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;
int main() {
  long long N, X;
  cin >> N >> X;
  long long a[N];
  for (int i = 0; i < N; i++) cin >> a[i];
  long long mn[N];
  long long mulmax = 0;
  for (int i = 2 * N - 1; i >= N; i--) {
    mn[i % N] = a[i % N];
    long long mul = 1;
    for (int j = i - 1; j >= i - N; j--, mul++)
      if (mn[i % N] >= mul * X + a[j % N]) {
        mn[i % N] = mul * X + a[j % N];
        mulmax = max(mulmax, mul);
      }
  }
  for (int i = 2 * N - 1; i >= N; i--) {
    mn[i % N] = a[i % N];
    for (int j = i - 1; j >= i - mulmax; j--)
      if (mn[i % N] > a[j % N]) mn[i % N] = a[j % N];
  }
  long long tot = mulmax * X;
  for (int i = 0; i < N; i++) tot += mn[i];
  cout << tot;
  return 0;
}
