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;
int main() {
  long long int n, x;
  cin >> n >> x;
  vector<long long int> arr(n, 0);
  vector<long long int> dp(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  long long int mini_index = 999999999, mini;
  for (int i = 0; i < n; i++) {
    if (arr[i] < mini) {
      mini = arr[i];
      mini_index = i;
    }
  }
  long long int ans = 0;
  dp[mini_index] = mini;
  ans += mini;
  for (long long int i = mini_index; i < n - 1; i++) {
    if (arr[i + 1] <= dp[i] + x) {
      dp[i + 1] = arr[i + 1];
      ans += arr[i + 1];
    } else {
      dp[i + 1] += dp[i] + x;
      ans += dp[i + 1] - dp[i] + 1;
    }
  }
  if (mini_index != 0) {
    if (arr[0] <= dp[n - 1] + x) {
      dp[0] = arr[0];
      ans += arr[0];
    } else {
      dp[0] += dp[n - 1] + x;
      ans += dp[0] - dp[n - 1] + 1;
    }
  }
  cout << ans << endl;
  return 0;
}
