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 n;
long long x;
vector<long long> a;
int main() {
  cin >> n;
  cin >> x;
  a.assign(n, 0);
  for (int i = (0); i <= (n - 1); i++) cin >> a[i];
  long long sum = 0;
  for (int i = (0); i <= (n - 1); i++) sum += a[i];
  long long mii = 0;
  for (int i = (1); i <= (n - 1); i++)
    if (a[mii] > a[i]) mii = i;
  int l = mii + 1;
  for (int r = (mii + 1); r <= (mii + n - 1); r++) {
    long long temp = (a[mii] + x) * (r - l + 1);
    for (int i = (mii); i <= (mii + n - 1); i++) {
      if (l <= i && i <= r) {
        continue;
      } else {
        temp += a[i % n];
      }
    }
    sum = min(sum, temp);
  }
  cout << sum << endl;
  return 0;
}
