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 BillCalculator {

    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer(br.readLine());

        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());

        if(k*1L*(k + 1) / 2 > n || n == 8 && k == 3 || n == 4 && k == 2){
            System.out.println("NO");
        } else {

            int diff = n - k*(k + 1) / 2;

            int factor = diff / k;

            int remainder = diff % k;

            int start = factor + 1;

            StringBuilder sb = new StringBuilder();

            int ans[] = new int[k + 1];

            for(int i = 1;i <= k;i++){
                ans[i] = start++;
            }

            System.out.println("YES");

            if(remainder > 0) {
                int extra = Math.min(2*ans[k - 1] - ans[k], remainder);
                remainder -= Math.min(2*ans[k - 1] - ans[k], remainder);
                ans[k] += extra;
            }
            if(remainder > 0){
                ans[k - 1] += remainder;
            }

            for(int i = 1;i <= k;i++)
                sb.append(ans[i] + " ");

            System.out.println(sb);
        }
    }
}