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;
long long n, first;
long long cost[4444];
long long getmin[4444][4444];
long long shift(int s) {
  long long ret = 0;
  for (int i = 0; i < n; i++) {
    ret += getmin[i][i + s];
  }
  return ret;
}
int main() {
  cin >> n >> first;
  for (int i = 0; i < n; i++) cin >> cost[i];
  for (int i = 0; i < n; i++) cost[i + n] = cost[i];
  for (int i = 0; i < 2 * n; i++) {
    long long t = cost[i];
    for (int j = i; j < 2 * n; j++) {
      t = min(t, cost[j]);
      getmin[i][j] = t;
    }
  }
  long long res = 9223372036854775807LL;
  for (int i = 0; i < n; i++) {
    long long t = first * i + shift(i);
    res = min(res, t);
  }
  cout << res << "\n";
  return 0;
}
