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;
long long ara[2004];
long long n, x;
long long check(long long r) {
  int bam = -r;
  long long ans = 0;
  for (int i = 0; i < n; i++, bam++) {
    long long mn = ara[i];
    for (int j = bam; j <= i; j++) {
      int pos = ((j % n) + n) % n;
      mn = min(mn, ara[pos]);
    }
    ans += mn;
  }
  ans = ans + x * r;
  return ans;
}
int main() {
  cin >> n >> x;
  for (int i = 0; i < n; i++) {
    cin >> ara[i];
  }
  long long lo = 0, hi = n - 1;
  while (hi - lo > 3) {
    long long m1 = (hi - lo) / 3 + lo;
    long long m2 = (hi - lo) / 3 + m1;
    if (check(m1) > check(m2)) {
      lo = m1;
    } else {
      hi = m2;
    }
  }
  long long ans = 4e18;
  for (int i = lo; i <= hi; i++) {
    ans = min(ans, check(i));
  }
  cout << ans << "\n";
}
