#P414B. Mashmokh and ACM
Mashmokh and ACM
No submission language available for this problem.
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, ..., 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 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).
The first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).
Output a single integer — the number of good sequences of length k 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).
Samples
3 2
5
6 4
39
2 1
2
Note
In the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3].