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 = 2003;
long long a[N], b[N], x, ans = 0;
long long n;
int main() {
  cin >> n >> x;
  for (long long i = 1; i <= n; i++) cin >> a[i], b[i] = a[i] + n * x;
  for (long long i = 1; i <= n; i++)
    for (long long j = 1; j <= n; j++)
      b[i] = min(b[i], a[j] + x * (i - j >= 0 ? i - j : i - j + n));
  for (long long i = 0; i <= n - 1; i++) {
    bool ok = false;
    for (long long j = 1; j <= n; j++) {
      if (a[j - i > 0 ? j - i : j - i + n] + x * i == b[j]) {
        ans += a[j - i > 0 ? j - i : j - i + n], ok = true;
      }
    }
    if (ok && i != 0) ans += x;
  }
  cout << ans;
  return 0;
}
