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 int INF = 1e9;
const int MOD = INF + 7;
const long long LLINF = 1e18;
int main(void) {
  int N, x;
  cin >> N >> x;
  vector<long long> a(N);
  for (int(i) = 0; (i) < (N); (i)++) cin >> a[i];
  long long ans = LLINF;
  vector<vector<long long> > b(N, vector<long long>(N, 0));
  for (int(k) = 0; (k) < (N); (k)++) {
    for (int(i) = 0; (i) < (N); (i)++) {
      if (k == 0) {
        b[i][0] = a[i];
      } else {
        int id = (i - k + N) % N;
        b[i][k] = min<long long>(b[i][k], a[id]);
      }
    }
  }
  for (int(k) = 0; (k) < (N); (k)++) {
    long long sum = k * x;
    for (int(i) = 0; (i) < (N); (i)++) sum += b[i][k];
    ans = min(ans, sum);
  }
  cout << ans << endl;
}
