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 a[2050], x, n, m, f[2050][2050], sum, ans;
int main() {
  scanf("%lld%lld", &n, &x);
  for (register int i = 1; i <= n; i++) scanf("%lld", &a[i]);
  sum = 0x3f3f3f3f3f;
  for (register int i = 1; i <= n; i++) f[i][0] = a[i];
  for (register int i = 1; i <= n; i++) {
    for (register int j = 1; j <= n - 1; j++) {
      long long tim = i - j;
      if (tim <= 0) tim += n;
      f[i][j] = min(f[i][j - 1], a[tim]);
    }
  }
  for (register int i = 0; i <= n - 1; i++) {
    ans = 0;
    for (register int j = 1; j <= n; j++) ans += f[j][i];
    sum = min(sum, ans + x * i);
  }
  printf("%lld\n", sum);
}
