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 vi = vector<int>;
using vvi = vector<vi>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vd = vector<double>;
using vvd = vector<vd>;
const ll mod = ((ll)1e9) + 7;
struct node {
  ll to, index;
};
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(50);
  ll n, x;
  cin >> n >> x;
  vl a(n);
  for (ll i = 0, i_len = (n); i < i_len; ++i) cin >> a[i];
  ll ans = 0;
  for (ll i = 0, i_len = (n); i < i_len; ++i) {
    ll mi = a[i];
    ll j = (i - 1 + n) % n;
    ll cnt = 1;
    while (j != i) {
      mi = min(mi, a[j] + cnt * x);
      j = (j - 1 + n) % n;
    }
    ans += mi;
  }
  cout << ans << endl;
  return 0;
}
