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 Pi = pair<int, int>;
using Pl = pair<ll, ll>;
int main() {
  int N;
  cin >> N;
  ll x;
  cin >> x;
  vector<ll> a(N * 2);
  for (int i = (int)(0); i < (int)(N); i++) cin >> a[i];
  for (int i = (int)(0); i < (int)(N); i++) a[N + i] = a[i];
  ll ans = 0;
  ll cnt = 0;
  for (ll i = N; i < N * 2; i++) {
    ll now = (long long)4e18;
    ll nowa = (long long)4e18;
    ll nowcnt = 0;
    for (ll j = 0; j < i + 1; j++) {
      if (now > a[j] + x * (i - j)) {
        now = a[j] + x * (i - j);
        nowa = a[j];
        nowcnt = i - j;
      }
    }
    ans += nowa;
    cnt = max(cnt, nowcnt);
  }
  ans += x * cnt;
  cout << ans << endl;
}
