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: Accepted)

using System;
class Program
{
        static void Main(string[] args)
        {
                // 整数の入力
                //int a = int.Parse(Console.ReadLine());
                // スペース区切りの整数の入力
                string [] tmp = Console.ReadLine().Split(' ');
                long N = int.Parse(tmp[0]);
        long x = int.Parse(tmp[1]);
                string [] a = Console.ReadLine().Split(' ');
        long[,] b = new long[2001, 2001];

        for (int xx = 0; xx < 2001; xx++) {
            for (int yy = 0; yy < 2001; yy++) {
                b[xx, yy] = 0;
            }
        }

        long t = 0;
        long bl = 0;
                long s = 0;

        long ans = long.MaxValue;

        for (long k = 0; k < N; k++) {
            for (int i = 0; i < N; i++) {
                bl = (i < k) ? 1 : 0;
                t = i - k + N * bl;
                //Console.WriteLine(a[t]);
                if (k == 0) {
                    b[k, i] = int.Parse(a[t]);
                } else {
                    b[k, i] = Math.Min(b[k-1, i], int.Parse(a[t]));
                }
            }
            s = 0;
            for (int z = 0; z < N; z++) {
                s += b[k, z];
            }

            ans = Math.Min(s + x * k, ans);
            //Console.WriteLine(ans);
        }

                //出力
                Console.WriteLine(ans);
        }
}