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;
long long int MOD = 1000000007;
long long int memo[300] = {};
int main() {
  long long int n, x;
  cin >> n >> x;
  long long int a[2005];
  for (int i = 0; i < (n); i++) cin >> a[i];
  long long int dism = 0;
  long long int ans = 0;
  for (int i = 0; i < (n); i++) {
    long long int getx = 0;
    long long int cost = 1e18;
    long long int getin;
    for (int j = 0; j < (n); j++) {
      long long int newcost;
      long long int dis;
      if (i >= j) {
        newcost = a[j] + (i - j) * x;
        dis = (i - j);
      } else {
        newcost = a[j] + (n - (j - i)) * x;
        dis = (n - (j - i));
      }
      if (newcost < cost) {
        cost = newcost;
        getx = dis;
        getin = j;
      }
    }
    cerr << i << ' ' << getin << endl;
    dism = max(dism, getx);
    ans += a[getin];
  }
  cout << ans + dism * x << endl;
}
