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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;


class A {
    int N;
    long x;
    long[] a,aa;
    long[] ini;
    long[] cost;
    public A() {
        a = new long[2002];
        aa = new long[2002];
        ini = new long[2002];
        cost = new long[2002];
        
    }
    public void run(){
        string[] str = Console.ReadLine().Split(' ');
        N = int.Parse(str[0]);
        x = long.Parse(str[1]);
        str =  Console.ReadLine().Split(' ');
        for(int i=0;i<N;i++){
            aa[i] = a[i] = long.Parse(str[i]);
            ini[i] = a[i];
            cost[i] = 0;
        }
        
        long maxC = 0;
        //int maxI = -1;
        for(int cnt = 0; cnt < 2*N+2 ; cnt++){
            int now = cnt % N;
            int prev = (cnt+N-1)%N;
            if(a[prev]+x<=a[now]){
                a[now] = a[prev]+x;
                ini[now] = ini[prev];
                cost[now] = cost[prev]+1; 
                if(cost[now]>maxC){
                    maxC = cost[now];
                    //maxI = now;
                }
            }
        }
        
        long ans=0;
        for(int i=0;i<N;i++){
            long min = 10000000000;
            for(int j=0;j<=maxC;j++){
                int now = (i+j)%N;
                min = Math.Min(min, aa[now]);
            }
            ans += min;
        }
        ans += x* maxC;
        /*
        
        long ans=0;
        for(int i=0;i<N;i++){
            if(cost[i]==0) ans += a[i];
        }
        for(int t=1;t<N+1;t++){
            bool changed = false;
            for(int i=0;i<N;i++){
                if(cost[i]>=t){
                    changed = true;
                    if(cost[i]==t){
                        ans += ini[i];
                    }
                }
            }
            if(changed){
                ans += x;
            } else {
                break;
            }
        }*/
        Console.WriteLine(ans);
    }
}

class Program {
    static void Main(string[] args){
        A a = new A();
        a.run();
    }
}