Polycarp has to solve exactly n problems to improve his programming skill before an important programming competition. But this competition will be held very soon, most precisely, it will start in k days. It means that Polycarp has exactly k days for training!

Polycarp doesn't want to procrastinate, so he wants to solve at least one problem during each of k days. He also doesn't want to overwork, so if he solves x problems during some day, he should solve no more than 2x problems during the next day. And, at last, he wants to improve his skill, so if he solves x problems during some day, he should solve at least x+1 problem during the next day.

More formally: let [a_1, a_2, ..., a_k] be the array of numbers of problems solved by Polycarp. The i-th element of this array is the number of problems Polycarp solves during the i-th day of his training. Then the following conditions must be satisfied: 

  * sum of all a_i for i from 1 to k should be n; 
  * a_i should be greater than zero for each i from 1 to k; 
  * the condition a_i < a_{i + 1} ≤ 2 a_i should be satisfied for each i from 1 to k-1. 



Your problem is to find any array a of length k satisfying the conditions above or say that it is impossible to do it.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 10^5) — the number of problems Polycarp wants to solve and the number of days Polycarp wants to train.

Output

If it is impossible to find any array a of length k satisfying Polycarp's rules of training, print "NO" in the first line.

Otherwise print "YES" in the first line, then print k integers a_1, a_2, ..., a_k in the second line, where a_i should be the number of problems Polycarp should solve during the i-th day. If there are multiple answers, you can print any.

Examples

Input


26 6


Output


YES
1 2 4 5 6 8 


Input


8 3


Output


NO


Input


1 1


Output


YES
1 


Input


9 4


Output


NO
import sys
from math import floor,ceil
def fun(n,k):
	array=[0]*k
	remaining=n-int(k*(k+1)/2)
	if remaining<0:
		print("NO")
		sys.exit()

	right_most=remaining%k
	high=ceil(remaining/k)
	low=floor(remaining/k)

	for i in range(k-right_most,k):
		array[i]=high

	for i in range(k-right_most):
		array[i]=low

	for i in range(k):
		array[i]+=i+1

	if k-1!=remaining or k==1:
		print("YES")
		print(*array)
		sys.exit()
	elif k==2 or k==3:
		print("NO")
		sys.exit()
	else:
		array[1]-=1
		array[k-1]+=1
		print("YES")
		print(*array)
		sys.exit()


n,k=map(int,input().split( ))
fun(n,k)