Favorite Arrays 2

Seonggwan likes every array that satisfies all of the following conditions.

• The length of the array is $N$.
• Every element of the array is an integer between $1$ and $K$, inclusive.
• If two adjacent elements are $A$ and $B$ in that order, then $A \le B$ or $A \bmod B \ne 0$.

For example, when $N = 4$ and $K = 7$, the array $[1, 7, 7, 2]$ is one that Seonggwan likes. Its three adjacent pairs satisfy $1 \le 7$, $7 \le 7$, and $7 \bmod 2 \ne 0$.

Given $N$ and $K$, write a program that counts the arrays Seonggwan likes.

The first line contains $N$ and $K$, separated by a space. ($1 \le N \le 50000$, $1 \le K \le 50000$)

On the first line, print the number of arrays Seonggwan likes, modulo 1,000,000,007.