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.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long x = sc.nextLong();
		long[] a = new long[N];
		LinkedList<Boolean> flag = new LinkedList<>();
		for (int i=0; i<N; i++) {
			a[i] = sc.nextLong();
			flag.add(false);
		}
		long res = 0;
		while (true) {
			for (P p=getMin(a, flag); p.x()<x; p=getMin(a, flag)) {
				res += p.x();
				flag.set(p.y(), true);
			}
			if (satisfied(flag)) break;
			flag.offer(flag.poll());
			res += x;
		}
		System.out.println(res);
		sc.close();
	}
	
	private static P getMin(long[] a, List<Boolean> flag) {
		long min = Long.MAX_VALUE;
		int index = -1;
		for (int i=0; i<a.length; i++) {
			if (flag.get(i)) continue;
			if (a[i]<min) {
				min = a[i];
				index = i;
			}
		}
		return new P(min, index);
	}
	
	private static boolean satisfied(List<Boolean> flag) {
		for (int i=0; i<flag.size(); i++) {
			if (!flag.get(i)) return false;
		}
		return true;
	}

	private static class P {
		private final long v1;
		private final int v2;
		public P(long v1, int v2) {
			this.v1 = v1;
			this.v2 = v2;
		}
		public long x() { return v1; }
		public int y() { return v2; }
	}
}