Mashmokh and ACM

1000ms

262144K

Description:

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, ..., b_l (1 ≤ b₁ ≤ b₂ ≤ ... ≤ b_l ≤ n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally $\text{[math]}$ 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).

Sample Input:

3 2

Sample Output:

Sample Input:

6 4

Sample Output:

Sample Input:

2 1

Sample Output:

Note:

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

Informação

Provedor Codeforces

Código CF414B