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 = [int(x) for x in input().split()]
if n < k:
    print("NO")
else:
    p = []
    t = n
    i = 1
    j = 0
    while t != 0:
        if t & i != 0:
            p.append(2**j)
            t = t & (t - 1)
        j += 1
        i <<= 1

    if len(p) > k:
        print("NO")
    else:
        # print(p)
        print("YES")
        i = 0
        diff = k - len(p)
        while diff != 0:
            if p[i] == 1:
                i += 1
                continue

            p[i] //= 2
            p.append(p[i])
            diff -= 1
        p = map(str, p)
        print(" ".join(p))