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) {
		// TODO Auto-generated method stub
		long x,kk,ans;
		int n;
		Scanner in =new Scanner(System.in);
		n=in.nextInt();x=in.nextLong();
		long []  a=new long[n+1000];
		long [][] dp = new long[n+500][n+500];
		for(int i=1;i<=n;i++) {
			a[i]=in.nextLong();
		}
		ans=1000000000000000000L;kk=-1;
		for(int i=1;i<=n;i++) {
			dp[i][0]=a[i];
			for(int k=1;k<n;k++) {
				int pi=((i-k) + n) % n;
				if(pi<=0)pi=n+pi;
				if(dp[i][k-1]>=a[pi])dp[i][k]=a[pi];
				else dp[i][k]=dp[i][k-1];
//				if(bal1>a[pi] + ((long)k)*x) {
//					bal1=a[pi]+(k)*x;bal2=k;bal3=a[pi];
//				}
			}
//			if(bal2>kk)kk=bal2;
//			ans+=bal3;
			
		}
		long sum=0;
		for(int k=0;k<n;k++) {
			sum=0;
			for(int i=1;i<=n;i++) {
				sum+=dp[i][k];
			}
			if(sum<ans)ans=sum+k*x;
		}
		System.out.println(ans);
	}

}