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, m, i, j, a[2020];
long long c, r;
int main() {
  scanf("%d%d", &n, &m);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    r += a[i];
  }
  for (j = 1; j < n; j++)
    if (m * j < r) {
      multiset<int> s;
      for (i = 1; i <= j; i++) s.insert(a[n - j]);
      for (c = i = 0; i < n; i++) {
        s.insert(a[i]);
        c += *s.begin();
        s.erase(s.find(a[(n + i - j) % n]));
      }
      r = min(r, c + m * j);
    }
  printf("%lld\n", r);
  return 0;
}
