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 inf = 1e9;
int n, x;
int a[5000];
int b[5000];
int main() {
  int m = inf, s;
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i + n] = a[i];
    b[i] = b[i + n] = inf;
    if (a[i] < m) {
      m = a[i];
      s = i;
    }
  }
  long long ans = 0;
  int po = s;
  int cnt = 0, izryt = 0;
  b[s] = a[s];
  for (int i = 0; i < n; i++) {
    int v = i + s;
    if (b[v - 1] + x < a[v]) {
      b[v] = b[v - 1] + x;
      cnt++;
      ans += a[po];
    } else {
      po = v % n;
      b[po] = a[po];
      cnt = 0;
      ans += a[po];
    }
    izryt = max(izryt, cnt);
  }
  cout << ans + izryt * x << endl;
}
