CF896D Nephren Runs a Cinema

Lakhesh loves to make movies, so Nephren helps her run a cinema. We may call it No. 68 Cinema.  However, one day, the No. 68 Cinema runs out of changes (they don't have 50-yuan notes currently), but Nephren still wants to start their business. (Assume that yuan is a kind of currency in Regulu Ere.) There are three types of customers: some of them bring exactly a 50-yuan note; some of them bring a 100-yuan note and Nephren needs to give a 50-yuan note back to him/her; some of them bring VIP cards so that they don't need to pay for the ticket. Now $ n $ customers are waiting outside in queue. Nephren wants to know how many possible queues are there that they are able to run smoothly (i.e. every customer can receive his/her change), and that the number of 50-yuan notes they have after selling tickets to all these customers is between $ l $ and $ r $ , inclusive. Two queues are considered different if there exists a customer whose type is different in two queues. As the number can be large, please output the answer modulo $ p $ .

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We use A, B and C to indicate customers with 50-yuan notes, customers with 100-yuan notes and customers with VIP cards respectively. For the first sample, the different possible queues that there are $ 2 $ 50-yuan notes left are AAAB, AABA, ABAA, AACC, ACAC, ACCA, CAAC, CACA and CCAA, and the different possible queues that there are $ 3 $ 50-yuan notes left are AAAC, AACA, ACAA and CAAA. So there are $ 13 $ different queues satisfying the first sample. Similarly, there are $ 35 $ different queues satisfying the second sample.