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 main() {
  int d, i, j, N;
  long long a[2010], P = 0, r = 0, t[2010] = {0}, x;
  scanf("%d%lld", &N, &x);
  for (i = 0; i < N; i++) scanf("%lld", &a[i]);
  for (i = 0; i < N; i++) t[i] = a[i];
  for (i = 0; i < N; i++) {
    if (i == N - 1)
      j = 0;
    else
      j = i + 1;
    if (i > j)
      d = i - j;
    else
      d = N + i - j;
    if (t[i] > t[j] + x * d) {
      t[i] = t[j];
      r += x;
    }
  }
  for (i = 0; i < N; i++) P += t[i];
  P += r;
  printf("%lld\n", P);
  return 0;
}
