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;
template <typename C>
void MA(C& a, C b) {
  if (a < b) a = b;
}
template <typename C>
void MI(C& a, C b) {
  if (a > b) a = b;
}
const int N = 2000 + 7;
int a[N];
int mini[N][N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  ;
  int n, x;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    mini[i][i] = a[i];
  }
  for (int i = 2; i <= n; i++) {
    for (int j = 0; j < n; j++) {
      mini[j][(j + i - 1) % n] =
          min(mini[j][(j + i - 2 + n) % n], a[(j + i - 1) % n]);
    }
  }
  long long res = 1e18;
  for (int i = 0; i <= n; i++) {
    long long tempres = i * x;
    for (int j = 0; j < n; j++) {
      tempres += mini[(j - i + n) % n][j];
    }
    res = min(res, tempres);
  }
  cout << res << endl;
}
