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;
bool check(const deque<bool>& c) {
  for (auto b : c)
    if (!b) return false;
  return true;
}
int main(void) {
  unsigned int n, x;
  unsigned long long time = 0;
  cin >> n >> x;
  deque<pair<int, unsigned int>> a(n);
  deque<bool> c(n, false);
  for (int i = 0; i < n; i++) cin >> a[i].second, a[i].first = i;
  sort(a.begin(), a.end(),
       [](const pair<int, unsigned int>& a, const pair<int, unsigned int>& b) {
         return a.second < b.second;
       });
  bool f = false;
  do {
    int i = 0;
    while (c[a[i].first]) i++;
    if (f && a[i].second > x) {
      time += x;
      c.push_front(c.back());
      c.pop_back();
    } else {
      time += a[i].second;
      c[a[i].first] = true;
      f = true;
    }
  } while (!check(c));
  cout << time << endl;
  return 0;
}
