Problem:
Score : 500 points

Problem Statement

There is a building with n rooms, numbered 1 to n.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).

Initially, there was one person in each room in the building.

After that, we know that there were exactly k moves happened up to now.

We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?

Find the count modulo (10^9 + 7).

Constraints

All values in input are integers.

3 \leq n \leq 2 \times 10^5

2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List
import qualified Data.Vector as V

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main = do
    [n, k] <- getIntList
    print $ solve n k

solve n k = modN $ sum [mulMod (comb n r) (comb (n-1) r) | r <- [0..n-1], r <= k]

moduloN :: Int
moduloN = 10 ^ 9 + 7

modN = flip mod moduloN

mulMod x y = modN $ x * y

finv :: Int -> Int
finv k = finvs V.! k
    where finvs :: V.Vector Int
          finvs = V.generate (2 * 10 ^ 5 + 1) finv'
              where finv' 0 = 1
                    finv' n = modN $ finvs V.! (n - 1) * inv n

inv :: Int -> Int
inv k = invs V.! k
    where inv' 1 = 1
          inv' n = modN (-(invs V.! r) * q)
              where (q, r) = moduloN `divMod` n
          invs :: V.Vector Int
          invs = V.generate (2 * 10 ^ 5 + 1) inv'

fact :: Int -> Int
fact k = facts V.! k
    where fact' 0 = 1
          fact' n = modN $ n * (facts V.! (n - 1))
          facts :: V.Vector Int
          facts = V.generate (2 * 10 ^ 5 + 1) fact'

comb :: Int -> Int -> Int
comb n k | n < 0 || k < 0 || n < k = 0
         | otherwise = modN $ modN (fact n * finv k) * finv (n - k)