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 codeforces {
    public static void main(String[] args) throws IOException {
        Scanner scan = new Scanner(System.in);
        long n = scan.nextLong();
        int k = scan.nextInt();
        long a[] = new long[k];
        long sum = 0;
        for (int i = 0; i < k; i++) {
            a[i] = (long)(i + 1);
            sum += a[i];
        }

        long add = (n - sum) / (long)k;
        if (add > 0) {
            for (int i = 0; i < k; i++) {
                a[i] += add;
                sum += add;
            }
        }

        int last = (int)(n - sum);
        if (sum > n) System.out.println("NO");
        else {
            if (last != k - 1 || last == 0) {
                for (int i = 0; i < k; i++) {
                    if (k - i - 1 < last) a[i]++;
                }
            }
            else {
                last--;
                for (int i = 0; i < k - 1; i++) {
                    if (k - i - 1 < last) a[i]++;
                }
                if (last + 1 > 1) {
                    a[k - 1] += 2;
                }
                else a[k - 1]++;
            }

            boolean ok = true;
            for (int i = 1; i < k; i++) {
                if (a[i] > a[i - 1] * 2) ok = false;
            }

            if (!ok) System.out.println("NO");
            else {
                System.out.println("YES");
                for (int i = 0; i < k; i++) System.out.print(a[i] + " ");
            }
        }
    }
}