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.util.Scanner;

public class D_555 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        int k = in.nextInt();

        //impossible cases
        //During each day he has to solve at least one problem and one more than the previous day
        long min = (k * (k + 1L)) / 2L;
        if (n < min) {
            System.out.println("NO");
            System.exit(0);
        }

        long[] a = new long[k];
       

        long h = (n - min) / k;
        a[0] = h + 1;
        for (int i = 1; i < k; i++) {
            a[i] = a[i - 1] + 1;
        }
        long sum = min + k * h;
        outer:
        while (sum < n) {
            for (int i = 0; i < k; i++) {
                if (sum + (k - i) <= n && (2 * a[i - 1] > a[i])) {
                    while (i < k && sum <= n) {
                        a[i++]++;
                        sum++;
                    }
                    continue outer;
                }
            }
            System.out.println("NO");
            System.exit(0);
        }

        /*
        long actsum = 0;
        for (int i = 0; i < k; i++) {
            actsum += a[i];
        }

        System.out.println(actsum);

*/
        System.out.println("YES");
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
        System.out.println();
    }
}
