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 ld = long double;
using P = pair<int, int>;
using Graph = vector<vector<int>>;
int dx[] = {0, 1, 0, -1};
int dy[] = {1, 0, -1, 0};
int main() {
  ll N, x;
  ll ans = 0;
  cin >> N >> x;
  vector<ll> a(N);
  vector<vector<pair<ll, ll>>> ref(N, vector<pair<ll, ll>>(N));
  for (int i = 0; i < N; i++) cin >> a[i];
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      if (i <= j)
        ref[i][j] = {a[i] + (j - i) * x, j - i};
      else
        ref[i][j] = {a[i] + (N - i + j) * x, N - i + j};
    }
  }
  ll MAX_time = 0;
  for (int j = 0; j < N; j++) {
    ll cost = 100000000000;
    ll time = 0;
    for (int i = 0; i < N; i++) {
      if (cost > ref[i][j].first) {
        cost = ref[i][j].first;
        time = ref[i][j].second;
      }
    }
    MAX_time = max(MAX_time, time);
    ans += cost - time * x;
  }
  ans += MAX_time * x;
  cout << ans << endl;
}
