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)

#include <cstdio>
#include <cstdint>
#include <iostream>
#include <iomanip>
#include <string>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <algorithm>
#include <utility>
#include <cmath>
#include <climits>
#include <bitset>

#define ll long long int
#define pb push_back
#define mk make_pair
#define pq priority_queue

using namespace std;
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;

int main(int argc, char const* argv[])
{
  int n;
  ll x;
  cin >> n >> x;
  vector<ll> a;
  for(int i = 0; i < n; i++){
    ll y;
    cin >> y;
    a.pb(y);
  }
  ll res = 0;
  ll xmaxi = 0;
  for(int i = 0; i < n; i++){
    ll mini = a[i];
    int at = i;
    for(int j = 0; j < n; j++){
      int sub = n - j + i;
      if(sub >= n)sub -= n;
      if(mini > sub * x + a[j]){
        mini = sub * x + a[j];
        at = j;
      }else if(mini == sub * x + a[j]){
        if(a[at] > a[j]){
          at = j;
        }
      }
    }
    res += a[at];
    xmaxi = max(xmaxi, mini - a[at]);
  }
  res += xmaxi;
  cout << res << endl;
	return 0;
}