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 int MOD = 1000000007;
const long long int INF = (long long int)1e15;
long long int A[2005];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long int N, X;
  cin >> N >> X;
  for (long long int(i) = (0); (i) < (N); ++(i)) {
    cin >> A[i];
  }
  long long int mx = 0;
  for (long long int(i) = (0); (i) < (N); ++(i)) {
    long long int mn = A[i];
    for (long long int(j) = (0); (j) < (N); ++(j)) {
      long long int s = A[(N + i - j) % N] + j + X;
      if (s < mn) {
        mx = std::max(j, mx);
        mn = s;
      }
    }
  }
  long long int ans = mx * X;
  for (long long int(i) = (0); (i) < (N); ++(i)) {
    long long int mn = A[i];
    for (long long int(j) = (0); (j) < (mx + 1); ++(j)) {
      mn = std::min(mn, A[(N + i - j) % N]);
    }
    ans += mn;
  }
  cout << ans << endl;
  return 0;
}
