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

// Imports
import java.util.*;
import java.io.*;

public class D1157 {

    /**
     * @param args the command line arguments
     * @throws IOException, FileNotFoundException 
     */
    public static void main(String[] args) throws IOException, FileNotFoundException {
        
        // TODO UNCOMMENT WHEN ALGORITHM CORRECT
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        
        // BufferedReader f = new BufferedReader(new StringReader("26 6"));
        
        // TODO code application logic here
        StringTokenizer st = new StringTokenizer(f.readLine());
        
        long n = Integer.parseInt(st.nextToken());
        long m = Integer.parseInt(st.nextToken());
        
        if(n - m*(m+1)/2 < 0) {
            System.out.println("NO");
        }
        else {
            long[] arr = new long[(int)m];
            long k = n - m*(m+1)/2;
            for(int i = 0; i < m; i++) {
                if(i >= m - k%m) {
                    arr[i] = k/m + 1;
                }
                else {
                    arr[i] = k/m;
                }
                arr[i] += i + 1;
            }
            
            if(k == m-1) {
                if(m > 3) {
                    arr[1] --;
                    arr[(int)m - 1] ++;
                }
                if(m == 2 || m == 3) {
                    System.out.println("NO");
                }
                else {
                    System.out.println("YES");
                    StringBuilder sb = new StringBuilder();
                
                    for(int i = 0; i < arr.length; i++) {
                        System.out.print(arr[i]);
                        if(i < arr.length - 1) {
                            System.out.print(" ");
                        }
                    }
                    System.out.println();
                }
            }
            else {
                
                System.out.println("YES");
                StringBuilder sb = new StringBuilder();
                
                for(int i = 0; i < arr.length; i++) {
                    System.out.print(arr[i]);
                    if(i < arr.length - 1) {
                        System.out.print(" ");
                    }
                }
                System.out.println();
            }
            
        }
    }

}
