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 n, x, cost[2010], i[2010], ile, tab[2010], sum;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> x;
  for (int a = 1; a <= n; a++) cin >> tab[a];
  for (int a = 1; a <= n; a++) {
    cost[a] = tab[a];
    for (int b = 1; b < a; b++) {
      if (tab[b] + (a - b) * x < cost[a]) {
        cost[a] = tab[b] + (a - b) * x;
        i[a] = a - b;
      }
    }
    for (int b = a + 1; b <= n; b++) {
      if (tab[b] + (n - b + a) * x < cost[a]) {
        cost[a] = tab[b] + (n - b + a) * x;
        i[a] = n - b + a;
      }
    }
  }
  for (int a = 1; a <= n; a++) {
    sum += cost[a] - i[a] * x;
    ile = max(ile, i[a]);
  }
  cout << sum + ile * x << "\n";
  return 0;
}
