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 int INF = 1 << 29;
const double EPS = 1e-9;
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
int n, a, x[60], aaa;
long long int res = 0ll;
long long int sumr[2500] = {}, suml[2500] = {};
int main() {
  int t[2000][2], a[2000];
  int n, x, ma = 0;
  long long int ans = 0ll;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    t[i][0] = a[i];
    t[i][1] = i;
  }
  for (int i = 0; i < n; i++) {
    for (int j = (i + n - 1) % n; j != i; j = (j + n - 1) % n) {
      if (t[i][0] >= a[j] + (i + n - j) % n * x) {
        t[i][0] = a[j] + (i + n - j) % n * x;
        t[i][1] = j;
        ma = max(ma, (i + n - j) % n);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    ans += a[t[i][1]];
  }
  ans += ma * x;
  cout << ans << endl;
  return 0;
}
