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.math.BigInteger;
import java.util.*;

public class Main {
    public static void main(String [] args)throws  IOException{
        Scanner sc=new Scanner(System.in);
        long x=sc.nextLong(),y=sc.nextLong();
        BigInteger b=new BigInteger(Long.toString(y)),a=b.add(new BigInteger("1")),c=new BigInteger(Long.toString(x));
        a=a.multiply(b);
        a=a.divide(new BigInteger("2"));
        if(a.compareTo(c)==1){
            System.out.println(-1);
            System.exit(0);
        }
        long e=gcd(x,y);
        if(e==-1)
            System.out.println(-1);
        else{
            long sum=0;
            for(int i=1;i<=y;i++){
                if(i!=y) {
                    System.out.print((i * e) + " ");
                    sum+=i*e;
                }
                else
                    System.out.println(x-sum);
            }
        }
    }
    static long gcd(long a,long b){
        long r=-1,s=(b*(b+1))/2;
        for(int i=1;i<=Math.sqrt(a);i++){
            if(a%i==0){
                if(a/i>=s)
                    r=Math.max(r,i);
                if((a/(a/i))>=s)
                    r=Math.max(r,a/i);
            }
        }
        return r;
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(String file) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}