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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int N = s.nextInt();
		int x = s.nextInt();
		int[] a = new int[N];
		int[] a2 =new int[N];
		for(int i=0;i<N;i++){
			a[i]=s.nextInt();
		}
		int min=a[0];
		int minno=0;
		for(int i=1;i<N;i++){
			min=Math.min(min, a[i]);
			if(min==a[i]){
				minno=i;
			}
		}
		
		long t= a[minno];
		int count = 0;
		int countm = 0;
		int t2=a[minno];
		a2[minno]=a[minno];

		for(int i=minno+1;i<N;i++){
			if(a[i]<=t+x){
				count=0;
				t=a[i];
				a2[i]=a[i];
				t2=a[i];
			}else{
				count++;
				t=t+x;
				a2[i]=t2;
			}
			if(count>countm){
				countm=count;
			}
		}
		for(int i=0;i<minno;i++){
			if(a[i]<=t+x){
				count=0;
				t=a[i];
				a2[i]=a[i];
				t2=a[i];
			}else{
				count++;
				t=t+x;
				a2[i]=t2;
			}
			if(count>countm){
				countm=count;
			}
		}
		
		long result=(long)countm*x;
		for(int i=0;i<N;i++){
			result+=(long)a2[i];
		}
		System.out.println(result);
	}
}