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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Numerics;


#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

namespace competitive_programming
{
    public class Program
    {
        static void Main(string[] args)
        {
#if DEBUG
            var scanner = new IO.StreamScanner(File.Open("input.txt", FileMode.Open));
#else
            var scanner = new IO.StreamScanner(Console.OpenStandardInput());
#endif

            var n = scanner.Integer();
            var x = scanner.Long();
            var candies = new List<long>();
            for (int i = 0; i < n; i++) candies.Add(scanner.Long());

            var ret = 0L;
            for (int i = 0; i < n - 1; i++)
            {
                if (candies[i] + candies[i + 1] <= x) continue;
                var eat = (candies[i] + candies[i + 1]) - x;
                ret += eat;
                candies[i + 1] = Math.Max(0, candies[i + 1] - eat);
            }

            IO.Printer.Out.WriteLine(ret);
            IO.Printer.Out.Flush();
        }    
    }

#if DEBUG
    [TestClass]
    public class TestClass
    {
        [TestMethod]
        public void Test()
        {
        }
    }
#endif
}

#region INOUT

namespace IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
        }

        public static Printer Out { get; set; }

        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }
}

#endregion