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 <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  ~debug() { cerr << endl; }
  template <class c>
  typename enable_if<sizeof dud<c>(0) != 1, debug&>::type operator<<(c i) {
    cerr << boolalpha << i;
    return *this;
  }
  template <class c>
  typename enable_if<sizeof dud<c>(0) == 1, debug&>::type operator<<(c i) {
    return *this << range(begin(i), end(i));
  }
  template <class c, class b>
  debug& operator<<(pair<b, c> d) {
    return *this << "(" << d.first << ", " << d.second << ")";
  }
  template <class c>
  debug& operator<<(rge<c> d) {
    *this << "[";
    for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
    return *this << "]";
  }
};
using int64 = long long;
const int64 INF = (1LL << 60);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int N;
  int64 X;
  vector<int64> A, dp, pref;
  cin >> N >> X;
  A.resize(N);
  for (int i = 0; i < N; i++) cin >> A[i];
  sort(A.begin(), A.end());
  int64 result = INF;
  dp = vector<int64>(N + 1, INF);
  dp[0] = 0;
  pref = vector<int64>(N + 1, 0);
  for (int i = 1; i <= N; i++) pref[i] = pref[i - 1] + A[i - 1];
  for (int i = 1; i <= N; i++) {
    dp[i] = dp[i - 1] + A[i - 1];
    for (int j = 1; j < i; j++) {
      dp[i] = min(dp[i], dp[j] + X * (i - j) + pref[i - j]);
    }
  }
  cout << dp[N] << "\n";
  return 0;
}
