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>
int a[2005], x, f[2005], n, ans, ff;
using std::min;
int main() {
  scanf("%d%d", &n, &x);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) {
    f[i] = a[i];
    if (a[i] <= x) continue;
    for (int j = i - 1, t = x; j >= 1 && t + a[j] < f[i]; j--, t += x)
      f[i] = t + a[j], ff = 1;
  }
  if (ff == 1)
    f[1] = min(f[1], f[n]);
  else {
    int m = 1000000000;
    for (int j = 2; j <= n; j++) m = min(a[j - 1] + x - a[j], m);
    f[1] = min(f[1], m + f[n]);
  }
  for (int i = 1; i <= n; i++) ans = ans + f[i];
  printf("%d\n", ans);
}
