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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;
using static Extensions;
using static MathExtensions;

public static class Program
{
    public static void Solve()
    {
        var n = I;
        var x = I;
        var a = Repeat(n, () => I).ToArray();
        var ans = a.Select(t => Max(0, t - x)).Sum();
        a = a.Select(t => Min(t, x)).ToArray();

        Repeat(n - 1, i =>
        {
            var t = Max(0, a[i] + a[i + 1] - x);
            a[i + 1] -= t;
            ans += t;
        });

        Console.WriteLine(ans);
    }

    #region Scanners
    static Scanner _scanner;
    static char C => _scanner.NextChar();
    static string S => _scanner.NextString();
    static int I => _scanner.NextInt();
    static long L => _scanner.NextLong();
    static BigInteger B => _scanner.NextBigInteger();
    static double D => _scanner.NextDouble();
    static decimal M => _scanner.NextDecimal();
    #endregion

    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput());
        sw.NewLine = "\n";
#if DEBUG
        sw.AutoFlush = true;
#else
        sw.AutoFlush = false;
#endif
        Console.SetOut(sw);
        _scanner = new Scanner(Console.OpenStandardInput());
        Solve();
        Console.Out.Flush();
    }
}

public static partial class Extensions
{
}

#region Library
public class Scanner
{
    private readonly Stream _stream;
    private const int _bufferSize = 1024;
    private readonly byte[] _buf = new byte[_bufferSize];
    private int _len, _ptr;

    public Scanner(Stream stream)
    {
        _stream = stream;
    }

    public byte ReadByte()
    {
        if (_ptr >= _len)
        {
            _len = _stream.Read(_buf, 0, _bufferSize);
            _ptr = 0;
        }
        return _buf[_ptr++];
    }

    public char ReadChar() => (char)ReadByte();

    public string ReadLine()
    {
        var r = new StringBuilder();
        if (_ptr == 0) r.Append(ReadChar());
        for (; _ptr < _len; _ptr++) r.Append((char)_buf[_ptr]);
        return r.ToString();
    }

    public char NextChar() => char.Parse(NextString());

    public string NextString()
    {
        var r = new StringBuilder();
        var b = ReadChar();
        while (b != ' ' && b != '\n')
        {
            r.Append(b);
            b = ReadChar();
        }
        return r.ToString();
    }

    public int NextInt() => (int)NextLong();

    public long NextLong()
    {
        var r = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n')
        {
            r = r * 10 + b - '0';
            b = ReadByte();
        }
        return n ? -r : r;
    }

    public BigInteger NextBigInteger()
    {
        var r = new BigInteger();
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != ' ' && b != '\n')
        {
            r = r * 10 + b - '0';
            b = ReadByte();
        }
        return n ? -r : r;
    }

    public double NextDouble()
    {
        var i = 0L;
        var b = ReadByte();
        var n = b == '-';
        if (n) b = ReadByte();
        while (b != '.' && b != ' ' && b != '\n')
        {
            i = i * 10 + b - '0';
            b = ReadByte();
        }
        if (b != '.') return n ? -i : i;
        b = ReadByte();
        var f = 0L;
        var p = 0;
        while (b != ' ' && b != '\n')
        {
            f = f * 10 + b - '0';
            b = ReadByte();
            p++;
        }
        var r = i + (double)f / MathExtensions.Pow(10, p);
        return n ? -r : r;
    }

    public decimal NextDecimal() => decimal.Parse(NextString());

    public T Next<T>(Converter<string, T> parser) => parser(NextString());
}

[DebuggerStepThrough]
public static partial class Extensions
{
    public static void Assert(bool condition)
    {
        if (!condition) throw new Exception("Assertion failed");
    }

    public static string AsString(this IEnumerable<char> source) => new string(source.ToArray());

    public static void ForEach<T>(this IEnumerable<T> source, Action<T> action)
    {
        foreach (var item in source) action(item);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, _> func)
    {
        foreach (var item in source) func(item);
    }

    public static void ForEach<T>(this IEnumerable<T> source, Action<T, int> action)
    {
        var i = 0;
        foreach (var item in source) action(item, i++);
    }

    public static void ForEach<T, _>(this IEnumerable<T> source, Func<T, int, _> func)
    {
        var i = 0;
        foreach (var item in source) func(item, i++);
    }

    public static T Iterate<T>(int count, T seed, Func<T, T> func)
    {
        var r = seed;
        Repeat(count, () => { r = func(r); });
        return r;
    }

    public static void Repeat(int count, Action action)
    {
        for (var i = 0; i < count; i++) action();
    }

    public static void Repeat(int count, Action<int> action)
    {
        for (var i = 0; i < count; i++) action(i);
    }

    public static IEnumerable<T> Repeat<T>(Func<T> func)
    {
        for (var i = 0; ; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<T> func)
    {
        for (var i = 0; i < count; i++) yield return func();
    }

    public static IEnumerable<T> Repeat<T>(Func<int, T> func)
    {
        for (var i = 0; ; i++) yield return func(i);
    }

    public static IEnumerable<T> Repeat<T>(int count, Func<int, T> func)
    {
        for (var i = 0; i < count; i++) yield return func(i);
    }

    public static void Swap<T>(ref T x, ref T y)
    {
        var tmp = x; x = y; y = tmp;
    }
}

[DebuggerStepThrough]
public static class MathExtensions
{
    public static int Gcd(int left, int right)
    {
        int r;
        while ((r = left % right) != 0) { left = right; right = r; }
        return right;
    }

    public static long Gcd(long left, long right)
    {
        long r;
        while ((r = left % right) != 0L) { left = right; right = r; }
        return right;
    }

    public static BigInteger Gcd(BigInteger left, BigInteger right)
        => BigInteger.GreatestCommonDivisor(left, right);

    public static int HighestOneBit(int x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        return x - (x >> 1);
    }

    public static long HighestOneBit(long x)
    {
        x |= x >> 01;
        x |= x >> 02;
        x |= x >> 04;
        x |= x >> 08;
        x |= x >> 16;
        x |= x >> 32;
        return x - (x >> 1);
    }

    public static int Lcm(int left, int right) => left / Gcd(left, right) * right;

    public static long Lcm(long left, long right) => left / Gcd(left, right) * right;

    public static BigInteger Lcm(BigInteger left, BigInteger right)
        => left / Gcd(left, right) * right;

    public static int Pow(int value, int exponent)
    {
        var r = 1;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Pow(long value, int exponent)
    {
        var r = 1L;
        while (exponent > 0)
        {
            if ((exponent & 1) == 1) r *= value;
            value *= value;
            exponent >>= 1;
        }
        return r;
    }

    public static long Fact(int value)
    {
        var r = 1L;
        for (var i = 2; i <= value; i++) r *= i;
        return r;
    }
}
#endregion