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.StringTokenizer;

public class MaxGCDE20C {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner();
        long n = in.nextLong();
        long k = in.nextLong();
        if (k >= 200000 || k * (k + 1) / 2 > n) {
            System.out.println("-1");
            return;
        }
        
        long tri = k * (k + 1) / 2;
        ArrayList<Long> factors = new ArrayList<Long>();
        long val = -1;
        for (long i = 1; i < Math.sqrt(n) + 0.000001; i++) {
            if (n % i == 0) {
                factors.add(i);
                if (n / i < tri) {
                    val = factors.get(factors.size() - 2);
                    break;
                }
            }
        }
        
        if (val == -1) {
            ArrayList<Long> factorsNew = new ArrayList<Long>();
            for (int i = factors.size() - 1; i >= 0; i--) {
                long num = n / factors.get(i);
                if (factors.get(i) < tri) {
                    if (factorsNew.size() >= 1) {
                        val = factorsNew.get(factorsNew.size() - 1);
                    } else {
                        val = factors.get(factors.size() - 1);
                    }
                    break;
                }
                factorsNew.add(num);
            }
        }
        
        for (long i = 1; i < k; i++) {
            System.out.print(val * i + " ");
        }
        long finalVal = k + n / val - tri;
        System.out.println(finalVal * val);
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }
}
