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:
import functools
import heapq

n,k = [int(i) for i in input().split()]
s = "{0:b}".format(n)
if k < s.count('1') or k > n :
    print('NO')
else:
    print('YES')
    t = [ (2**i)*(-1) for i,v in enumerate(s[::-1]) if v == '1']
    heapq.heapify(t)
    while len(t) < k:
        x = heapq.heappop(t)
        heapq.heappush(t,x>>1)
        heapq.heappush(t,x>>1)
    print(" ".join(str(i) for i in ([-1*i for i in t]) ))