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() {
  long long int n, x, a[2000], mintime[2000], c, maxx, froma[2000];
  cin >> n;
  cin >> x;
  maxx = 0;
  int i, j;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    mintime[i] = a[i];
    froma[i] = i;
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      c = x * ((i - j + n) % n) + a[j];
      if (c < mintime[i]) {
        mintime[i] = c;
        if ((i - j + n) % n > maxx) {
          maxx = (i - j + n) % n;
        }
        froma[i] = j;
      }
    }
  }
  c = 0;
  for (i = 0; i < n; i++) {
    c = c + a[froma[i]];
  }
  c = c + maxx * x;
  cout << c;
  return 0;
}
