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>
#pragma GCC optimize("O3")
using namespace std;
using vi = vector<int>;
using vll = vector<long long int>;
using vb = vector<bool>;
using vvb = vector<vector<bool>>;
using vc = vector<char>;
using vvi = vector<vector<int>>;
using vvll = vector<vector<long long int>>;
using vvc = vector<vector<char>>;
using ll = long long int;
using P = pair<long long int, long long int>;
using Map = map<long long int, long long int>;
ll INF = 1LL << 60;
ll M = 1000000007;
int main() {
  ll N, x;
  cin >> N >> x;
  vll a(N);
  ll mn = INF;
  for (ll i = 0; i < N; i++) {
    cin >> a[i];
    mn = min(mn, a[i]);
  }
  ll m = mn + x;
  ll ans = 0;
  for (ll i = 0; i < N; i++) {
    if (a[i] <= m) {
      ans += a[i];
    } else {
      ans += m;
    }
  }
  cout << (ans) << "\n";
}
