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, x;
  cin >> n >> x;
  long long ma = 1000000000000000;
  long long num;
  long long a[n];
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    if (ma > a[i]) {
      ma = a[i];
      num = i;
    }
  }
  long long b[n];
  for (long long i = 0; i < n; i++) {
    b[i] = a[(num + i) % n];
  }
  long long ans = 1000000000000000000;
  for (long long i = 1; i <= n; i++) {
    long long now = b[0];
    long long sum = b[0];
    long long p = 1;
    for (long long j = 1; j < n; j++) {
      if (p == i) {
        sum += b[j];
        now = b[j];
        p = 1;
        continue;
      }
      if (now < b[j]) {
        sum += now + x;
        p++;
      }
      if (now >= b[j]) {
        sum += b[j];
        now = b[j];
        p = 1;
      }
    }
    ans = min(ans, sum);
  }
  cout << ans << endl;
}
