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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//
//  main.cpp
//  Colorful Slimes
//
//  Created by 王博浩 on 2019/8/12.
//  Copyright © 2019 王博浩. All rights reserved.
//

#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
ll dp[2010][2010];
int main()
{
    ll n,x;
    ll a[2010];
    cin>>n>>x;
    int i;
    for(i=1;i<=n;i++)
        cin>>a[i];
    int k;
    for(i=1;i<=n;i++)
        dp[i][0]=a[i];
    for(k=1;k<n;k++)
    {
        for(i=1;i<=n;i++)
        {
            int temp=i-k;
            if(temp<=0) temp+=n;
            dp[i][k]=min(dp[i][k-1],(ll)a[temp]);
        }
    }
    ll sum=0;ll ans=0x3f3f3f3f;
    for(i=0;i<n;i++)
    {
        sum=0;
        for(int j=1;j<=n;j++)
            sum+=dp[j][i];
        sum+=i*x;
        ans=min(ans, sum);
    }
    cout<<ans<<endl;
    return 0;
}