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;
const long long MOD = (1e+9) + 7;
const long long INF = (long long)1000000007 * 1000000007;
const long double eps = 1e-11;
const long double pi = acos(-1.0);
int main() {
  int n;
  cin >> n;
  long long x;
  long long a[2000];
  cin >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long ma = 0;
  long long sum = 0;
  for (int i = 0; i < n; i++) {
    long long mi = INF;
    int chk;
    int chk2;
    for (int j = 0; j < n; j++) {
      int v = (i - j + n) % n;
      if (mi >= a[v] + x * (long long)j) {
        mi = a[v] + x * (long long)j;
        chk = v;
        chk2 = j;
      }
    }
    sum += a[chk];
    ma = max(ma, (long long)chk2);
  }
  sum += ma * x;
  cout << sum << endl;
  return 0;
}
