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;
struct xxx {
  long long a;
  int id;
} d[2010];
long long b[2010];
int ID[2010];
bool cmp(xxx a, xxx b) { return a.a < b.a; }
int main() {
  long long ans = 1e18;
  int n;
  long long x;
  scanf("%d%lld", &n, &x);
  for (int i = 1; i <= n; i++)
    scanf("%lld", &d[i].a), d[i].id = i, b[i] = d[i].a;
  sort(d + 1, d + n + 1, cmp);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= i; j++) ID[j] = d[j].id;
    sort(ID + 1, ID + i + 1);
    long long res = 0, tot = 0;
    for (int j = 1; j <= i; j++) {
      if (j == i) {
        long long k = n - ID[j] + ID[1];
        res = max(res, k - 1);
        tot += k * b[ID[j]];
      } else {
        long long k = ID[j + 1] - ID[j];
        res = max(res, k - 1);
        tot += k * b[ID[j]];
      }
    }
    ans = min(ans, tot + res * x);
  }
  printf("%lld", ans);
  return 0;
}
