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 n, x;
void shift(vector<int> &s) {
  int tmp = s[n - 1];
  for (int i = n - 1; i > 0; i--) {
    s[i] = s[i - 1];
  }
  s[0] = tmp;
}
int get_min1(vector<int> &s, vector<int> &a, int &ind) {
  int res = 2000000000;
  for (int i = 0; i < n; i++) {
    if (!s[i] && res > a[i]) {
      res = a[i];
      ind = i;
    }
  }
  return res;
}
int get_min2(vector<int> &s, vector<int> &a, int &ind) {
  int res = 2000000000;
  for (int i = 0; i < n; i++) {
    if (!s[(i + n - 1) % n] && res > a[i]) {
      res = a[i];
      ind = i;
    }
  }
  return res;
}
int main() {
  cin >> n >> x;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  vector<int> sl(n);
  long long res = 0;
  for (int i = 0; i < n; i++) {
    int ind1, ind2;
    int c1 = get_min1(sl, a, ind1);
    int c2 = x + get_min2(sl, a, ind2);
    if (c1 <= c2) {
      res += c1;
      sl[ind1] = 1;
    } else {
      res += c2;
      shift(sl);
      sl[ind2] = 1;
    }
  }
  cout << res;
}
