F - Small Products

Score : $600$ points

Problem Statement

Find the number of sequences of length $K$ consisting of positive integers such that the product of any two adjacent elements is at most $N$, modulo $10^9+7$.

Constraints

• $1\leq N\leq 10^9$
• 1 $2\leq K\leq 100$ (fixed at 21:33 JST)
• $N$ and $K$ are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the number of sequences, modulo $10^9+7$.

3 2

5

$(1,1)$, $(1,2)$, $(1,3)$, $(2,1)$, and $(3,1)$ satisfy the condition.

10 3

147

314159265 35

457397712