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;
int main() {
  int N, x;
  cin >> N >> x;
  vector<int> vec;
  int ins = 0;
  for (int a = 0; a < N; a++) {
    int b;
    cin >> b;
    vec.push_back(b);
  }
  int ans = 0;
  for (int a = 0; a < N; a++) {
    int hoge = vec.at(a);
    int slime = vec.at(a);
    int ins_co = 0;
    for (int b = 0; b < N; b++) {
      if (a == b) continue;
      int cost = 0;
      if (a > b) {
        cost = N - a + b;
      } else {
        cost = b - a;
      }
      if (hoge > vec.at(b) + cost * x) {
        hoge = vec.at(b) + cost * x;
        slime = vec.at(b);
        ins_co = cost;
      }
    }
    ans += slime;
    ins = max(ins, ins_co);
  }
  ans += ins * x;
  cout << ans << endl;
}
