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Codeforces Round 449 (Div. 1) |
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Finished |

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chinese remainder theorem

combinatorics

math

number theory

*2900

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D. Nephren Runs a Cinema

time limit per test

2.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLakhesh 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*.

Input

One line containing four integers *n* (1 ≤ *n* ≤ 10^{5}), *p* (1 ≤ *p* ≤ 2·10^{9}), *l* and *r* (0 ≤ *l* ≤ *r* ≤ *n*).

Output

One line indicating the answer modulo *p*.

Examples

Input

4 97 2 3

Output

13

Input

4 100 0 4

Output

35

Note

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.

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