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 Main {

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        long n = scanner.nextInt();
        int m = scanner.nextInt();
        long[] a = new long[m + 1];
        long[] b = new long[m + 1];
        b[1] = 1;
        for (int i = 2; i <= m; i++)
            b[i] = Math.min(b[i - 1] * 2, 0x7fffffff);

        long gaosi, mi;
        long l = 1, r = 0x7fffffff, mid;
        while (l < r) {
            mid = (l + r + 1) / 2;
            gaosi = (mid + mid + m - 1) * m / 2;
            mi = mid * (b[m] * 2 - 1);
            if (mi >= n && gaosi <= n) {
                l = mid;
            } if (mi < n) {
                l = mid + 1;
            } else if (gaosi > n) {
                r = mid - 1;
            }
        }
        a[1] = l;
        n -= l;

        for (int i = 2; i <= m; i++) {
            l = a[i - 1] + 1;
            r = a[i - 1] * 2;

            while (l < r) {
                mid = (l + r + 1) / 2;
                gaosi = (mid + mid + m - i) * (m - i + 1) / 2;
                if (gaosi > n)
                    r = mid - 1;
                else
                    l = mid;
            }

            a[i] = l;
            n -= l;
        }

        if (n == 0) {
            StringBuilder stringBuilder = new StringBuilder();
            stringBuilder.append("YES\n");
            for (int i = 1; i <= m; i++)
                stringBuilder.append(a[i]).append(' ');
            System.out.println(stringBuilder.toString());
        } else {
            System.out.println("NO");
        }

    }

}
