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: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.util.OptionalLong;
import java.util.stream.LongStream;
import java.util.function.IntToLongFunction;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BColorfulSlimes solver = new BColorfulSlimes();
        solver.solve(1, in, out);
        out.close();
    }

    static class BColorfulSlimes {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt(), x = in.nextInt();
            long[] a = LongStream.range(0, n).map(z -> in.nextInt()).toArray();

            IntToLongFunction p = m -> {
                long value = m * x;
                for (int i = 0; i < n; i++) {
                    long min = Long.MAX_VALUE;
                    for (int offset = 0; offset <= m; offset++) {
                        min = Math.min(min, a[(i + n - offset) % n]);
                    }
                    value += min;
                }
                return value;
            };

            int min = 0, max = n - 1;
            while (max - min > 2) {
                // System.out.println(min + "-" + max);
                int low = (min + max) / 3;
                int high = (min + max) * 2 / 3;
                if (p.applyAsLong(low) < p.applyAsLong(high)) {
                    max = high;
                } else {
                    min = low;
                }
            }

            out.println(IntStream.rangeClosed(min, max).mapToLong(p).min().orElse(0));
        }

    }
}