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() {
  int n, x;
  scanf("%d %d", &n, &x);
  vector<int> a(n);
  for (int i = 0; n > i; i++) {
    scanf("%d", &a[i]);
  }
  long long int ans = LLONG_MAX;
  for (int ccou = 0; n > ccou; ccou++) {
    long long int bufans = 0;
    int guru = 0;
    for (int i = 0; n > i; i++) {
      int Minhok = INT_MAX;
      for (int j = 0; ccou >= j; j++) {
        int num = i - j;
        if (num < 0) num = n + num;
        if (Minhok > a[num]) guru = max(guru, j);
        Minhok = min(Minhok, a[num]);
      }
      bufans += Minhok;
    }
    bufans += (long long int)x * guru;
    ans = min(ans, bufans);
  }
  printf("%lld\n", ans);
  return 0;
}
