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)

//package AtCoder.Indeed11;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) {
        int n = in.NI(); long x = in.NL();
        long[] q = new long[n];
        long[] q2 = new long[n];
        for (int i=0;i<n;i++) q[i] = in.NL();
        for (int i=0;i<n;i++) q2[i] = q[i];

        long ans = Long.MAX_VALUE;
        long tans = 0;
        for (int i=0;i<n-1;i++) {
            int j = i + 1;
            long tobesub = Long.max(0, q[j] + q[i] - x);
            if (q[j]>=tobesub) {
                q[j]-=tobesub;
                tans += tobesub;
                tobesub=0;
            } else {
                q[j] = 0; tobesub-=q[j];
                tans+=q[j];
            }

            if (tobesub>0) {
                q[i]-=tobesub; tans+=tobesub;
                tobesub=0;
            }
        }

        ans = Long.min(tans, ans);
        tans = 0;

        for (int i=0;i<n-1;i++) {
            int j = i + 1;
            long tobesub = Long.max(0, q2[j] + q2[i] - x);
            if (q2[i]>=tobesub) {
                q2[i]-=tobesub;
                tans += tobesub;
                tobesub=0;
            } else {
                q2[i] = 0; tobesub-=q2[i];
                tans+=q2[i];
            }

            if (tobesub>0) {
                q2[j]-=tobesub; tans+=tobesub;
                tobesub=0;
            }
        }
        ans = Long.min(tans, ans);
        out.println(ans);

        out.close();
    }

    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int NI() {
            return Integer.parseInt(next());
        }

        public long NL() {
            return Long.parseLong(next());
        }

    }
}