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.Scanner;
import java.util.Arrays;
public class D1157{
	public static void main(String args[]){
		Scanner sc=new Scanner(System.in);
		long n=sc.nextInt();
		long k=sc.nextInt();
		int f=0;
		long a[]=new long[(int)k+1];
		long max=Long.MAX_VALUE;
		for(int i=1;i<=k;i++){
			long minus=(k-i)*(k-i+1)/2;
			//System.out.println(minus+" minus n "+n);
			if(n<minus){
				f=1;
				break;
			}
			//n-=minus;
			//System.out.println((n-minus)+" minus,,,,, n"+(k-i+1));
			long rem=(n-minus)/(k-i+1);

			if(rem==0){
				f=1;
				break;
			}
			rem=Math.min(max,rem);
			//System.out.println(rem+" rem");
			n-=rem*(k-i+1);
			
			a[i]+=rem+a[i-1];
			max=a[i];
						//System.out.println("max "+max);
		}
		if(f==0&&n==0){
		System.out.println("YES");
		for(int i=1;i<=k;i++){
			//a[i]+=a[i-1];
			System.out.print(a[i]+" ");
		}
		System.out.println();
		}
		else
		
		System.out.println("NO");
		
		
		
	}
	
}