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 N = 4e3 + 5;
int st[N][15];
int lg[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, x;
  cin >> n >> x;
  vector<int> a(2 * n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i + n] = a[i];
    st[i][0] = st[i + n][0] = a[i];
  }
  for (int j = 1; j < 15; j++) {
    for (int i = 0; i + (1 << j) <= 2 * n; i++) {
      st[i][j] = min(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
    }
  }
  for (int i = 2; i < N; i++) {
    lg[i] = 1 + lg[i / 2];
  }
  long long int mi_cst = LLONG_MAX;
  for (int k = 0; k < n; k++) {
    long long int cst = k * x;
    int p = lg[k + 1];
    for (int i = n; i < 2 * n; i++) {
      cst += min(st[i - k][p], st[i - (1 << p) + 1][p]);
    }
    mi_cst = min(mi_cst, cst);
  }
  cout << mi_cst << '\n';
}
