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 a[3005];
int main() {
  int n;
  long long x;
  scanf("%d%lld", &n, &x);
  set<long long> s[3005];
  int i;
  for (i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
  }
  long long ans = 1000000007;
  ans = ans * ans;
  int st;
  for (st = 0; st <= n + 3; st++) {
    for (i = 1; i <= n; i++) {
      int ne = i + st;
      if (ne > n) ne -= n;
      s[ne].insert(a[i]);
    }
    long long cur = 0;
    for (i = 1; i <= n; i++) cur += *s[i].begin();
    cur += st * x;
    if (cur < ans) ans = cur;
  }
  cout << ans;
  return 0;
}
