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;
using s64 = long long;
int main() {
  int n, extra;
  cin >> n >> extra;
  vector<int> cost(n);
  for (int i = 0; i < n; ++i) {
    cin >> cost[i];
  }
  vector<vector<int>> low(n);
  for (int i = 0; i < n; ++i) {
    low[i].resize(n);
    low[i][i] = cost[i];
    for (int k = 1; k < n; ++k) {
      int j = (i + k) % n;
      low[i][j] = min(low[i][(j + n - 1) % n], cost[j]);
    }
  }
  s64 answer = accumulate(cost.begin(), cost.end(), 0);
  for (int i = 1; i < n; ++i) {
    s64 current = (s64)i * extra;
    for (int r = 0; r < n; ++r) {
      current += low[(r + n - i) % n][r];
    }
    answer = min(answer, current);
  }
  cout << answer << endl;
  return 0;
}
