Problem:
Score : 100 points

Problem Statement

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves.
Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive).
Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7.
Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

All values in input are integers.

1 \leq N \leq 100

0 \leq K \leq 10^5

0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

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 Control.Monad.ST
import Data.Array.ST
import qualified Data.Vector.Unboxed as VU

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

main = do
    [n,k] <- getIntList
    as <- VU.fromList <$> getIntList
    print $ solve n k as

solve n k as = runST $ do
    arr <- newArray ((-1,-1),(n,k)) 0 :: ST s (STUArray s (Int,Int) Int)
    writeArray arr (0,0) 1
    forM_ [0..n] $ \i -> do
        let ai = as VU.! (i-1)
        forM_ [0..k] $ \j -> do
            if i == 0 then
                writeArray arr (0,j) (if j == 0 then 1 else 0)
            else do
                ij1 <- readArray arr (i,j-1)
                i1j <- readArray arr (i-1,j)
                ijm <- readArray arr (i-1, max (j-ai-1) (-1))
                writeArray arr (i,j) $ (ij1 + i1j - ijm) `mod` 1000000007
    readArray arr (n,k)