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

public class P803C {

  private static void solve() {
    long n = nextLong();
    long k = nextLong();

    long ans = -1;
    for (long i = 1; i * i <= n; i++) {
      if (n % i == 0) {
        if (good(i, k)) {
          ans = Math.max(n / i, ans);
        }

        if (good(n / i, k)) {
          ans = Math.max(i, ans);
        }
      }
    }

    if (ans == -1) {
      out.println(-1);
    } else {
      long sum = (k * (k + 1)) / 2;

      for (int i = 1; i < k; i++) {
        out.print((i * ans) + " ");
      }

      out.println((k + ((n / ans) - sum)) * ans);
    }
  }

  private static boolean good(long test, long k) {
    return getSum(k).compareTo(BigInteger.valueOf(test)) <= 0;
  }

  private static BigInteger getSum(long k) {
    BigInteger kb = BigInteger.valueOf(k);
    return kb.multiply(kb.add(BigInteger.ONE))
             .divide(BigInteger.valueOf(2));
  }

  private static void run() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);

    solve();

    out.close();
  }

  private static StringTokenizer st;
  private static BufferedReader br;
  private static PrintWriter out;

  private static String next() {
    while (st == null || !st.hasMoreElements()) {
      String s;
      try {
        s = br.readLine();
      } catch (IOException e) {
        return null;
      }
      st = new StringTokenizer(s);
    }
    return st.nextToken();
  }

  private static int nextInt() {
    return Integer.parseInt(next());
  }

  private static long nextLong() {
    return Long.parseLong(next());
  }

  public static void main(String[] args) {
    run();
  }
}