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;
int main() {
  long long n, x;
  cin >> n >> x;
  vector<long long> a;
  for (int i = 0; i < (n); i++) {
    long long b;
    cin >> b;
    a.push_back(b);
  }
  int b[n][n];
  long long res = 1e13;
  for (int i = 0; i < (n); i++) {
    b[0][i] = a[i];
  }
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < (n); j++) {
      int t;
      if (j >= i)
        t = a[j - i];
      else
        t = a[n - (i - j)];
      b[i][j] = min(b[i - 1][j], t);
    }
  }
  for (int i = 0; i < (n); i++) {
    for (int j = 0; j < (n); j++) {
      cout << b[i][j] << "  ";
    }
    cout << endl;
  }
  for (int i = 0; i < (n); i++) {
    long long num = 0;
    for (int j = 0; j < (n); j++) {
      num += b[i][j];
    }
    if (res > num + x * i) res = num + x * i;
  }
  cout << res << endl;
  return 0;
}
