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.

TASK

CONSTRAINTS

• 1 <= N <= 1,000,000
• 7 <= M <= 10,000,000

입력

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

출력

입출력 예

입력

5 
7 
PLPPL 

출력

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

입력

12 
10000 
LPLLPLPPLPLL 

출력

39

GRADING

출처:International Olympiad In Informatics 2008