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 PYTHON):

Solution:
import math
import heapq

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

s = bin(n)

num_min = sum(map(int, s[2:]))
num_max = n

if k >= num_min and k <= num_max:
    print "YES"
    other = k - num_min
    s2 = s[::-1]
    L = []
    for i in range(len(s2[:-2])):
        if s2[i] == '1':
            heapq.heappush(L, int(math.pow(2, i))*-1)
    while(len(L) < k):
        b = (-1)*heapq.heappop(L)
        heapq.heappush(L, (-1)*b/2)
        heapq.heappush(L, (-1)*b/2)
    print " ".join(map(lambda x:str(-x), L))
else:
    print "NO"