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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class Solution {
    public static void main(String[] args) {
        try {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

            String string1 = br.readLine();

            System.out.print(start(string1));
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public static String start(String string1) {
        String[] numbers = string1.split(" ");
        int tasks = Integer.parseInt(numbers[0]);
        int days = Integer.parseInt(numbers[1]);

        long[] dayTasks = new long[days];

        long sum = 0;
        for (int i = 0; i < days; i++) {
            dayTasks[i] = i + 1;
            sum += i + 1;
        }

        if (sum > tasks) {
            return "NO\n";
        }

        long diff = tasks - sum;
        long add = diff / days;

        for (int i = 0; i < days; i++) {
            dayTasks[i] += add;
            sum += add;
        }

        if (tasks != sum) {
            dayTasks[days - 1] += tasks - sum;

            if (dayTasks[days - 2] * 2 < dayTasks[days - 1]) {
                dayTasks[days - 1] -= 1;
                dayTasks[days - 2] += 1;
                
                if (days > 2 && dayTasks[days - 3] * 2 < dayTasks[days - 2] || dayTasks[days - 1] == dayTasks[days - 2]) {
                    return "NO\n";
                }
            }
        }

        StringBuilder result = new StringBuilder("YES\n");
        for (int i = 0; i < days; i++) {
            result.append(dayTasks[i]).append(" ");
        }

        return result.toString().trim();
    }
}