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.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args)throws Exception {
		BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
		String[] input1 = br.readLine().split(" ");
		int N = Integer.parseInt(input1[0]);
		int x = Integer.parseInt(input1[1]);
		//[][0]は飼う時間
		//[][1]に　1が入っているとxよりも早く飼える
		//[][2]に　1が入ってると飼っている状態
		//[][3]に　1が入っていると色を変えた
		long [][]slime = new long[N][4];
		int count = 0;
		long total=0;
		long result = 0;
		String []input2 = br.readLine().split(" ");
		for(int j=0;j<N;j++) {
			int i = Integer.parseInt(input2[count]);
			total += i;
			slime[count][0] = i;
			if(i < x) {
				slime[count][1] = 1;
				slime[count][2] = 1;
				result += i;
			}
			count++;
		}
		if(total < x) {
			System.out.println(total);
			return;
		}else {
			while(true) {
				for(int i =N-1 ;i>=0;i--) {
					if(slime[i][3] == 0 ) {
						if(slime[i][2] ==1) {
							if(i+1 < N) {
								slime[i][2] = 0;
								slime[i+1][2] = 1;
								slime[i+1][3] = 1;
							}else{
								slime[i][2] = 0;
								slime[0][2] = 1;
								slime[0][3] = 1;
							}
						}
					}
				}
				result += x;
				for(int i =0 ;i<N;i++) {
					slime[i][3] = 0;
					if(slime[i][1] == 1 && slime[i][2] == 0) {
						slime[i][2] = 1;
						result += slime[i][0];
					}
				}
				int breakco = 0;
				for(int i =0 ;i<N;i++) {
					if(slime[i][2] == 1) {
						breakco++;
					}
				}
				if(breakco == N) {
					break;
				}
			}
			if(result >=total) {
				System.out.println(total);
			}else {
				System.out.println(result);
			}
		}
	}
}