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Codeforces Round 240 (Div. 1) |
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Finished |

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combinatorics

dp

number theory

*1400

No tag edit access

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B. Mashmokh and ACM

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMashmokh'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).

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 (10^{9} + 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].

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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