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>
std::stack<long long> S;
int main() {
  long long n, a[6100] = {}, mark[6100] = {}, x, i, j;
  long long value = 0, m, sum = 0, maxshift = 0, saveshift, savemark, c = 0;
  scanf("%lld%lld", &n, &x);
  for (i = 0; i < n; i++) scanf("%lld", &a[i]), a[n + i] = a[i];
  m = 2000000000;
  for (i = 0; i < n; i++) {
    if (m > a[i]) m = a[i], savemark = i;
  }
  S.push(a[savemark]);
  sum += a[savemark];
  for (i = savemark + 1; i < savemark + n; i++) {
    if (a[i] < a[savemark] + x) {
      S.pop();
      S.push(a[i]);
      sum += a[i];
    } else {
      sum += (S.top() + x);
    }
  }
  printf("%lld", sum);
}
