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 main() {
  long long n, t;
  cin >> n >> t;
  long long a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  long long ans = 1LL << 60;
  for (int k = 0; k < n; k++) {
    long long M = 1LL << 60, x = 0, z = 0, r = 0;
    map<long long, long long> ma;
    for (int j = 0; j < n; j++) {
      int i = (j + k) % n;
      if (M >= a[i]) {
        M = a[i];
        x = i;
      }
      ma[x]++;
      M += t + a[x];
    }
    for (map<long long, long long>::iterator it = ma.begin(); it != ma.end();
         it++) {
      z += a[it->first] * (it->second);
      r = max(r, it->second - 1);
    }
    ans = min(ans, z + r * t);
  }
  cout << ans << endl;
  return 0;
}
