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;

/**
 *
 * @author htdong
 * @date 2018年4月20日 上午11:52:19
 */

public class Main {

    static class SegmentTree {
        private int[] tr;

        public SegmentTree(int n) {
            tr = new int[n << 1];
        }

        private int idx(int l, int r) {
            return (l + r) | (l != r ? 1 : 0);
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        long m = in.nextLong();
        if (m * (m + 1) / 2 > n) {
            System.out.println("NO");
        } else {
            int[] a = new int[(int) m];
            n -= m * (m + 1) / 2;
            for (int i = 0; i < m; ++i) {
                a[i] = i + 1 + (int) (n / m);
            }
            n %= m;
            while (n > 0) {
                long k = n;
                for (int i = (int) m - 1; i >= 0; --i) {
                    if (i - 1 < 0 || a[i] + 1 <= a[i - 1] * 2) {
                        --n;
                        ++a[i];
                        if (n == 0) {
                            break;
                        }
                    } else {
                        break;
                    }
                }
                if (k == n) {
                    System.out.println("NO");
                    break;
                }
            }
            if (n == 0) {
                System.out.println("YES");
                for (int i = 0; i < m; ++i) {
                    System.out.print(a[i]);
                    if (i + 1 == m) {
                        System.out.println();
                    } else {
                        System.out.print(" ");
                    }
                }
            }
        }
        in.close();
    }
}