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[2005], c[2005];
typedef struct {
  long long x;
  long long len;
} Best;
Best s[2005];
int main(void) {
  int n, x, i, j;
  long long p, temp, mx, cx, ans;
  scanf("%d%d", &n, &x);
  for (i = 1; i <= n; i++) scanf("%lld", &a[i]);
  p = a[1];
  temp = 1;
  for (i = 1; i <= n; i++) {
    if (a[i] < p) p = a[i], temp = i;
  }
  for (i = 1; i <= n; i++) {
    c[i] = a[temp++];
    if (temp > n) temp = 1;
    s[i].x = c[i], s[i].len = 0;
  }
  mx = 0;
  for (i = 2; i <= n; i++) {
    for (j = 1; j <= i - 1; j++) {
      cx = max(0ll, s[j].len + i - j - mx);
      if (s[i].x > s[j].x + cx * x) {
        s[i].x = s[j].x + cx * x;
        s[i].len = s[j].len + i - j;
        mx = max(cx, s[j].len + i - j);
      }
    }
  }
  ans = 0;
  for (i = 1; i <= n; i++) ans += s[i].x;
  printf("%lld\n", ans);
  return 0;
}
