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;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<long long>;
using vvll = vector<vll>;
int main() {
  long long n;
  cin >> n;
  long long x;
  cin >> x;
  vll a(n);
  for (long long i = 0; i < (long long)(n); i++) cin >> a[i];
  vll d(n, 0);
  for (long long i = 0; i < (long long)(n); i++) {
    long long min = 1e10;
    for (long long j = 0; j < (long long)(n); j++) {
      if (i + j < n) {
        if (a[i + j] < min) min = a[i + j];
        d[j] += min;
      } else {
        if (a[i + j - n] < min) min = a[i + j - n];
        d[j] += min;
      }
    }
  }
  long long mini = 1e10;
  for (long long i = 0; i < (long long)(n); i++) {
    d[i] += x * i;
    mini = min(mini, d[i]);
  }
  cout << mini << endl;
}
