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
n,k=map(int,input().split())
m=(k*(k+1))//2
if(n>=m):
	#print("YES")
	a=[]
	a.append(0)
	rem=n-m
	t=rem//k
	for i in range(1,k+1):
		a.append(i+t)
	rem=rem%k
	if(t==0):
		if(k==1):
			print("YES")
			print(n)
		elif(k==2):
			if(n%2!=0):
				print("YES")
				print(n//k,n//k+1)
			else:
				print("NO")
		elif(k==3):
			if(rem==2):
				print("NO")
			elif(rem==1):
				print("YES")
				print("1 2 4")
		else:
			for i in range(k,0,-1):
				#print(rem)
				temp=2*a[i-1]-a[i]
				#print(temp)
				blah=min(temp,rem)
				rem=rem-blah
				a[i]+=blah
				if(rem==0):
					break
			print("YES")
			a=a[1:]
			print(*a)
	else:
		if(k==1):
			print("YES")
			print(n)
		elif(k==2):
			print("YES")
			if(n%2==0):
				print(n//k-1,n//k+1)
			else:
				print(n//k,n//k+1)
		else:
			for i in range(k,0,-1):
				temp=2*a[i-1]-a[i]
				blah=min(temp,rem)
				rem=rem-blah
				a[i]+=blah
				if(rem==0):
					break
			print("YES")
			a=a[1:]
			print(*a)
else:
	print("NO")