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.*;

/******************************\
 * The solution is at the top *
 *                            *
 *   Created by : azhar556    *
\******************************/

public class Solution {
    static void solve() {
        int n = ni();
        int k = ni();
        long aritDasar = (long)k * (k + 1) / 2;
        if (n < aritDasar) {
            out.println("NO");
        }
        else {
            long kepalaArit = 1 + ((n - aritDasar) / k);
            long aritNya = aritDasar + ((kepalaArit - 1) * k);
            //err.print(aritNya + " " + aritDasar);
            if (aritNya <= n) {
                if (k < 5 ) {
                    long geoNya = kepalaArit * ((1 << k) - 1);
                    if (n > geoNya) {
                        out.println("NO"); return;
                    }
                }
                out.println("YES");
                long yangDitambah = n - aritNya;
                //err.print(yangDitambah);
                if (kepalaArit == 1 && yangDitambah == k - 1 && yangDitambah != 0) {
                    for (int i = 1; i <= k; i++) {
                        int res = i;
                        if (i >= 3) res++;
                        if (i == k) res++;
                        out.print(res + " ");
                    }   
                }
                else {
                    for (int i = 0; i < k; i++) {
                        long res = i + kepalaArit;
                        if (i >= k - yangDitambah) res++;
                        out.print(res + " ");
                    }
                }
            }
            else {
                out.println("NO");
            }
        }
    }    

    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        int t;// = ni();
        t = 1;
        while (t-- > 0) solve(); 
        err.println("Time elapsed : " + (System.currentTimeMillis() - time) / 1000F + " s.");
        err.close(); out.close();
    }

    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    static PrintWriter err = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.err)));
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer token;
        
    static String ns() {
        while (token == null || !token.hasMoreTokens()) {
            try {
                token = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return token.nextToken();
    }
    static char nc() {
        return Character.valueOf(ns().charAt(0));
    }
    static int ni() {
        return Integer.parseInt(ns());
    }
    static double nd() {
        return Double.parseDouble(ns());
    }
    static long nl() {
        return Long.parseLong(ns());
    }
}
