you have $$$n$$$ $$$(1 \leq n \leq 7000)$$$ days and $$$m$$$ $$$(1 \leq m \leq 10^{18})$$$ songs labeled from 0 to $$$m-1$$$.

you're given two parameters $$$k$$$ and $$$p$$$. $$$(0 < k < m)$$$ and $$$(1 \leq p \leq 4)$$$.

on each day $$$i$$$ you're given 3 parameters $$$x_i$$$ $$$a_i$$$ and $$$b_i$$$. meaning $$$x_i$$$ songs will be played starting from $$$b_i$$$-th song, and stepping by $$$k$$$. So songs with indexes $$$b_i, b_i + k (mod \; m), ..., b_i + (x_i - 1) * k (mod \; m)$$$ will be played. Each one of them will be played $$$a_i$$$ times.

you need to select $$$p$$$ different songs with non-adjacent labels. The value of each selection is defined by multiplying the number of times each of the $$$p$$$ songs is played.

Compute the sum of the values for all possible selections, modulo $$$10^9 + 7$$$.