 1
                c[i-1] += 2
                break

    res = []
    for i in range(32):
        for _ in range(c[i]):
            res.append(1<<i)

    print(' '.join(map(str, res)))