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;
const int N = 100005;
const long long inf = 1000000000000000000ll;
int n, x, now;
long long ans, sum;
int a[N], p[N];
int main() {
  int i, j;
  scanf("%d%d", &n, &x);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  ans = inf;
  for (i = 1; i < n; i++) a[i + n] = a[i];
  for (i = 1; i <= n; i++) {
    sum = a[i];
    now = i;
    for (j = i + 1; j < i + n; j++) {
      if (1ll * (j - now) * x + 1ll * a[i] <= 1ll * a[j]) {
        sum += 1ll * a[i] + 1ll * (j - now) * x;
        now = j;
      } else
        sum += 1ll * a[j];
    }
    ans = min(ans, sum);
  }
  printf("%lld\n", ans);
  return 0;
}
