{-# LANGUAGE BangPatterns #-} data Matrix a = Matrix !a !a !a !a matrixMul :: Matrix Integer -> Matrix Integer -> Integer -> Matrix Integer matrixMul (Matrix a b c d) (Matrix a' b' c' d') n = Matrix ((a * a' + b * c') `mod` n) ((a * b' + b * d') `mod` n) ((c * a' + d * c') `mod` n) ((c * b' + d * d') `mod` n) matrixPow :: Matrix Integer -> Integer -> Integer -> Matrix Integer matrixPow _ 0 _ = Matrix 1 0 0 1 matrixPow m i n = loop m m (i - 1) where loop acc !_ 0 = acc loop acc m 1 = matrixMul acc m n loop acc m i = case i `quotRem` 2 of (j, 0) -> loop acc (matrixMul m m n) j (j, _) -> loop (matrixMul acc m n) (matrixMul m m n) j fib :: Integer -> Integer -> Integer fib i m = let Matrix a b c d = matrixPow (Matrix 0 1 1 1) (i - 1) m in b main :: IO () main = interact $ show . solve . map (read :: String -> Integer) . words solve :: [Integer] -> Integer solve [n, m] = fib n m