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;
const int MAX_N = 2000;
int N, X;
int A[MAX_N];
struct Node {
  int cost;
  int dist;
  double value;
  Node(int cost = -1, int dist = -1) {
    this->cost = cost;
    this->dist = dist;
    this->value = cost + X * dist;
  }
};
int main() {
  cin >> N >> X;
  Node node_list[N];
  int a;
  for (int i = 0; i < N; ++i) {
    cin >> a;
    A[i] = a;
    node_list[i] = Node(a, 0);
  }
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N; ++j) {
      int u = (j + 1) % N;
      Node node = node_list[j];
      Node cand(node.cost, node.dist + 1);
      if (node_list[u].value > cand.value) {
        node_list[u] = cand.value;
      }
    }
  }
  int max_dist = 0;
  long long cost = 0;
  for (int i = 0; i < N; ++i) {
    Node node = node_list[i];
    max_dist = max(max_dist, node.dist);
    cost += node.cost;
  }
  cout << cost + max_dist * X << endl;
  return 0;
}
