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;
int a, b, c, d, k, i, m[2010], o[2010], l[2010][2010];
long long x, y, z;
string r;
stack<int> s;
queue<int> q;
vector<int> v[110];
int f(int t, int w, int h) {
  if (w >= a || t >= a) return 0;
  if (l[t][w]) return l[t][w];
  for (int u = w + 1; u <= a; u++) {
    if (l[t][w] == 0)
      l[t][w] = f(w + 1, u, max(h, u - w - 1)) + max(0, u - w - 1 - h) * b +
                (u - w) * o[w + 1];
    else
      l[t][w] =
          min(l[t][w], f(w + 1, u, max(h, u - w - 1)) +
                           max(0, u - w - 1 - h) * b + (u - w) * o[w + 1]);
  }
  return l[t][w];
}
int main() {
  scanf("%d %d", &a, &b);
  k = 1000000100;
  for (int t = 1; t <= a; t++) {
    scanf("%d", &m[t]);
    if (m[t] < k) {
      k = m[t];
      c = t;
    }
  }
  for (int t = 1; t <= a; t++) {
    o[t] = m[((t + c - 1) % a ? (t + c - 1) % a : t + c - 1)];
  }
  printf("\n%d", f(0, 0, 0));
  return 0;
}
