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>
long long n, a[2005], x, ans;
long long min(long long x, long long y) { return x < y ? x : y; }
int main() {
  scanf("%lld%lld", &n, &x);
  for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  for (int i = 1; i <= n; ++i) {
    long long tot = a[i];
    for (int j = 1; j <= n; ++j)
      if (i != j)
        tot = min(a[j] + ((i > j) ? (1ll * x * (i - j)) : (1ll * x * (j - i))),
                  tot);
    ans += tot;
  }
  printf("%lld\n", ans);
}
