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 <bits/stdc++.h>

using namespace std;

#define llong long long int
#define ldouble long double
#define rep(i, n) for (int i = 0; i < n; ++i)
#define all(x) x.begin(), x.end()
#define stl_rep(itr, x) for (auto itr = x.begin(); itr != x.end(); ++itr)

const static int MOD = 1000000000 + 7;
const static llong INF = 1LL << 60;
const static int dy[] = {0, 1, 0, -1};
const static int dx[] = {1, 0, -1, 0};

signed main (int argc, char *argv[]) {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    llong x;
    cin >> N >> x;
    vector<llong> slime(N);
    rep(i, N) {
        cin >> slime[i];
    }

    priority_queue<llong, vector<llong>, greater<llong> > PQ;
    rep(i, N) {
        llong ans = 0;
        rep(j, N) {
            if (i == j) ans += slime[i];
            else ans += min(slime[j], x + slime[i]);
        }
        PQ.push(ans);
    }

    cout << PQ.top() << endl;

    return 0;
}