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)

/**
 * @Author Mehdi Maick
 * Created on 04/12/2016.
 */

import java.util.*;
import java.io.*;

import static java.lang.Math.*;

public class Main {
    public static void solve(FastReader fs, PrintWriter pw) {
        int n = fs.nextInt();
        long x = fs.nextLong();
        long[] tab = fs.nextLongArray(n);
        long ans = 0;
        long sum = tab[0];
        for (int i = 1; i < n; i++) {
            sum += tab[i];
            if (tab[i] + tab[i - 1] > x) {
                long diff = ((tab[i] + tab[i - 1]) - x);
                if (tab[i] >= tab[i - 1]) {
                    tab[i] = tab[i] - diff;
                    ans += diff;
                } else {
                    tab[i - 1] = tab[i - 1] - diff;
                    ans += diff;
                }
            }
        }
        if(x == 0){
            pw.println(sum);
        }else {
            pw.println(ans);
        }
    }

    public static void main(String[] args) throws Exception {
        FastReader fs = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));

        solve(fs, pw);

        fs.close();
        pw.close();
    }

    static class FastReader {

        BufferedReader reader;
        StringTokenizer st;

        FastReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String line = reader.readLine();
                    if (line == null) {
                        return null;
                    }
                    st = new StringTokenizer(line);
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String s = null;
            try {
                s = reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        char nextChar() {
            return next().charAt(0);
        }

        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            int i = 0;
            while (i < n) {
                arr[i++] = nextInt();
            }
            return arr;
        }

        long[] nextLongArray(int n) {
            long[] arr = new long[n];
            int i = 0;
            while (i < n) {
                arr[i++] = nextLong();
            }
            return arr;
        }

        int[] nextIntArrayOneBased(int n) {
            int[] arr = new int[n + 1];
            int i = 1;
            while (i <= n) {
                arr[i++] = nextInt();
            }
            return arr;
        }

        long[] nextLongArrayOneBased(int n) {
            long[] arr = new long[n + 1];
            int i = 1;
            while (i <= n) {
                arr[i++] = nextLong();
            }
            return arr;
        }

        void close() {
            try {
                reader.close();
            } catch (IOException e) {
                System.err.println("There's been an error trying closing the reader ");
                e.printStackTrace();
            }
        }
    }


}