Problem:
Score : 300 points

Problem Statement

There are N boxes arranged in a row.
Initially, the i-th box from the left contains a_i candies.

Snuke can perform the following operation any number of times:

Choose a box containing at least one candy, and eat one of the candies in the chosen box.

His objective is as follows:

Any two neighboring boxes contain at most x candies in total.

Find the minimum number of operations required to achieve the objective.

Constraints

2 ≤ N ≤ 10^5

0 ≤ a_i ≤ 10^9

0 ≤ x ≤ 10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Print the minimum number of operations required to achieve the objective.

Sample Input 1

3 3
2 2 2

Sample Output 1

1

Eat one candy in the second box.
Then, the number of candies in each box becomes (2, 1, 2).

Sample Input 2

6 1
1 6 1 2 0 4

Sample Output 2

11

For example, eat six candies in the second box, two in the fourth box, and three in the sixth box.
Then, the number of candies in each box becomes (1, 0, 1, 0, 0, 1).

Sample Input 3

5 9
3 1 4 1 5

Sample Output 3

0

The objective is already achieved without performing operations.

Sample Input 4

2 0
5 5

Sample Output 4

10

All the candies need to be eaten.

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

import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Data.Char
import Control.Monad

solve vec n x = do
        vec' <- VU.unsafeThaw vec
        res <- forM [0..n-2] $ \i -> adjust vec' (i,i+1) x
        return $ sum res
    where
        adjust vec (i,j) x = do
            iv <- VUM.read vec i
            jv <- VUM.read vec j
            let diff = max (iv+jv-x) 0
            unless (diff == 0) $ do
                if (jv >= diff)
                    then do
                        VUM.write vec j (jv-diff)
                    else do
                        VUM.write vec j 0
                        VUM.write vec i (iv + (jv-diff))
            return diff

main = do
    [n, x] <- map read . words <$> getLine 
    as <- VU.unfoldrN n (B.readInt . B.dropWhile isSpace) <$> B.getLine
    solve as n x >>= print