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;
long long nextInt() {
  long long a;
  cin >> a;
  return a;
}
char nextChar() {
  char a;
  cin >> a;
  return a;
}
double nextDouble() {
  double a;
  cin >> a;
  return a;
}
string nextString() {
  string a;
  cin >> a;
  return a;
}
void inputVector(vector<long long> &v, long long &n) {
  for (long long i = 0; i < (n); i++) {
    v.push_back(nextInt());
  }
}
void inputVector(vector<double> &v, long long &n) {
  for (long long i = 0; i < (n); i++) {
    v.push_back(nextDouble());
  }
}
void inputVector(vector<string> &v, long long &n) {
  for (long long i = 0; i < (n); i++) {
    v.push_back(nextString());
  }
}
long long N;
long long dist(long long a, long long b) {
  if (a <= b) return b - a;
  return b + N - a;
}
class QInfo {
 public:
  long long index;
  long long cost;
  QInfo(long long a, long long b) {
    index = a;
    cost = b;
  }
  bool operator<(const QInfo &a) const { return cost > a.cost; }
};
bool make[2010];
signed main() {
  long long x;
  cin >> N >> x;
  vector<long long> a;
  inputVector(a, N);
  priority_queue<QInfo> q;
  for (long long i = 0; i < (N); i++) {
    q.push(QInfo(i, a[i]));
  }
  long long ret = 0;
  long long maxMove = 0;
  for (long long i = 0; i < (N); i++) {
    QInfo info = q.top();
    q.pop();
    long long index = info.index;
    long long cost = LLONG_MAX;
    long long pt = index;
    if (i > 0) {
      while (!make[pt]) {
        pt--;
        if (pt == -1) {
          pt = N - 1;
        }
      }
      cost = max(0LL, dist(pt, index) - maxMove) * x + a[pt];
    }
    if (a[index] < cost) {
      make[index] = true;
      ret += a[index];
    } else {
      ret += cost;
      maxMove = max(maxMove, dist(pt, index));
    }
  }
  cout << ret << endl;
  return 0;
}
