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 compare_ll(const void *a, const void *b) {
  return *(unsigned long long *)b - *(unsigned long long *)a;
}
int main(void) {
  unsigned long long a[2000] = {0};
  int N, i, cnt, cntmax;
  unsigned long long x;
  int flag;
  unsigned long long ans = 0;
  scanf("%lld %lld", &N, &x);
  for ((i) = 0; i < (N); i++) scanf("%lld", &a[i]);
  flag = 1;
  cntmax = 0;
  cnt = 0;
  while (flag == 1) {
    flag = 0;
    for (i = 1; i < N; i++) {
      if (a[i] > a[i - 1] + (x * (cnt + 1))) {
        a[i] = a[i - 1];
        flag = 1;
        cnt++;
      } else {
        if (cntmax < cnt) {
          cntmax = cnt;
        }
        cnt = 0;
      }
    }
    if (a[0] > a[N - 1] + (x * (cnt + 1))) {
      a[0] = a[N - 1];
      flag = 1;
      cnt++;
    }
  }
  for ((i) = 0; i < (N); i++) ans += a[i];
  ans += cntmax * x;
  printf("%lld", ans);
  return 0;
}
