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 N = 1e6 + 17, maxN = N * 4, D = 1e3 + 17, mod = 1e9 + 7;
const long long INF = 1e17 + 17;
int tt = 1;
long long x, n;
long long res;
long long s[N];
void solve() {
  cin >> n >> x;
  for (int i = 0; i < n; ++i) {
    cin >> s[i];
  }
  sort(s, s + n);
  res = s[0];
  for (int i = 1; i <= n; ++i) {
    if (s[i - 1] + x <= s[i]) {
      swap(s[i - 1], s[i]);
      res += x;
      res += s[i];
    } else {
      res += s[i];
    }
  }
  cout << res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  tt = 1;
  while (tt--) {
    solve();
  }
  return 0;
}
