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;
constexpr long long mod = (long long)1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, k;
  cin >> n >> k;
  vector<vector<long long>> dp(k + 1, vector<long long>(n + 1, 0));
  for (int i = 1; i <= n; i++) {
    dp[1][i] = 1;
  }
  for (int pos = 2; pos <= k; pos++) {
    for (int ending = 1; ending <= n; ending++) {
      for (int fact = 1; fact * fact <= ending; fact++) {
        if (fact * fact == ending && ending % fact == 0) {
          dp[pos][ending] =
              (dp[pos][ending] + dp[pos - 1][ending / fact]) % mod;
          continue;
        }
        if (ending % fact == 0) {
          dp[pos][ending] =
              (dp[pos][ending] + dp[pos - 1][ending / fact]) % mod;
          dp[pos][ending] = (dp[pos][ending] + dp[pos - 1][fact]) % mod;
        }
      }
    }
  }
  long long answer = 0;
  for (int i = 1; i <= n; i++) {
    answer = (answer + dp[k][i]) % mod;
  }
  cout << answer << '\n';
  return 0;
}