Mashmokh and ACM

题意翻译

如果一个数列中，后一个数都能被前面一个数整除，那么就叫这个数列为好数列。输入 $n, k$，求数列中最大元素不超过 $n$，数列长度为 $k$ 的好数列的种数（对 $1000000007$ 取模） 由 @ROBOT233 提供翻译

题目描述

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 $ b_{1},b_{2},...,b_{l} $ $ (1<=b_{1}<=b_{2}<=...<=b_{l}<=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 $ $ (10^{9}+7) $ .

输入输出格式

输入格式

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

输出格式

Output a single integer — the number of good sequences of length $ k $ modulo $ 1000000007 $ $ (10^{9}+7) $ .

输入输出样例

输入样例 #1

3 2

输出样例 #1

5

输入样例 #2

6 4

输出样例 #2

39

输入样例 #3

2 1

输出样例 #3

2

说明

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