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;
const int N = 1000000;
const long long int INF = std::numeric_limits<long long>::max();
string YN(bool b) { return (b ? "YES" : "NO"); }
string yn(bool b) { return (b ? "Yes" : "No"); }
long long int n, x, in[2010], v[4020];
int main() {
  cin >> n >> x;
  for (long long int i = (long long int)0; i < (long long int)n; ++i) {
    cin >> in[i];
    if (i == 0)
      v[i] = in[i];
    else
      v[i] = min(in[i], in[i - 1] + x);
  }
  long long int ans = 0;
  for (int i = 2010; i < 4020; ++i) {
    v[i] = min(in[i], in[i - 1] + x);
    ans += v[i];
  }
  cout << ans << endl;
  return 0;
}
