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>
ostream &operator<<(ostream &os, const vector<T> &A) {
  for (int i = 0; i < A.size(); i++) os << A[i] << " ";
  os << endl;
  return os;
}
template <>
ostream &operator<<(ostream &os, const vector<vector<int> > &A) {
  int N = A.size();
  int M;
  if (N > 0) M = A[0].size();
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < M; j++) os << A[i][j] << " ";
    os << endl;
  }
  return os;
}
struct edge {
  int from, to, d, c;
  edge(int _from = 0, int _to = 0, int _d = 0, int _c = 0) {
    from = _from;
    to = _to;
    d = _d;
    c = _c;
  }
  bool operator<(const edge &rhs) const {
    return (d == rhs.d) ? (c < rhs.c) : (d < rhs.d);
  }
};
struct flow {
  int to, cap, rev, cost;
  flow(int to = 0, int cap = 0, int rev = 0, int cost = 0)
      : to(to), cap(cap), rev(rev), cost(cost) {}
};
const int di[4] = {0, -1, 0, 1};
const int dj[4] = {-1, 0, 1, 0};
const int ci[5] = {0, 0, -1, 0, 1};
const int cj[5] = {0, -1, 0, 1, 0};
const long long LINF = LLONG_MAX / 2;
const int INF = INT_MAX / 2;
const double PI = acos(-1);
template <typename T, typename U>
bool chmin(T &x, const U &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <typename T, typename U>
bool chmax(T &x, const U &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
struct initializer {
  initializer() { cout << fixed << setprecision(11); }
};
initializer _____;
int N, M, K, T, Q;
int main() {
  long long N, X;
  cin >> N >> X;
  vector<long long> A(N);
  for (int i = 0; i < (int)(N); i++) cin >> A[i];
  long long ans = LLONG_MAX / 2;
  vector<vector<long long> > dp(N, vector<long long>(N, LLONG_MAX / 2));
  for (int i = 0; i < (int)(N); i++) dp[i][0] = A[i];
  for (int i = 0; i < (int)(N); i++)
    for (int j = 1; j < N; j++) {
      dp[(i + 1) % N][j] = min(dp[(i + 1) % N][j - 1], dp[i][j - 1]);
    }
  for (int k = 0; k < (int)(N); k++) {
    long long tmp = k * X;
    for (int i = 0; i < (int)(N); i++) tmp += dp[i][k];
    chmin(ans, tmp);
  }
  cout << ans << endl;
  return 0;
}
