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;
using ll = long long;
using P = pair<int, int>;
const int MAX = 2010;
const ll INF = 1e18;
const int MOD = 1e9 + 7;
int dx[] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[] = {0, 1, 0, -1, 1, 1, -1, -1};
ll b[MAX];
int main() {
  int N;
  ll x;
  cin >> N >> x;
  int a[N];
  for (int i = 0; i < N; i++) cin >> a[i];
  ll ans = 0;
  for (int i = 0; i < N; i++) {
    ll mini = a[i];
    int idx = -1;
    for (int j = 0; j < N; j++) {
      if (i == j) continue;
      ll tmp = (j < i ? i - j : N - j + i);
      if (tmp * x + a[j] < mini) {
        mini = tmp * x + a[j];
        idx = j;
      }
    }
    if (idx == -1) {
      ans += a[i];
    } else {
      ans += a[idx];
      b[idx] = max(b[idx], mini - a[idx]);
    }
  }
  for (int i = 0; i < N; i++) ans += b[i];
  cout << ans << endl;
  return 0;
}
