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;
long long w, j, i, m, n, a[2005][2005], k;
vector<int> v[2010];
int main() {
  scanf("%d %d", &m, &n);
  for (i = 1; i <= m; i++) {
    a[i][1] = 1;
  }
  for (i = 1; i <= m; i++) {
    for (j = 1; j * j <= i; j++) {
      if (i % j != 0) continue;
      if (j * j != i) {
        v[i].push_back(j);
        v[i].push_back(i / j);
      } else
        v[i].push_back(j);
    }
  }
  for (j = 1; j <= n; j++) {
    for (i = 1; i <= m; i++) {
      for (w = 0; w < v[i].size(); w++) {
        a[i][j] = (a[i][j] + a[v[i][w]][j - 1]) % 1000000007;
      }
    }
  }
  for (i = 1; i <= m; i++) k = (k + a[i][n]) % 1000000007;
  cout << k % 1000000007;
}