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;
template <typename T>
void DEBUG(T e) {
  if (true == false) return;
  std::cout << e << " ";
}
template <typename T>
void DEBUG(const std::vector<T> &v) {
  if (true == false) return;
  for (const auto &e : v) {
    std::cout << e << " ";
  }
  std::cout << std::endl;
}
template <typename T>
void DEBUG(const std::vector<std::vector<T>> &vv) {
  if (true == false) return;
  for (const auto &v : vv) {
    DEBUG(v);
  }
}
template <class T, class... Ts>
void DEBUG(T d, Ts... e) {
  if (true == false) return;
  DEBUG(d);
  DEBUG(e...);
}
template <class T>
void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    abort();
  }
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}
void solve(void) {
  long long n, x;
  cin >> n >> x;
  vector<long long> vec(n, 0);
  vector<long long> cost(n, 0);
  for (long long i = 0; i < n; i++) {
    cin >> vec[i];
    cost[i] = vec[i];
  }
  long long res = 0;
  for (long long i = 0; i < n; i++) {
    res += cost[i];
  }
  for (long long i = 1; i <= n; i++) {
    long long c = i * x;
    for (long long j = 0; j < n; j++) {
      cost[j] = min(cost[j], vec[(n + j - i) % n]);
    }
    for (long long i = 0; i < n; i++) {
      c += cost[i];
    }
    DEBUG(cost);
    chmin(res, c);
  }
  cout << res << endl;
  return;
}
int32_t main(int32_t argc, const char *argv[]) {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  std::cout << std::fixed;
  std::cout << std::setprecision(11);
  solve();
  return 0;
}
