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.io.*;
import java.util.*;
import static java.lang.Math.*;
public class Delete
{
    static class Pair implements Comparable<Pair> {
        int index,bit_no;
        Pair(int index,int bit_no) {
            this.index = index;
            this.bit_no=bit_no;
        }
        public int compareTo(Pair o){
            return index - o.index;
        }
        public String toString(){ return "index  = "+index+"    bit no = "+bit_no; }
    }
    static StringBuilder sb = new StringBuilder();
    static PrintWriter pw = new PrintWriter(System.out,true);
    static int n,arr[],brr[];
    public static void main(String[] args) throws IOException {
        //Code start from here
        Scanner sc = new Scanner((System.in));
        long n = sc.nextLong(),k = sc.nextLong();
        long arr[]= new long[(int)k];
        long nn = n-(k*(k+1)/2);
        if(nn<0)
            System.out.println("NO");
        else {
            for(int i =0;i<(int)k;i++){
                arr[i]=i+1+nn/k;
                if(i>= k - nn%k )
                    arr[i]++;
            }
            if(nn!=k-1) {
                sb.append("YES\n");
                print(arr);
            } else {
                if(k>3) {
                    arr[1]--;
                    arr[(int) k - 1]++;
                }
                if(k==2 || k==3)
                    sb.append("NO\n");
                else {
                    sb.append("YES\n");
                    print(arr);

                }
            }
        }

        pw.println(sb);
        pw.flush();
        pw.close();
    }
    static void print(long arr[]) {
        for(long i : arr)
            sb.append(i+" ");
    }
}
