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.math.BigDecimal;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long x = scanner.nextLong();
        long[] a = new long[n];
        long[] time = new long[n];
        long[] from = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextLong();
            time[i] = a[i];
            from[i] = i;
        }
        for (int i = 0; i < n; i++) {
            for (int j = 1; j < n; j++) {
                int index = (i + j) % n;
                int prev = (i + j - 1) % n;
                long orig = time[index];
                time[index] = Math.min(orig, time[prev] + x);
                if (time[index] != orig) {
                    from[index] = from[prev];
                }
            }
        }

        int maxCount = 0;
        BigDecimal result = new BigDecimal(0);
        for (int i = 0; i < n; i++) {
            int count = 0;
            BigDecimal r = new BigDecimal(time[i]);
            for (int j = 0; j < n; j++) {
                if (from[j] == i) {
                    count++;
                }
            }
            if (count == 0) {
                continue;
            }
            result = result.add(r.multiply(new BigDecimal(count)));
            maxCount = Math.max(maxCount, count);
        }
        System.out.println(new BigDecimal(maxCount - 1).multiply(new BigDecimal(x)).add(result));

    }

}