Problem:
Score : 400 points

Problem Statement

Snuke lives in another world, where slimes are real creatures and kept by some people.
Slimes come in N colors. Those colors are conveniently numbered 1 through N.
Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.

Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

2≤N≤2,000

a_i are integers.

1≤a_i≤10^9

x is an integer.

1≤x≤10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;
using System.Linq;

namespace AtTest.AGC_Challenge
{
    class _004_B
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nx = ReadInts();
            int n = nx[0];
            long x = nx[1];
            int[] array = ReadInts();
            Array.Reverse(array);
            long resTime = int.MaxValue;
            for (int i = 0; i < n; i++)
            {
                var sortedDict = new SortedDictionary<int, int>();
                for (int j = 0; j <= i; j++)
                {
                    if (!sortedDict.ContainsKey(array[j]))
                    {
                        sortedDict.Add(array[j], 0);
                    }
                    sortedDict[array[j]]++;
                }
                long time = 0;
                for (int j = 0; j < n; j++)
                {
                    time += sortedDict.First().Key;

                    sortedDict[array[j]]--;
                    if (sortedDict[array[j]] == 0)
                    {
                        sortedDict.Remove(array[j]);
                    }

                    if (!sortedDict.ContainsKey(array[(j + i + 1) % n]))
                    {
                        sortedDict.Add(array[(j + i + 1) % n], 0);
                    }
                    sortedDict[array[(j + i + 1) % n]]++;
                }
                resTime = Math.Min(resTime, time + x * i);
            }
            Console.WriteLine(resTime);
        }

        class PriorityQueue<T>
        {
            private readonly List<KeyValuePair<long, T>> list;
            private int count;

            public PriorityQueue()
            {
                list = new List<KeyValuePair<long, T>>();
                count = 0;
            }

            private void Add(KeyValuePair<long, T> pair)
            {
                if (count == list.Count)
                {
                    list.Add(pair);
                }
                else
                {
                    list[count] = pair;
                }
                count++;
            }

            private void Swap(int a, int b)
            {
                KeyValuePair<long, T> tmp = list[a];
                list[a] = list[b];
                list[b] = tmp;
            }

            public void Enqueue(long key, T value)
            {
                Add(new KeyValuePair<long, T>(key, value));
                int c = count - 1;
                while (c > 0)
                {
                    int p = (c - 1) / 2;
                    if (list[c].Key >= list[p].Key) break;

                    Swap(p, c);
                    c = p;
                }
            }

            public KeyValuePair<long, T> Dequeue()
            {
                KeyValuePair<long, T> pair = list[0];
                count--;
                if (count == 0) return pair;

                list[0] = list[count];
                int p = 0;
                while (true)
                {
                    int c1 = p * 2 + 1;
                    int c2 = p * 2 + 2;
                    if (c1 >= count) break;

                    int c = (c2 >= count || list[c1].Key < list[c2].Key)
                        ? c1 : c2;
                    if (list[c].Key >= list[p].Key) break;

                    Swap(p, c);
                    p = c;
                }
                return pair;
            }

            public bool Exist() { return count > 0; }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}