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 heapq

#file = open("input.txt", "r")
data = input().split()
n = int(data[0])
k = int(data[1])

pq = []

for i in range (30):
	if (n & (1 << i)): pq.append(-(1 << i))

heapq.heapify(pq)

if len(pq) > k or k > n: 
	print("NO")
	exit(0)
while len(pq) < k: 
	u = heapq.heappop(pq)
	heapq.heappush(pq, u // 2)
	heapq.heappush(pq, u // 2)

print("YES")
output = ""
while len(pq) > 0:
	u = -heapq.heappop(pq)
	output += str(u) + " "

print(output)