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() {
  int n, x, a[2005];
  while (~scanf("%d%d", &n, &x)) {
    long long sum = 0;
    int minn = 0x7fffffff, mini;
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      sum += a[i];
      if (a[i] < minn) mini = i, minn = a[i];
    }
    while (true) {
      long long dis = 0;
      for (int i = 0; i < n - 1; i++) {
        if (a[(mini - i + n - 1) % n] > a[(mini - i + n - 2) % n]) {
          dis += a[(mini - i + n - 1) % n] - a[(mini - i + n - 2) % n];
          a[(mini - i + n - 1) % n] = a[(mini - i + n - 2) % n];
        }
      }
      if (dis < x) break;
      sum -= dis - x;
    }
    printf("%lld\n", sum);
  }
}
