IOI '08 - Cairo, Egypt

Linear Garden

Ramesses II has just returned victorious from battle. To commemorate his victory, he has decided to build a majestic garden. The garden will contain a long line of plants that will run all the way from his palace at Luxor to the temple of Karnak. It will consist only of lotus plants and papyrus plants, since they symbolize Upper and Lower Egypt respectively.

The garden must contain exactly N plants. Also, it must be balanced: in any contiguous section of the garden, the numbers of lotus and papyrus plants must not differ by more than 2.

A garden can be represented as a string of letters 'L' (lotus) and 'P' (papyrus). For example, for N=5 there are 14 possible balanced gardens. In alphabetical order, these are: LLPLP, LLPPL, LPLLP, LPLPL, LPLPP, LPPLL, LPPLP, PLLPL, PLLPP, PLPLL, PLPLP, PLPPL, PPLLP, and PPLPL.

The possible balanced gardens of a certain length can be ordered alphabetically, and then numbered starting from 1. For example, for N=5, garden number 12 is the garden PLPPL.

Write a program that, given the number of plants N and a string that represents a balanced garden, calculates the number assigned to this garden modulo some given integer M.

Note that for solving the task, the value of M has no importance other than simplifying computations.

Input

Your program must read from the standard input the following data:

• Line 1 contains the integer N (1 ≤ N ≤ 1 000 000), the number of plants in the garden.
• Line 2 contains the integer M (7 ≤ M ≤ 100 000 000).
• Line 3 contains a string of N characters 'L' (lotus) or 'P' (papyrus) that represents a balanced garden.

Output

Your program must write to the standard output a single line containing one integer between 0 and M-1 (inclusive), the number assigned to the garden described in the input, modulo M.

Sample Input 1

5
7
PLPPL

Sample Output 1

5

The actual number assigned to PLPPL is 12. So, the output is 12 modulo 7, which is 5.

Sample Input 2

12
10000
LPLLPLPPLPLL

Sample Output 2

39

Note: In test cases worth a total of 40% of the points, N will not exceed 40.

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Best Solutions

Point Value: 20 (partial)
Time Limit: 1.50s
Memory Limit: 128M
Added: Jun 02, 2010

Languages Allowed:
C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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