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(void) {
  int N, x;
  string in;
  getline(cin, in);
  stringstream ss(in);
  ss >> N >> x;
  int *a = new int[N];
  getline(cin, in);
  int min_id = 0;
  stringstream ss2(in);
  for (int i = 0; i < N; ++i) {
    getline(ss2, in, ' ');
    a[i] = stoi(in);
    if (a[min_id] > a[i]) min_id = i;
  }
  int change = 0;
  int maxc = 0;
  int sum = 0;
  for (int i = 0; i < N; ++i) {
    int current = (min_id + i) % N;
    int prev = (min_id + i) ? min_id + i - 1 : N - 1;
    if (a[current] <= x || a[current] <= a[prev] + x * (change + 1)) {
      change = 0;
      sum += a[current];
    } else {
      ++change;
      a[current] = a[prev];
      if (maxc < change) maxc = change;
      sum += a[current];
    }
  }
  sum += x * maxc;
  printf("%d\n", sum);
  return 0;
}
