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:
pt = [2**x for x in range(31)]

def min_powers_of_two(n, l=[]):
    for i in range(31):
        if pt[i] == n:
            l.append(pt[i])
            return l
        elif pt[i] > n:
            l.append(pt[i-1])
            return min_powers_of_two(n-pt[i-1], l)

def k_powers_of_two(k, l, lsize):
    d = k-lsize
    if d == 0:
        return l
    else:
        l2 = []
        for li in l:
            if lsize < k and li != 1:
                l2.append(li//2)
                l2.append(li//2)
                lsize += 1
            else:
                l2.append(li)
        return k_powers_of_two(k, l2, lsize)

n, k = map(int, input().split())

if n < k:
    print("NO")
else:
    l = min_powers_of_two(n)
    if len(l) <= k:
        print("YES")
        print(*k_powers_of_two(k, l, len(l)))
    else:
        print("NO")