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 ll long long int
#define pb push_back
#define mp make_pair
#define INF (ll)(1e18)
#define inf 0x7fffffff
#define inff 100000
#define ff first
#define ss second
#define sz(x) ((int) (x).size())
#define fast cin.sync_with_stdio(0);cin.tie(0)
#define rep(i,N) for(int i = 0;i < N;i++)
#define frep(i,a,b) for(int i = a;i <= b;i++)
#define pii pair<int , int>
#define pll pair<ll , ll>
#define vii vector<int>
#define vpii vector< pii >
#define fill(A,v) memset(A,v,sizeof(A))
#define setbits(x) __builtin_popcountll(x)
#define print(A,j,k) for(int ii=j;ii<k;ii++)cout<<A[ii]<<" ";cout<<"\n"
#define all(x) (x).begin(), (x).end()
#define gcd __gcd
#define SQRT 350
#define CASES int t;cin>>t;while(t--)
#define FILE freopen("inp.txt" , "r" , stdin);
#define ld long double
 
const int MOD = 1e9 + 7;
const int N = 1e6 + 5;

ll n , x;

ll go(ll s , ll e) {
    // cout << "go " << s << ' ' << e << '\n';
    ll cost;
    if (e >= s) {
        //end >= start
        cost = e - s;
    }
    else {
        //start > end
        cost = e + (n - 1 - s);
    }
    // cout << "cost " << cost * x << '\n';
    return cost * x;
}

ll cost[2005][2005];
ll A[N];

int main(int argc, char const *argv[])
{
    fast;

    cin >> n >> x;

    for(int i = 0;i < n;i++)
        cin >> A[i];

    //cost[i][j] denote cost of converting color i into color j

    ll ans = 0;
    for(int i = 0;i < n;i++) {
        ll v = INF;
        for(int j = 0;j < n;j++) {
            if (i == j) 
                cost[j][i] = A[j];
            else {
                cost[j][i] = A[j] + go(j , i);
            }
            v = min(v , cost[j][i]);
        }
        ans += v;
    }

    cout << ans << '\n';

    return 0;
}