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 long long mod = 1000000007;
const long long inf = 11451419198109311;
const long double pi = 3.1415926535897932384626433;
struct edge {
  long long to, cost;
};
long long a[2005];
long long cs[2005][2005];
signed main() {
  long long n, x;
  cin >> n >> x;
  for (long long i = 0; i < n; i++) cin >> a[i];
  for (long long i = 0; i < n; i++) {
    for (long long j = 0; j < n; j++) {
      cs[i][(i + j) % n] = a[i] + x * j;
    }
  }
  long long sum = 0, mk = 0;
  for (long long i = 0; i < n; i++) {
    long long mx = inf;
    long long num = 0;
    for (long long j = 0; j < n; j++) {
      if (mx > cs[j][i]) {
        mx = cs[j][i];
        num = j;
      }
    }
    sum += a[num];
    mk = max(mk, (i + n - num) % n);
  }
  cout << sum + mk * x << endl;
}
