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())
u = list(bin(n))[2:]
u = list(map(int, u))
s = sum(u)
if s > k or k > n:
    print('NO')
else:
    k -= s
    while k > 0:
        for i in range(len(u) - 1):
            if u[i] > 0:
                u[i] -= 1
                u[i + 1] += 2
                k -= 1
                break
    print('YES')
    ans = []
    for i in range(len(u)):
        for _ in range(u[i]):
            ans.append(2 ** (len(u) - i - 1))
    print(*ans[::-1])