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 dp[2007];
vector<pair<int, int> > v;
int a[200000];
int main() {
  freopen("input.txt", "r", stdin);
  int n;
  cin >> n;
  int x;
  cin >> x;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    v.push_back({a[i], i});
  }
  sort(v.begin(), v.end());
  for (int i = 0; i < n; i++) dp[i] = a[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i != j) {
        int x2 = v[i].first;
        int y2 = v[i].second;
        int x1 = v[j].first;
        int y1 = v[j].second;
        dp[y2] = min(dp[y2], dp[y1] + abs((y2 - y1) * x));
      }
    }
  }
  long long int sum = 0;
  for (int i = 0; i < n; i++) sum += dp[i];
  cout << sum << endl;
}
