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:
'''input
16 4
'''
from sys import stdin
import math
import heapq

def myfunction(n, k):
	if n < k:
		print("NO")
		return

	myqueue = []
	binary = list(str(bin(n)))[2:]
	for i in range(len(binary)):
		if binary[i] != '0':
			myqueue.append(-1 * (2 ** (len(binary) - i - 1)))

	if len(myqueue) > k:
		print("NO")
		return

	elif len(myqueue) == k:
		print("YES")
		myqueue.sort(reverse = True)
		for p in range(k):
			print(-1 * myqueue[p], end=' ')
		return

	heapq.heapify(myqueue)
	while len(myqueue) != k:
		max_el = heapq.heappop(myqueue)
		if max_el == -1:
			print("NO")
			return

		heapq.heappush(myqueue, max_el // 2)
		heapq.heappush(myqueue, max_el // 2)
		if len(myqueue) == k:
			print("YES")
			myqueue = list(myqueue)
			myqueue.sort(reverse = True)
			for p in range(k):
				print(-1 * myqueue[p], end=' ')
			return
	




# main starts
n, k = list(map(int, stdin.readline().split()))
myfunction(n, k)