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;
int tim[2000];
int teb[2000];
int magic[2000] = {};
int prepre(int f, int k) { return f - k < 0 ? n + (f - k) : f - k; }
int cost(int i, int magic) {
  int ret = min(teb[i], tim[prepre(i, magic)]);
  teb[i] = ret;
  return ret;
}
int main() {
  cin >> n >> x;
  long supersum = 0;
  for (int i = 0; i < n; i++) {
    cin >> tim[i];
    teb[i] = tim[i];
    supersum += tim[i];
  }
  int mag = 0;
  for (int magic = 1; magic < n; magic++) {
    int sum = 0;
    for (int i = 0; i < n; i++) {
      sum += cost(i, magic);
    }
    if (supersum > sum + magic * x) {
      supersum = sum;
      mag = magic;
    }
  }
  supersum += (long)x * mag;
  cout << supersum << endl;
  return 0;
}
