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.*;

public class Main {
  static Scanner in = new Scanner(System.in);
  static PrintWriter out = new PrintWriter(System.out);
  
  public static void main(String[] args) {
    long n = in.nextLong();
    long k = in.nextLong();

    long remaining = n - k * (k + 1) / 2;
    // out.println("sum: " + (k * (k + 1) / 2));
    // out.println("remaining: " + remaining);
    
    boolean OK = remaining >= 0;
    if (!OK) out.println("NO");
    else {
      long[] ans = new long[(int)k];
      long dividen = remaining / k;
      for (int i = 0; i < k; i++) {
        ans[i] = i + 1;
        if (dividen > 0) {
          ans[i] += dividen;
          remaining -= dividen;
        }
      }

      long counter = k;
      while (remaining > 0 && counter >= 1) {
        long take = Math.min(remaining, ans[(int)counter - 1] - 2);
        // out.println("take: " + take);
        if (take < 0) {
          OK = false;
          break;
        }
        ans[(int)counter - 1] += take;
        remaining -= take;
        counter--;
      }
      if (OK) {
        out.println("YES");
        for (int i = 0; i < k; i++) {
          out.print(ans[i] + " ");
        }
      } else {
        out.println("NO");
      }
    }

    in.close();
    out.close();
  }
}