Problem: Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

* 1\leq N\leq 10^9
* ~~1~~ 2\leq K\leq 100 (fixed at 21:33 JST)
* N and K are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the number of sequences, modulo 10^9+7.

Examples

Input

3 2


Output

5


Input

10 3


Output

147


Input

314159265 35


Output

457397712

Solution (in JAVA):

Solution:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Main {


  private static void solve() {
    int n = ni();
    int k = ni();

    int mod = (int) 1e9 + 7;

    List<Integer> list = new ArrayList<>();
    for (int i = 1; (long) i * i <= n; i++) {
      int x = i;
      int y = n / i;

      list.add(x);
      if (x != y) {
        list.add(y);
      }
    }

    Collections.sort(list);
    int m = list.size();
    int[] p = list.stream().mapToInt(v -> v).toArray();
    int[] len = new int[m];
    for (int i = 0; i < m; i ++) {
      len[i] = p[i] - (i == 0 ? 0 : p[i - 1]);
    }

    Map<Integer, Integer> inv = new HashMap<>();
    for (int i = 0; i < m; i++) {
      inv.put(p[i], i);
    }

    long[][] dp = new long[k + 1][m];
    dp[0][0] = 1;

    for (int i = 0; i < k; i++) {
      long sum = 0;
      int s = 0;

      for (int j = m - 1; j >= 0; j --) {
        for (; s < m && p[j] * p[s] <= n; s ++) {
          sum += dp[i][s];
          sum %= mod;
        }
        dp[i + 1][j] = sum * len[j] % mod;
        dp[i + 1][j] %= mod;
      }
    }
    
    
    System.out.println(Arrays.stream(dp[k]).sum() % mod);

  }




  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

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

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

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

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}