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
// Don't place your source in a package

import java.math.BigInteger;
import java.util.*;
import java.lang.*;
import java.io.*;



// Please name your class Main
public class Main {
    static FastScanner fs=new FastScanner();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int Int() {
            return Integer.parseInt(next());
        }

        long Long() {
            return Long.parseLong(next());
        }

        String Str(){
            return next();
        }
    }


    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(System.out);


        int T=1;
        for(int t=0;t<T;t++){
            int n=Int();
            int k=Int();
            Solution sol=new Solution(out);
            sol.solution(n,k);
        }
        out.flush();

    }


    public static int Int(){
        return fs.Int();
    }
    public static long Long(){
        return fs.Long();
    }
    public static String Str(){
        return fs.Str();
    }

}






class Solution{
    PrintWriter out;
    public Solution(PrintWriter out){
        this.out=out;
    }



    public void solution(long n,long k){
        if(n<((1+k)*k/2)){
            out.println("NO");
            return;
        }



        long res[]=new long[(int)(k)];
        for(int i=0;i<res.length;i++){
            long l=0;long r=n;
            if(i>0){
                l=res[i-1];
                r=res[i-1]*2;
            }

            long ans=-1;

            while(l<=r){
                long mid=l+(r-l)/2;
                if(check(n-mid,k-(i+1),mid+1)){
                    ans=mid;
                    l=mid+1;
                }
                else{
                    r=mid-1;
                }
            }


            if(ans==-1){
                out.println("NO");
                return;
            }
            res[i]=ans;
            n-=ans;

        }

        if(n!=0){
            out.println("NO");
            return;
        }

        out.println("YES");
        for(long i:res){
            out.print(i+" ");
        }

    }

    public boolean check(long n,long k,long start){
        if(n<((start+start+k-1)*k/2)){
            return false;
        }
        return true;
    }



}



/*
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                      free bug dog
*/





