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 java.util.*;
import java.math.*;
public class Animal {
	public static void main(String[] args) {
		Scanner scanner=new Scanner(System.in);
		long n=scanner.nextInt();
		long k=scanner.nextInt();
		int a[]=new int [(int)(k+5)];long pre=0;long x;int fl=0;
		for(long i=k;i>=1;i--)
		{
			x=(2*n/i-i+1)/2;
			x=Math.max(x, pre+1);
			if(fl==1)
			{
				x=Math.min(x, 2*pre);
			}
			pre=x;fl=1;
			
			a[(int)(k-i+1)]=(int)x;
			//System.out.println(k+":"+x+":"+n);
			n-=x;
		}
		if(n!=0){
			System.out.println("NO");
		}else{
			System.out.print("YES"+"\n"+a[1]);
			for(int i=2;i<=k;i++)
				System.out.print(" "+a[i]);
		}
	}
	public static class Fun{
		public HashMap<Integer, Integer>h1=new HashMap<Integer, Integer>();
		
		public long sum(long a1,long k){
			return (a1+a1+k-1)*k/2;
		}
	}
}
