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;
const double eps = 1e-11;
int vex[4] = {1, 0, -1, 0};
int vey[4] = {0, 1, 0, -1};
long long int MOD = 1000000007;
int main() {
  vector<long long int> x[2001];
  int N;
  cin >> N;
  long long int c;
  cin >> c;
  long long int a[2001];
  for (int i = 0; i < (N); i++) {
    cin >> a[i];
  }
  int m = 0;
  long long int ans = 0;
  int NOW = 0;
  for (int j = 0; j < (N); j++) {
    pair<long long int, int> mi = pair<long long int, int>(1000000000005, 0);
    long long int cost;
    for (int i = 0; i < (N); i++) {
      int d = j - i;
      if (d < 0) {
        d += N;
      }
      if (d > NOW) {
        cout << d - NOW << endl;
      } else
        cost = a[i];
      if (cost < mi.first) {
        mi = make_pair(cost, d);
      }
    }
    NOW = max(mi.second, NOW);
    ans += mi.first;
  }
  cout << ans << endl;
}
