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.PrintWriter;
import java.util.*;

/**
 * Created by Andrey on 17.02.2019.
 */


public class Main {

    void solve(Scanner in, PrintWriter out) {
        long n = in.nextLong(), k = in.nextLong();


        int[] arr = new int[(int) k];

        for (int i = 1; i <= k; ++i) {
            arr[i - 1] = i;
        }

        if (k == 1) {

            out.println("YES");
            out.println(n);
            return;
        }

        if (n - k * (k + 1) / 2 < 0) {
            out.println("NO");
            return;
        } else {

            long need = n - k * (k + 1) / 2;

            long cN = need % k;
            long cA = need / k;


            for(int i = 0 ; i < k; ++i){
                arr[i] += cA;
            }

            for(int i = (int) (k - 1); i >= k - cN; --i){
                ++arr[i];
            }


        }



        if(arr[1] == 3 && arr[0] == 1){
            arr[1] -= 1;
            arr[(int) (k - 1)] += 1;
        }

        if(arr[(int) (k - 2)] * 2 <  arr[(int) (k - 1)]){
            out.println("NO");
            return;
        }

        out.println("YES");
        for (int i : arr) {
            out.print(i + " ");
        }


    }


    int gcd(int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }


    void run() {
        try (Scanner in = new Scanner(System.in);
             PrintWriter out = new PrintWriter(System.out)) {
            solve(in, out);
        }
    }

    public static void main(String[] args) {
        new Main().run();
    }
}