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)

#include <bits/stdc++.h>

#define each(i, c) for (auto& i : c)
#define unless(cond) if (!(cond))

using namespace std;

typedef long long int lli;
typedef unsigned long long ull;
typedef complex<double> point;

template<typename P, typename Q>
ostream& operator << (ostream& os, pair<P, Q> p)
{
  os << "(" << p.first << "," << p.second << ")";
  return os;
}

const int N = 2000 + 10;
const lli inf = 1LL << 50;

int main(int argc, char *argv[])
{
  int n, x;
  while (cin >> n >> x) {
    lli a[n];
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }

    lli dp[n];
    for (int i = 0; i < n; ++i) {
      dp[i] = a[i];
    }

    lli mn = inf;
    for (lli ench = 0; ench <= 2 * n; ++ench) {
      for (int slime = 0; slime < n; ++slime) {
        const int i = (slime - ench + n * 10) % n;
        dp[slime] = min(dp[slime], a[i]);
      }
      mn = min(mn, accumulate(dp, dp + n, 0LL) + ench * x);
    }
    
    cout << mn << endl;
  }
  return 0;
}