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.*;
public class Class{
	public static long getLow(long y,int x){
		long last=y+x-1;
		if(x%2==0)return ((y+last)*(x/2));
		else return ((y+last)*(x/2))+(y+last)/2;
	}
	public static long getHigh(long y,int x){
    return y*((long)Math.pow(2,x)-1);
	}
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        long n=sc.nextInt();
        int days=sc.nextInt();
        int j=(int)(n/(Math.pow(2,days)-1));
        while(getHigh(j,days)<n){
        	j++;
        }
        if(getLow(j,days)>n){
            System.out.print("NO");
            return;
        }
        
        long arrHigh[] =new long[days],arrLow[]=new long[days];
        long sum=getLow(j,days);
        boolean flag=true;
        for(int i=0;i<days;i++)arrHigh[i]=j*(int)Math.pow(2,i);
        for(int i=0;i<days;i++,j++)arrLow[i]=j;
        for(int i=arrLow.length-1;n>sum;i--){
        	if(i==0||arrLow[i]==arrLow[i-1]*2)i=days-1;
        	if(n>sum-arrLow[i]+arrLow[i-1]*2){
        		sum+=arrLow[i-1]*2;
        		sum-=arrLow[i];
        		arrLow[i]=arrLow[i-1]*2;
        	}
        	else {
        		arrLow[i]+=n-sum;
        		break;
        	}
        }
        { System.out.println("Yes");
        	System.out.println(Arrays.toString(arrLow).replace("[","").replace("]","").replaceAll(",",""));
        }
    }
}