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
//package com.karancp;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.InputStream;


public class karan {
    public static void main(String args[])
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader z = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        task solver =new task();
        solver.solve(z,out);
        out.close();
    }
    static class task
    {
        static int gcd(int a,int b)
        {
            if(b==0)return a;
            else return gcd(b,a%b);
        }
        static long max(long a,long b)
        {
            return Math.max(a,b);
        }
        static long min(long a,long b)
        {
            return Math.min(a,b);
        }


        public static void solve(InputReader z, PrintWriter out)
        {
           long n=z.nextInt();
           int k=z.nextInt();
           if(k==1)
           {
               out.println("YES");
               out.println(n);
           }
           else
           {
               long tt=k;
               long s=(long)((tt)*(tt+1))/2;
               //out.println(s);
               if(n<s)
               {
                   out.println("NO");
               }
               else
               {
                   s=((tt-1)*tt)/2;
                  // out.println(s);
                   long a=(long)(n-s)/k;
                   int i;
                   long ar[]=new long[k+1];
                   long temp=a;
                   s=0;
                   for(i=1;i<=k;i++)
                   {
                       ar[i]=a;
                       a++;
                       s+=ar[i];
                   }
                   long dif=n-s;
                  // out.println(dif);
                   if(dif==0)
                   {
                       out.println("YES");
                      for(i=1;i<=k;i++)
                      {
                          out.print(ar[i]+" ");
                      }
                   }
                   else
                   {
                       for(i=k;i>1;i--)
                       {
                           long las=ar[i-1]-1;
                          // out.println(las);
                           //out.println(dif);
                           if(dif>las)
                           {

                               dif-=las;
                               ar[i]+=las;
                           }
                           else
                           {

                               ar[i]+=dif;
                               dif-=dif;
                           }
                       }
                       if(dif==0)
                       {
                           out.println("YES");
                           for(i=1;i<=k;i++)
                           {
                               out.print(ar[i]+" ");
                           }
                       }
                       else out.println("NO");
                   }
               }
           }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }

    }



}
