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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.ArrayList;

public class Main {
    public static void main(String[] args) throws Exception {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            String line;
            while ((line = br.readLine()) != null) {
                String[] s = line.split(" ");
                int n = Integer.parseInt(s[0]);
                int x = Integer.parseInt(s[1]);
                s = br.readLine().split(" ");
                int[] a = new int[n];
                for(int i=0; i<n; i++){
                    a[i] = Integer.parseInt(s[i]);
                }
                int[][] b = new int[n][];
                for(int i=0; i<n; i++){
                    int[] bi = new int[n];
                    for(int k=0; k<n; k++){
                        if(k==0){
                            bi[0] = a[(i-k>=0)?i-k:i-k+n];
                        }else{
                            bi[k] = Math.min(bi[k-1], a[(i-k>=0)?i-k:i-k+n]);
                        }
                    }
                    b[i] = bi;
                }
                int min = Integer.MAX_VALUE;
                for(int k=0; k<n; k++){
                    int sum = 0;
                    for(int i=0; i<n; i++){
                        sum+=b[i][k];
                    }
                    if(k*x+sum<min){
                        min=k*x+sum;
                    }
                }
                System.out.println(min);
            }
        }
    }
}