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 N = 2000 + 7;
long long n;
long long x, a[N], cur, sol;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> x;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    cur += a[i];
  }
  sol = cur;
  for (long long take = 1; take <= n; take++) {
    long long mxdif = 0;
    long long j;
    for (long long i = 0; i < n; i++) {
      mxdif = max(mxdif, a[(i + 1) % n] - a[i]);
      if (a[(i + 1) % n] - a[i] == mxdif) {
        j = i;
      }
    }
    if (mxdif == 0) {
      break;
    }
    cur -= mxdif;
    a[(j + 1) % n] = a[j];
    sol = min(sol, take * x + cur);
  }
  cout << sol << "\n";
}
