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 sys
import os.path
import math
from collections import deque
if(os.path.exists('input_file.txt')):
    sys.stdin = open("input_file.txt", "r")
    sys.stdout = open("output_file.txt", "w")

deq=deque()
n,k=map(int,input().split())
f=1
if (n%2!=0 & k==1) or k>n:print("NO")
else:
	for i in range(0,len(bin(n)[2:])):
		if (1<<i)&n>0:
			deq.append(1<<i)
		if k<len(deq):
			f=0
			print("NO")
			break
	l=[]
	k-=len(deq)
	while k>0:
		a=deq.popleft()
		if a==1:deq.append(1)
		else:
			deq.append(a//2)
			deq.append(a//2)
			k-=1
	if f:
		print("YES")
		for i in (deq):print(i,end=' ')
		print()
	# else:print("NO")