You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal.

Greatest common divisor of sequence is maximum of such numbers that every element of sequence is divisible by them.

If there is no possible sequence then output -1.

Input

The first line consists of two numbers n and k (1 ≤ n, k ≤ 1010).

Output

If the answer exists then output k numbers — resulting sequence. Otherwise output -1. If there are multiple answers, print any of them.

Examples

Input

6 3


Output

1 2 3


Input

8 2


Output

2 6


Input

5 3


Output

-1


import java.io.*;
import java.util.ArrayList;
import java.util.Collections;

public class C803 {
    public static void main(String[] args) throws IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        String[] s1 = inp.readLine().split(" ");
        long sum = Long.parseLong(s1[0]);
        long size = Long.parseLong(s1[1]);

        ArrayList<Long> list = new ArrayList<>();
        long root = (int) Math.sqrt(sum);
        for(int i=1;i<=root;i++){
            if(i==root){
                if(sum%i==0) {
                    if (Math.pow(root, 2) == sum) {
                        list.add(root);
                    } else {
                        list.add(root);
                        list.add(sum/root);
                    }
                }
            }else if(sum%i==0){
                list.add((long) i);
                list.add(sum/i);
            }
        }

        Collections.sort(list,Collections.reverseOrder());
        long mullti = -1;
        for(int i=0;i< list.size();i++){
            if(check(list.get(i),size,sum)){
                mullti = list.get(i);
                break;
            }
        }

        if(mullti>0) {
            for (int i = 0; i < size - 1; i++) {
                long a = (i + 1) * mullti;
                sum -= a;
                out.write(a + " ");
            }
            long a = sum;
            out.write(a + " ");
            out.flush();
        }
        else{
            System.out.println(-1);
        }

    }
    static boolean check(long gcd,long terms, long reqd){
        if(terms>=603838835l){
            return false;
        }
        long sum = (terms*(2*gcd+(terms-1)*gcd))/2;
        if(sum<0){
            return false;
        }
        //System.out.println(sum);
        if(sum<=reqd){
            return true;
        }
        return false;
    }
}