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 Main {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt();
        if(1L * k * (k + 1) / 2 > n) {
            println("NO");
            return;
        }
        n -= 1L * k * (k + 1) / 2;

        int first_value = n / k + 1;
        long[] ans = new long[k];
        for(int i = 0; i < k; i++) {
            ans[i] = first_value + i;
        }
        n = n % k;

        int i = k - 1;
        while(i > 0 && n > 0) {
            long cur = Math.min(n, ans[i - 1] * 2 - ans[i]);
            ans[i] += cur;
            //println(cur + " " + n);
            n -= cur;
            i--;
        }
        if(n > 0) {
            print("NO");
            return;
        }

        println("YES");
        for(long el : ans) {
            print(el + " ");
        }
    }

    /*static class Pair implements Comparable<Pair> {
        double a;
        int pos;

        Pair(double value, int pos) {
            a = value;
            this.pos = pos;
        }

        public int compareTo(Pair p) {
            if(this.a > p.a) return 1;
            else if(this.a == p.a) return 0;
            return -1;
        }
    }*/

    static void print(Object o) {
        System.out.print(o.toString());
    }

    static void println(Object o) {
        System.out.println(o.toString());
    }
}
