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[1000001], dp2[1000001];
vector<int> use, use2;
void hawawa() {
  int n, x;
  cin >> n >> x;
  vector<int> a(n);
  for (auto&& i : a) {
    cin >> i;
  }
  int minindex = 0, minimum = a[0];
  for (int i = 1; i < n; i++) {
    if (a[i] < minimum) {
      minimum = a[i];
      minindex = i;
    }
  }
  auto b = a;
  b[minindex] = 0;
  for (int i = 1; i < n; i++) {
    int index = (i + minindex) % n;
    int before = (i + minindex - 1) % n;
    if (b[index] > a[before] + b[before] + x) {
      a[index] = a[before];
      b[index] = b[before] + x;
    } else {
      b[index] = 0;
    }
  }
  int mx = 0;
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    ans += a[i];
    mx = max(mx, b[i]);
  }
  ans += mx;
  cout << ans << "\n";
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  hawawa();
  return 0;
}
