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;
const int N = 2000 + 7;
pair<long long, long long> w[N][N];
long long res, x, n, a[N];
long long dis[N];
int main() {
  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 (j >= i)
        w[i][j] = {a[i] + (j - i) * x, j - i};
      else
        w[i][j] = {a[i] + (j + n - i) * x, j + n - i};
    }
  }
  long long maxd = 0;
  for (int i = 1; i <= n; i++) {
    long long mn = w[1][i].first, d = i - 1;
    for (int j = 1; j <= n; j++) {
      if (w[j][i].first < mn) mn = w[j][i].first, d = w[j][i].second;
    }
    maxd = max(d, maxd);
    res += mn - d * x;
  }
  cout << res + maxd * x;
  return 0;
}
