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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author Silviase
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    Scanner in = new Scanner(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    CBoxesAndCandies solver = new CBoxesAndCandies();
    solver.solve(1, in, out);
    out.close();
  }

  static class CBoxesAndCandies {

    public void solve(int testNumber, Scanner in, PrintWriter out) {
    /*
      解法
      a[0],a[1]について,まずa[1]から減らすべきであることは分かっている.
      a[1]でも足りなければさかのぼって減らせばいいことがわかる.
      a b a....みたいな形になっていきそうだけど...
      サンプルはどうだろう
      1   1 6 1 2 0 4なら1,6->1,0にして0,1->1,2(1,0)にして0,4->0,1で6,2,3の11個
      多分問題は無さそう...?
      なんかキラーケースがあるような気がするんだけど…
     */
      int n = in.nextInt();
      int x = in.nextInt();
      int[] a = new int[n];
      int sum = 0;
      for (int i = 0; i < n; i++) {
        a[i] = in.nextInt();
      }
      for (int i = 1; i < n; i++) {
        int niko = a[i] + a[i - 1];
        if (a[i - 1] > x) {
          sum += (niko - x);
          a[i] = 0;
          a[i - 1] = x;
        } else if (niko > x) {
          sum += (niko - x);
          a[i] = x - a[i - 1];
        }
      }
      out.println(sum);

      // マジで直感的だけど通らなさそうな不安にさせるやつヤメロ
    }

  }
}