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())
tab = list(map(int, str(bin(n))[2:]))
nb = sum(tab)
n_tab = len(tab)
p = len(tab)
while (nb < k and n_tab > 1):
    if (tab[p - n_tab] == 0):
        n_tab -= 1
    else:
        tab[p - n_tab] -= 1
        tab[p - n_tab + 1] += 2
        nb += 1

if (nb == k):
    print("YES")
    l = []
    for i in range(p):
        for j in range(tab[p - i - 1]):
            l.append(pow(2, i))
    print((" ".join(map(str, l))))
else:
    print("NO")