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;
typedef struct {
  unsigned long long number;
  unsigned long long cost;
} data;
bool compare(data lhs, data rhs) {
  if (lhs.cost == rhs.cost)
    return lhs.number < rhs.number;
  else
    return lhs.cost < rhs.cost;
}
int main() {
  unsigned long long N, x, a;
  cin >> N >> x;
  data arr[N];
  int had[N + 1];
  for (int i = 0; i < N; i++) {
    cin >> a;
    arr[i].number = i;
    arr[i].cost = a;
    had[i] = 0;
  }
  std::sort(arr, arr + N, compare);
  int total_had = 0;
  unsigned long long total_cost = 0;
  int curr_index_arr = 0;
  while (total_had < N) {
    if (arr[curr_index_arr].cost <= x) {
      total_cost += arr[curr_index_arr].cost;
      had[arr[curr_index_arr].number] = 1;
      total_had++;
      curr_index_arr++;
    } else {
      total_cost += x;
      unsigned long long temp;
      for (int i = 0; i < N; i++) {
        if (i == N - 1) temp = had[i];
        if (i > 0) had[i] = had[i - 1];
      }
      had[0] = temp;
      curr_index_arr--;
    }
  }
  cout << total_cost << endl;
  return 0;
}
