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 lint = int64_t;
using namespace std;
int main() {
  lint N, x;
  lint a[2010] = {};
  cin >> N >> x;
  for (int i = 0; i < N; i++) cin >> a[i];
  lint ans[2010][2] = {};
  for (int i = 0; i < N; i++)
    for (int j = 0; j < 2; j++) ans[i][j] = 1e18;
  for (int i = 0; i < N; i++) {
    lint tans[2] = {};
    for (int j = 0; j < N; j++) {
      tans[0] = a[j];
      if (j <= i)
        tans[1] = x * (i - j);
      else
        tans[1] = x * (N - (j - i));
      if (tans[0] + tans[1] < ans[i][0] + ans[i][1]) {
        ans[i][0] = tans[0];
        ans[i][1] = tans[1];
      }
    }
  }
  lint asum = 0;
  for (int i = 0; i < N; i++) asum += ans[i][0];
  lint Max = 0;
  for (int i = 0; i < N; i++) Max = max(Max, ans[i][1]);
  cout << asum + Max << endl;
  return 0;
}
