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 min[2010] = {0};
int a[2010], pos[2010];
int main(void) {
  int n, x, max = 0;
  scanf("%d%d", &n, &x);
  long long sum = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    min[i] = a[i];
    pos[i] = i;
  }
  for (int i = 1; i <= n; i++) {
    for (int j = i + 1; j <= n; j++) {
      if (1ll * (j - i) * x + 1ll * a[i] < 1ll * min[j]) {
        pos[j] = i;
        min[j] = 1ll * (j - i) * x + 1ll * a[i];
      }
      if (1ll * (i + n - j) * x + 1ll * a[j] < 1ll * min[i]) {
        min[i] = 1ll * (i + n - j) * x + 1ll * a[j];
        pos[i] = j;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (max < (pos[i] <= i ? i - pos[i] : i - pos[i] + n)) {
      max = (pos[i] <= i ? i - pos[i] : i - pos[i] + n);
    }
    sum += a[pos[i]];
  }
  printf("%lld\n", 1ll * max * x + 1ll * sum);
}
