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 a, b, c, d;
int i[3000];
int u[3000];
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> a >> b;
  for (int n = 0; n < a; n++) cin >> i[n], u[n] = i[n];
  long long ans = 0;
  int o = 0;
  for (int n = 0; n < a; n++) {
    long long f = i[n] + b;
    for (int m = n + 1; m < n + a; m++) {
      if (f >= u[m % a]) break;
      u[m % a] = i[n];
      f += b;
      if (o < m - n) o = m - n;
    }
  }
  for (int n = 0; n < a; n++) ans += u[n];
  cout << ans + b * o << '\n';
  return (0);
}
