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)

/* Filename: AGC004B.java
 * Author: Mushiyo
 */

import java.util.Scanner;
import java.util.Arrays;

public class Main{

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);

		while (input.hasNext()) {
			int N = input.nextInt(), x = input.nextInt();
			int[] a = new int[N];
			boolean[] isCatched = new boolean[N];
			int countCatched = 0;
			long time = 0;
			for (int i = 0; i < a.length; ++i) {
				a[i] = input.nextInt();

				if (a[i] <= x) {
					isCatched[i] = true;
					++countCatched;
					time += a[i];
				}
			}

			while (countCatched < N) {
				//System.err.println(countCatched);
				//System.err.println(Arrays.toString(isCatched));
				int i = 0;
				while (i < isCatched.length && isCatched[i]) {
					++i;
				}

				if (a[i] <= x) {
					time += a[i];
					isCatched[i] = true;
					++countCatched;
				} else {
					rightShift(isCatched);
					time += x;
					
					int min = Integer.MAX_VALUE;
					int minIndex = -1;
					for(int j = 0; j < isCatched.length; ++j){
						if(a[j] <= x && isCatched[j] == false){
							if(a[j] < min){
								min = a[j];
								minIndex = j;
							}
						}
					}
					
					if(minIndex >= 0){
						isCatched[minIndex] = true;
						time += a[minIndex];
						++countCatched;
					}
				}
			}

			System.out.println(time);
		}
	}

	private static void rightShift(boolean[] a) {
		boolean tmp = a[a.length - 1]; 
		for (int i = a.length - 1; i > 0; --i) {
			a[i] = a[i - 1];
		}

		a[0] = tmp;
	}

}