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:
from math import log
n, k = map(int, input().split())
if n >= k:
    mass_2k = dict()
    while n:
        z = 2**(int(log(n, 2)))
        n -= z
        k -= 1
        if z in mass_2k:
            mass_2k[z] += 1
        else:
            mass_2k[z] = 1
    if k >= 0:
        while k > 0:
            ll = 0
            for b in mass_2k:
                if b > ll and mass_2k[b] != 0:
                    ll = b
            if ll//2 in mass_2k:
                mass_2k[ll // 2] += 2
            else:
                mass_2k[ll // 2] = 2
            k -= 1
            mass_2k[ll] -= 1
        print("YES")
        for u in mass_2k:
            if mass_2k[u]:
                for y in range(mass_2k[u]):
                    print(u, end=" ")
    else:
        print("NO")
else:
    print("NO")