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 MOD = 1e9 + 7;
const int N = 1e6 + 5;
long long int n, x;
long long int go(long long int s, long long int e) {
  long long int cost;
  if (e >= s) {
    cost = e - s;
  } else {
    cost = e + (n - 1 - s);
  }
  return cost * x;
}
long long int cost[2005][2005];
long long int A[N];
int main(int argc, char const *argv[]) {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> A[i];
  long long int ans = 0;
  for (int i = 0; i < n; i++) {
    long long int v = (long long int)(1e18);
    for (int j = 0; j < n; j++) {
      if (i == j)
        cost[j][i] = A[j];
      else {
        cost[j][i] = A[j] + go(j, i);
      }
      v = min(v, cost[j][i]);
    }
    ans += v;
  }
  cout << ans << '\n';
  return 0;
}
