Given n and k, find the number of a sequences of integers $a_1, a_2, \cdots,a_{k + 1}$ such that

$a_{i+1}$ divides $a_{i}$ for $1 \le i \le k$ and $a_1 = n, a_{k + 1} = 1$.

Find the answer modulo $10^9 + 7$ for $(n,k) = \left((1101^{17})\cdot (2019^{29}), 3\cdot 367\cdot 673\right)$.