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 a[10005], b[10050];
int main() {
  int n, x;
  scanf("%d%d", &n, &x);
  for (int i = 1; i <= n; ++i) scanf("%d", a + i), a[i + n] = a[i];
  for (int i = 1; i <= n; ++i) {
    for (int j = i + 1; j <= n + i - 1; ++j)
      if ((b[i] + j - i) * x + a[i] < (a[j] + b[j] * x))
        a[j] = a[i], b[j] = b[i] + j - i;
      else
        break;
  }
  long long ans = 0;
  int p = 0;
  for (int i = 1; i <= n; ++i)
    if (a[i] + b[i] * x > a[i + n] + b[i + n] * x)
      a[i] = a[i + n], b[i] = b[i + n];
  for (int i = 1; i <= n; ++i) ans += a[i], p = max(p, b[i]);
  printf("%lld", ans + 1ll * p * x);
}
