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;
vector<int> a;
vector<bool> b;
bool check() {
  for (int i = 0; i < (N); i++) {
    if (!b[i]) return true;
  }
  return false;
}
int main() {
  cin >> N >> X;
  a.resize(N + 1);
  b.resize(N);
  for (int i = 0; i < (N); i++) {
    cin >> a[i];
    b[i] = false;
  }
  a[N] = X;
  int ans = 0;
  while (check()) {
    int min = 1000000001;
    ;
    int mini = 0;
    for (int i = 0; i < (N + 1); i++) {
      if (b[i]) continue;
      if (min > a[i]) {
        min = a[i];
        mini = i;
      }
    }
    if (mini != N) {
      b[mini] = true;
      ans += a[mini];
    } else {
      bool temp = b[N - 1];
      for (int i = (N)-1; i >= (1); i--) {
        b[i] = b[i - 1];
      }
      b[0] = temp;
      ans += X;
    }
  }
  cout << ans;
}
