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.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vint = vector<int>;
using pint = pair<int, int>;
const double EPS = 1e-9;
const int inf = numeric_limits<int>::max();
void solve() {
  const int MAX_N = 2000 + 5;
  int t[MAX_N] = {};
  priority_queue<int, std::vector<int>, std::greater<int> > q;
  int N, x, a[MAX_N];
  cin >> N >> x;
  for (int i = 0; i < int(N); ++i) cin >> a[i];
  for (int i = 0; i < int(N); ++i) {
    t[i] = inf;
  }
  for (int i = 0; i < int(N); ++i) {
    for (int j = 0; j < int(N); ++j) {
      t[j] = min(t[j], a[(N + j - i) % N]);
    }
    int sum = 0;
    for (int j = 0; j < int(N); ++j) sum += t[j];
    q.push(i * x + sum);
  }
  cout << q.top() << endl;
}
int main() {
  solve();
  return 0;
}
