Problem: Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.

A sequence of l integers b1, b2, ..., bl (1 ≤ b1 ≤ b2 ≤ ... ≤ bl ≤ n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally <image> for all i (1 ≤ i ≤ l - 1).

Given n and k find the number of good sequences of length k. As the answer can be rather large print it modulo 1000000007 (109 + 7).

Input

The first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).

Output

Output a single integer — the number of good sequences of length k modulo 1000000007 (109 + 7).

Examples

Input

3 2


Output

5


Input

6 4


Output

39


Input

2 1


Output

2

Note

In the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3].

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<long long int> adj[2005];
long long int a[2005][2005];
int main() {
  long long int n, m, k = 1e9 + 7, t, sum = 0;
  cin >> n >> m;
  for (long long int i = 1; i <= n; i++) {
    for (long long int j = 1; j <= sqrt(i); j++) {
      if (i % j == 0) {
        adj[i].push_back(j);
        if (j != sqrt(i)) adj[i].push_back(i / j);
      }
    }
  }
  for (long long int i = 1; i <= n; i++) a[1][i] = 1;
  if (m == 1) sum = n;
  for (long long int i = 2; i <= m; i++) {
    for (long long int j = 1; j <= n; j++) {
      for (auto f : adj[j]) {
        a[i][j] += a[i - 1][f] % k;
        a[i][j] %= k;
      }
      if (i == m) sum += a[i][j];
      sum %= k;
    }
  }
  cout << sum << endl;
  return 0;
}