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;

class ColorfulSlimes
{
	static public void Main(string[] args)
	{
		int N, x;
		string[] vals = Console.ReadLine().Split(' ');

		N = int.Parse(vals[0]);
		x = int.Parse(vals[1]);
		vals = Console.ReadLine().Split(' ');
		int[] a = new int[N+1];
		for(int i=1; i<=N; i++)
			a[i] = int.Parse(vals[i-1]);

		int[,] b = new int[N+1,N];
		for(int i=1; i<=N; i++)
		{
			b[i,0] = a[i];
		}
		for(int i=1; i<=N; i++)
		{
			for(int k=1; k<=N-1; k++)
			{
				int j;
				if(i - k >= 1)
					j = i - k;
				else
					j = i - k + N;
				b[i,k] = Math.Min(b[i,k-1], a[j]); 
			}
		}

		long minTime = long.MaxValue;
		for(int k = 0; k <= N-1; k++)
		{
			long t = 0;
			for(int i=1; i <= N; i++)
			{
				t += b[i,k];
			}
			t += k * x;
			if(t < minTime)
			{
				minTime = t;
			}
		}
		Console.WriteLine(minTime);	
	}

}