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 MAX = 2000 + 10;
long long arr[MAX];
int from[MAX];
int main() {
  int n;
  long long x;
  long long last = 0, ans;
  scanf("%d %lld", &n, &x);
  for (int i = 0; i < n; i++) {
    scanf("%lld", &arr[i]);
    last += arr[i];
    from[i] = i;
  }
  ans = last;
  for (int i = 1; i < n; i++) {
    last += x;
    for (int j = 0; j < n; j++) {
      int target = (from[j] - i + n) % n;
      if (arr[target] < arr[from[j]]) {
        last -= arr[from[j]] - arr[target];
        from[j] = target;
      }
    }
    ans = min(ans, last);
  }
  printf("%lld\n", ans);
  return 0;
}
