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 n, k, mn = 1e9, to, d[2010];
int vis[2010];
queue<int> q;
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &d[i]);
    q.push(i);
    vis[i]++;
  }
  int ans = 0;
  while (!q.empty()) {
    int x = q.front();
    q.pop();
    int y = x + 1;
    if (y > n) y -= n;
    while (d[x] + k < d[y]) {
      d[y] = d[x] + k;
      if (!vis[y]) {
        vis[y]++;
        q.push(y);
      }
      y++;
      if (y > n) y -= n;
    }
  }
  for (int i = 1; i <= n; ++i) ans += d[i];
  cout << ans << endl;
}
