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;
long long int a[2222];
long long int b[2222];
int main(void) {
  long long int n, x;
  cin >> n >> x;
  cin >> a[1];
  b[1] = a[1];
  int t, tm;
  tm = a[1];
  for (int i = 2; i <= n; i++) {
    cin >> a[i];
    b[i] = min(a[i], b[i - 1] + x);
    if (tm > b[i]) {
      tm = b[i];
      t = i;
    }
  }
  b[1] = min(b[1], b[n] + x);
  if (tm > b[1]) {
    tm = b[1];
    t = 1;
  }
  long long int res = 0;
  for (int i = 1; i <= n; i++) {
    if (a[i] > b[i])
      res += tm + x;
    else
      res += a[i];
  }
  cout << res << endl;
  return 0;
}
