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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

class Main {
        public static void main(String args[]) {
                Scanner sc = new Scanner(System.in);
                int N = sc.nextInt(), x = sc.nextInt();
                int[] a = new int[N];
                for (int i = 0; i < N ; i++) {
                        a[i] = sc.nextInt();
                }
                int ans = 0;
                int xmax = 0;
                for (int i = 0; i < N; i++) {
                        int tmp = 1 << 20;
                        for (int j = 0; j < N; j++) {
                                if (tmp > a[(i - j + N) % N] + j * x) {
                                        tmp = Math.min(tmp, a[(i - j + N) % N] + j * x);
                                        xmax = Math.max(xmax, j);
                                }
                        }
                }
                for (int i = 0; i < N; i++) {
                        int tmp = 1 << 20;
                        for (int j = 0; j <= xmax; j++) {
                                if (tmp > a[(i - j + N) % N] + j * x) {
                                        tmp = Math.min(tmp, a[(i - j + N) % N]);
                                }
                        }
                        ans += tmp;
                }
                System.out.println(ans + xmax * x);
        }
}