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;
void debug_out() { std::cout << std::endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cout << H << " ";
  debug_out(T...);
}
template <typename T>
std::ostream& operator<<(std::ostream& os, std::vector<T> vec) {
  for (std::size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
  return os;
}
struct Edge {
  int to;
  ll weight;
  Edge(int t, ll w) : to(t), weight(w) {}
};
struct edge {
  int from;
  int to;
  ll weight;
  edge(int f, int t, ll w) : from(f), to(t), weight(w) {}
};
using Graph = vector<vector<Edge>>;
using graph = vector<vector<int>>;
using edges = vector<edge>;
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
T lcm(T a, T b) {
  return (a * b) / gcd(a, b);
}
bool isPalindrome(string s) {
  string t = s;
  reverse((t).begin(), (t).end());
  return s == t;
}
constexpr ll LNF = 1LL << 60;
constexpr int INF = 1e9 + 7;
const double PI = 3.14159265358979323846;
vector<int> dx = {-1, 0, 1, 0, -1, 1, -1, 1};
vector<int> dy = {0, -1, 0, 1, 1, -1, -1, 1};
int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int n;
  ll x;
  cin >> n >> x;
  vector<ll> a(n);
  ll ans = 0ll;
  for (int i = (int)(0); i < (int)(n); i++) {
    cin >> a[i];
    ans += a[i];
  }
  for (int i = (int)(1); i < (int)(n); i++) {
    ll s = 0;
    for (int j = (int)(0); j < (int)(n); j++) {
      if (j == 0) {
        chmin(a[j], a[n - 1]);
      } else {
        chmin(a[j], a[j - 1]);
      }
      s += a[j];
    }
    chmin(ans, s + x * i);
  }
  cout << ans << endl;
}
