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 n, x, a[2050];
int main() {
  scanf("%lld %lld", &n, &x);
  for (int i = 0; i < n; i++) {
    scanf("%lld", &a[i]);
  }
  long long mv_m = 0, over_all = 0;
  for (int i = 0; i < n; i++) {
    long long mc = 0, nw = i, mn = LLONG_MAX, idx = i;
    while (mc + x < a[i]) {
      nw--;
      if (nw < 0) {
        nw = n - 1;
      }
      mc += x;
      if (mn > mc + a[nw]) {
        mn = mc + a[nw];
        mv_m = max(mv_m, mc / x);
        idx = nw;
      }
    }
    over_all += a[idx];
  }
  printf("%lld", over_all + mv_m * x);
}
