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.Arrays;
import java.util.Scanner;

public class CodeForces555D {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long n = scanner.nextInt();
        long k = scanner.nextInt();

        if (n < k * (k + 1) / 2 || k == 2 && n == 4 || k == 3 && n == 8) {
            System.out.println("NO");
        } else {
            long a = (n - k * (k - 1) / 2) / k;
            long[] b = new long[(int) k];
            for (int i = 0; i < k; i++) {
                b[i] = a + i;
            }
            long d = n - a * k - k * (k - 1) / 2;
            int j = (int) k - 1;
            while (d > 0) {
                long x = (b[j] - 1) * 2 - b[j];
                if (d < x) {
                    x = d;
                }
                b[j] += x;
                d -= x;
                j--;
            }

            System.out.println("YES\n" + Arrays.toString(b).replaceAll("[\\[\\],]", ""));

//            long sum = 0;
//            for (int i = 0; i < k; i++) {
//                sum += b[i];
//            }
//            System.out.println(sum);
        }

    }
}