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: Accepted)

// by batr (TBhero.17)                      
// This will be Accepted!
// why am I so dumb ? :c
 
#include <bits/stdc++.h>
 
#define jyldam ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
 
#define pb push_back
#define mp make_pair
 
#define B begin()
#define E end()
#define sz size()
#define skip continue
#define all(x) (x).begin(), (x).end()
 
#define ai a[i]
#define F first
#define S second          
 
#define st(x) st+=x
#define pli pair<long long, int>
 
using namespace std;
 
typedef long long ll;
typedef long double ld;     
 
const int N = 1e6 + 17, M = N * 4, D = 2e3 + 17, mod = 1e9 + 7;
const ll INF = 1e17 + 17;
 
int tt = 1;  
int n, x;
int a[D][D];
ll b[D][D];
ll ans;
 
void solve () {          
			cin >> n >> x;
			for (int i = 1; i <= n; i++) {
					cin >> a[i][0];
					ans += a[i][0];
			}		                 
			for (int k = 1; k < n; k++) {
					ll lol = k * 1ll * x;
					for (int i = 1; i <= n; i++) {
							int id = i;
							if (id > 1) {
								id--;
							}
							else {
								id = n;
							}
							a[i][k] = min(a[i][0], a[id][k-1]);
							lol += a[i][k];
					}
					ans = min(lol, ans);
			}
			cout << ans;
}
		
int main() {
		jyldam;   
                  
		while (tt--) {   
			solve();
		}
   	
		return 0;
}