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;
static const long long inf = 1ll << 60;
long long N, X;
long long A[2005];
long long ans;
long long s;
signed main() {
  cin >> N >> X;
  for (long long i = 0; i < N; ++i) {
    cin >> A[i];
  }
  long long temp = inf;
  for (long long i = 0; i < N; ++i) {
    if (temp > A[i]) {
      s = i;
      temp = A[i];
    }
  }
  ans += A[s];
  long long t = s;
  t++;
  if (t == N) t = 0;
  while (t != s) {
    if (A[t] > X + A[s]) {
      ans += A[s] + X;
    } else {
      ans += A[t];
    }
    t++;
    if (t == N) t = 0;
  }
  cout << ans << endl;
}
