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;
using lint = long long int;
int main() {
  int N;
  int get[2002];
  lint x, a[2002], adash[2002], maxcast = 0, ans;
  cin >> N >> x;
  for (int i = 1; i <= N; i++) cin >> a[i];
  for (int i = 1; i <= N; i++) {
    for (int j = 1; j <= N; j++) {
      if (i >= j) {
        adash[j] = a[j] + x * (i - j);
      } else {
        adash[j] = a[j] + x * (N - j + i);
      }
    }
    lint min = 99999999999999;
    lint minindex = 0;
    for (int j = 1; j <= N; j++) {
      if (min > adash[j]) {
        min = adash[j];
        minindex = j;
      }
    }
    get[i] = minindex;
    lint temp;
    if (i >= minindex) {
      temp = i - minindex;
    } else {
      temp = N - minindex + i;
    }
    maxcast = max(maxcast, temp);
  }
  ans = maxcast * x;
  for (int i = 1; i <= N; i++) {
    ans += a[get[i]];
  }
  cout << ans << endl;
  return 0;
}
