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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
 
#define int long long
 
#define Vanya Unstoppable
 
using namespace std;

const int N = 2007;

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);
    
    int n, x;
    cin >> n >> x;
    
    int a[n + 1];
    for (int i = 1; i <= n; ++i) {
        cin >> a[i];
    }
    
    int dp[n + 1][n + 1][n + 1];
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= n; ++j) {
            for (int k = 0; k <= n; ++k) {
                dp[i][j][k] = 1e18;
            }
        }
    }
    
    dp[0][0][0] = 0;
    for (int i = 0; i < n; ++i) {
        for (int cnt = 0; cnt <= n; ++cnt) {
            for (int mx = 0; mx <= n; ++mx) {
                for (int j = 0; j <= n; ++j) {
                    int new_i = i + 1;
                    int new_cnt = cnt + j;
                    int new_mx = max(mx, j);
                    if (new_i <= n && new_cnt <= n && new_mx <= n) {
                        dp[new_i][new_cnt][new_mx] = min(dp[new_i][new_cnt][new_mx], dp[i][cnt][mx] + a[new_i] * j);
                    }
                }
            }
        }
    }
    
    int ans = 1e18;
    for (int i = 1; i <= n; ++i) {
        int val = dp[n][n][i] + (i - 1) * x;
        ans = min(ans, val);
    }
    
    cout << ans;
}