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;
const int inf = (int)1e9;
const long long linf = (long long)1e18;
const int mod = (int)(1e9 + 7);
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
const int ddx[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int ddy[] = {1, 1, 0, -1, -1, -1, 0, 1};
struct oreno_initializer {
  oreno_initializer() {
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
} oreno_initializer;
int n, x, a[2525], b[2525];
long long t, r = linf;
int main() {
  cin >> n >> x;
  for (int(i) = 0; (i) < (int)(n); (i)++) cin >> a[i];
  for (int(i) = 0; (i) < (int)(n); (i)++) a[i + n] = a[i];
  fill(b, b + 2 * n, 1145141919);
  for (int(k) = 0; (k) < (int)(n); (k)++) {
    t = k * x;
    for (int(i) = (n); (i) < (int)(2 * n); (i)++)
      b[i] = min(b[i], a[i - k]), t += b[i];
    r = min(r, t);
  }
  cout << r << "\n";
}
