import Data.List (foldl', scanl) import Data.Int (Int) md :: Int md = 10^9 + 7 modadd :: Int -> Int -> Int modadd a b = (a + b) `mod` md modmul :: Int -> Int -> Int modmul a b = a * b `mod` md modpow :: Int -> Int -> Int modpow a b | b == 0 = 1 | odd b = a * modpow a (b - 1) `mod` md | otherwise = modpow (a * a `mod` md) (b `div` 2) modinv :: Int -> Int modinv a = modpow a (md - 2) -- (x-1)(x-2)...(x-n+1) -- ------------------------ a[0] + ... -- (0-1)(0-2)...(0-n+1) lagrange :: [Int] -> Int -> Int lagrange a x | x < n = a !! x | otherwise = let (sm, _, _, _) = foldl' f (0, 0, 1, q) a in sm where n = length a p = foldl' modmul 1 [(x - i) | i <- [0..n-1]] q = foldl' modmul 1 [-i | i <- [1..n-1]] f :: (Int, Int, Int, Int) -> Int -> (Int, Int, Int, Int) f (sm, k, l, r) ak = (nextSm, k + 1, nextL, nextR) where nextSm = modadd sm $ ak `modmul` p `modmul` modinv (l `modmul` r `modmul` (x - k)) nextL = l `modmul` (k + 1) nextR = r `modmul` negate (modinv (n - 1 - k)) computeSmall :: Int -> [Int] computeSmall k = scanl f 0 [1..k + 2] where f s x = s `modadd` (modpow x k) solve :: Int -> Int -> Int solve n k = lagrange (computeSmall k) (n `mod` md) main = do [n, k] <- map read . words <$> getLine :: IO [Int] print $ solve n k