Subtask 1

We can solve this by brute force; Each turn there are at most ~2 \cdot 7 + 6 = 20~ valid moves you can make, and with ~1 \leq N \leq 2~ turns there are at most ~20^2 = 400~ possibilities.

Time complexity: ~O(20^N)~

Subtask 2

~20^{1000} \approx 1.07 \cdot 10^{1301}~. In no universe are we brute forcing this one.

However, note that at any given turn, there are 7 cards, each with 3 possible states. This means there are a total of ~3^7 = 2187~ configurations every turn. We can thus do dynamic programming; for each turn, keep track of how many possibilities there are for all ~2187~ configurations.

Indexing a DP array by a state and iterating over every possible state could be difficult. One way of doing this is to number the suits ~0, 1, 2~ and interpret each state as a base-3 number. Finding a way to extract and/or modify a digit in this number is left as an exercise to the reader.

Time complexity: ~O(2187 \cdot N) = O(N)~

(P.S.: If you are tasked with finding an answer "modulo <large prime>", usually ~10^9 + 7~, it's most likely a dynamic programming problem!)