P2193 HXY and Sequence

HXY had a sudden idea: she wants to find a sequence of positive integers such that every number in the sequence does not exceed $n$, the length of the sequence is $p$, and except for the first number, every number is divisible by the previous number (i.e., is a multiple of the previous number). She quickly found one such sequence. But she felt that was not enough and wants to know how many such sequences there are, but she was frightened by the astonishing constraints. Now she has come to you; please help her solve this problem. Since the result may be very large, please output the value modulo $10^9+7$.

The first line contains two positive integers $n$ and $p$.

Output a single line with one positive integer, which is the number of sequences that satisfy the conditions, modulo $10^9+7$.

Constraints: For $10\%$ of the testdata, $p=1$. For $30\%$ of the testdata, $1 \leq n,p \leq 10$. For $60\%$ of the testdata, $1 \leq n,p \leq 5 \times 10^2$. For $100\%$ of the testdata, $1 \leq n,p \leq 2 \times 10^3$. Translated by ChatGPT 5