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 MAX_N = 100030;
const long long MODD = 1000000009;
long long A[MAX_N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long n, x;
  cin >> n >> x;
  for (int i = 0; i < n; i++) cin >> A[i];
  long long ans = 0;
  long long max_turns = 0;
  for (int i = 0; i < n; i++) {
    long long curr = A[i];
    long long y = A[i];
    long long val = 0;
    for (int j = i - 1; j != i; j--) {
      if (j < 0) j = n - 1;
      val += x;
      if (val > A[i]) break;
      if (val + A[j] < curr) {
        max_turns = max(max_turns, val / x);
        curr = val + A[j];
        y = A[j];
      }
    }
    ans += y;
  }
  cout << ans + max_turns * x << endl;
  return 0;
}
