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 collections import OrderedDict
n, k = map(int, input().split())
a = dict()
e = 1
while e <= 1000000000:
     a[e] = 0
     e *= 2
a = OrderedDict(sorted(a.items()))
l = list(a.keys())
l.reverse()

while(n):
    for i in l:
        if i <= n:
            a[i] += 1
            n -= i
            break

x = sum(a.values())
if x > k:
    print("NO")
    exit()
k -= x

while k:
    cnd = sum(a[v] for v in a if v > 1)
    if cnd == 0:
        break
    else:
        for i in a:
            if i > 1 and a[i] > 0:
                a[i] -= 1
                a[i/2] += 2
                k -= 1
                break

if k > 0:
    print("NO")
else:
    print("YES")
    for i in a:
        for j in range(a[i]):
            print(i, end = ' ')