{-# LANGUAGE BangPatterns #-} {-# LANGUAGE CPP #-} {-# LANGUAGE DerivingStrategies #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE MagicHash #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE TypeApplications #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeInType #-} {-# LANGUAGE UnboxedTuples #-} import Data.Bits import Data.Coerce import qualified Data.Ratio as R import qualified Data.Vector.Generic as VG import qualified Data.Vector.Generic.Mutable as VGM import qualified Data.Vector.Unboxed as VU import qualified Data.Vector.Unboxed.Mutable as VUM import GHC.Exts #define MOD 1000000007 main :: IO () main = do [a, b, n] <- map (read :: String -> Int) . words <$> getLine let matrix = M (mint a) (mint b) (mint 1) (mint 0) print $ solver matrix n solver :: Matrix2x2 Mint -> Int -> Mint solver m n = let (M _ _ c _) = m @^ n in c data Matrix2x2 a = M !a !a !a !a infixr 8 @^ infixl 7 @* (@*) :: Matrix2x2 Mint -> Matrix2x2 Mint -> Matrix2x2 Mint (M a b c d) @* (M x y z w) = M (a * x + b * z) (a * y + b * w) (c * x + d * z) (c * y + d * w) {-# INLINE (@*) #-} (@^) :: Matrix2x2 Mint -> Int -> Matrix2x2 Mint (@^) _ 0 = M 1 0 0 1 m @^ i = loop m m (i - 1) where loop acc _ 0 = acc loop acc _ 1 = acc loop acc m i = case i `divMod` 2 of (j, 0) -> loop acc (m @* m) j (j, _) -> loop (acc @* m) (m @* m) j modulus :: Num a => a modulus = MOD {-# INLINE modulus #-} infixr 8 ^% infixl 7 *%, /% infixl 6 +%, -% (+%) :: Int -> Int -> Int (I# x#) +% (I# y#) = case x# +# y# of r# -> I# (r# -# ((r# >=# MOD#) *# MOD#)) {-# INLINE (+%) #-} (-%) :: Int -> Int -> Int (I# x#) -% (I# y#) = case x# -# y# of r# -> I# (r# +# ((r# <# 0#) *# MOD#)) {-# INLINE (-%) #-} (*%) :: Int -> Int -> Int (I# x#) *% (I# y#) = case timesWord# (int2Word# x#) (int2Word# y#) of z# -> case timesWord2# z# im# of (# q#, _ #) -> case minusWord# z# (timesWord# q# m#) of v# | isTrue# (geWord# v# m#) -> I# (word2Int# (plusWord# v# m#)) | otherwise -> I# (word2Int# v#) where m# = int2Word# MOD# im# = plusWord# (quotWord# 0xffffffffffffffff## m#) 1## {-# INLINE (*%) #-} (/%) :: Int -> Int -> Int (I# x#) /% (I# y#) = go# y# MOD# 1# 0# where go# a# b# u# v# | isTrue# (b# ># 0#) = case a# `quotInt#` b# of q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#)) | otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#) {-# INLINE (/%) #-} (^%) :: Int -> Int -> Int x ^% n | n > 0 = go 1 x n | n == 0 = 1 | otherwise = go 1 (1 /% x) (-n) where go !acc !y !m | m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1) | m == 1 = acc *% y | otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1) newtype Mint = Mint { getMint :: Int } deriving newtype (Eq, Ord, Read, Show, Real) mint :: Integral a => a -> Mint mint x = fromIntegral $ mod (fromIntegral x) MOD {-# INLINE mint #-} mintValidate :: Mint -> Bool mintValidate (Mint x) = 0 <= x && x < MOD {-# INLINE mintValidate #-} instance Bounded Mint where minBound = Mint 0 maxBound = Mint $ modulus - 1 instance Enum Mint where toEnum = mint fromEnum = coerce instance Integral Mint where quotRem x y = (x / y, x - x / y * y) toInteger = coerce (toInteger @Int) instance Num Mint where (+) = coerce (+%) (-) = coerce (-%) (*) = coerce (*%) abs = id signum = const (Mint 1) fromInteger x = coerce @Int @Mint . fromInteger $ mod x modulus instance Fractional Mint where (/) = coerce (/%) fromRational q = fromInteger (R.numerator q) / fromInteger (R.denominator q) newtype instance VUM.MVector s Mint = MV_Mint (VUM.MVector s Int) newtype instance VU.Vector Mint = V_Mint (VU.Vector Int) instance VU.Unbox Mint instance VGM.MVector VUM.MVector Mint where basicLength (MV_Mint v) = VGM.basicLength v {-# INLINE basicLength #-} basicUnsafeSlice i n (MV_Mint v) = MV_Mint $ VGM.basicUnsafeSlice i n v {-# INLINE basicUnsafeSlice #-} basicOverlaps (MV_Mint v1) (MV_Mint v2) = VGM.basicOverlaps v1 v2 {-# INLINE basicOverlaps #-} basicUnsafeNew n = MV_Mint `fmap` VGM.basicUnsafeNew n {-# INLINE basicUnsafeNew #-} basicInitialize (MV_Mint v) = VGM.basicInitialize v {-# INLINE basicInitialize #-} basicUnsafeReplicate n x = MV_Mint `fmap` VGM.basicUnsafeReplicate n (coerce x) {-# INLINE basicUnsafeReplicate #-} basicUnsafeRead (MV_Mint v) i = coerce `fmap` VGM.basicUnsafeRead v i {-# INLINE basicUnsafeRead #-} basicUnsafeWrite (MV_Mint v) i x = VGM.basicUnsafeWrite v i (coerce x) {-# INLINE basicUnsafeWrite #-} basicClear (MV_Mint v) = VGM.basicClear v {-# INLINE basicClear #-} basicSet (MV_Mint v) x = VGM.basicSet v (coerce x) {-# INLINE basicSet #-} basicUnsafeCopy (MV_Mint v1) (MV_Mint v2) = VGM.basicUnsafeCopy v1 v2 {-# INLINE basicUnsafeCopy #-} basicUnsafeMove (MV_Mint v1) (MV_Mint v2) = VGM.basicUnsafeMove v1 v2 {-# INLINE basicUnsafeMove #-} basicUnsafeGrow (MV_Mint v) n = MV_Mint `fmap` VGM.basicUnsafeGrow v n {-# INLINE basicUnsafeGrow #-} instance VG.Vector VU.Vector Mint where basicUnsafeFreeze (MV_Mint v) = V_Mint `fmap` VG.basicUnsafeFreeze v {-# INLINE basicUnsafeFreeze #-} basicUnsafeThaw (V_Mint v) = MV_Mint `fmap` VG.basicUnsafeThaw v {-# INLINE basicUnsafeThaw #-} basicLength (V_Mint v) = VG.basicLength v {-# INLINE basicLength #-} basicUnsafeSlice i n (V_Mint v) = V_Mint $ VG.basicUnsafeSlice i n v {-# INLINE basicUnsafeSlice #-} basicUnsafeIndexM (V_Mint v) i = coerce `fmap` VG.basicUnsafeIndexM v i {-# INLINE basicUnsafeIndexM #-} basicUnsafeCopy (MV_Mint mv) (V_Mint v) = VG.basicUnsafeCopy mv v elemseq _ = seq {-# INLINE elemseq #-}