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 ll = long long;
const ll MOD = 1e9 + 7;
const ll MOD2 = 998244353;
const ll INF = 1 << 30;
const ll INF2 = 9e18;
const double INF3 = 9e14;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const int tx[8] = {-1, 0, 1, -1, 1, -1, 0, 1},
          ty[8] = {-1, -1, -1, 0, 0, 1, 1, 1};
int main() {
  ll n, x, a[2010], ans = 0;
  vector<ll> v[2010];
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i == j)
        v[j].push_back(a[i]);
      else
        v[j].push_back(a[i] + x);
    }
  }
  for (int i = 0; i < n; i++) {
    sort((v[i]).begin(), (v[i]).end());
  }
  for (int i = 0; i < n; i++) {
    ans += v[i][0];
  }
  cout << ans << endl;
  return 0;
}
