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 DX[4] = {0, 1, 0, -1}, DY[4] = {-1, 0, 1, 0};
const int INF = 1e9;
const long long INFLL = 1e18;
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << "(" << p.first << "," << p.second << ")";
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto i = begin(v); i != end(v); i++)
    os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
signed main() {
  long long N, x;
  cin >> N >> x;
  vector<long long> a(N);
  for (int i = 0; i < (int)(N); i++) cin >> a[i];
  long long ans = 0;
  long long b = a[0];
  for (int i = 1; i < (int)(N); i++) {
    b = min(b + x, a[i]);
    ans += b;
  }
  b = min(b + x, a[0]);
  ans += b;
  cout << ans << endl;
  return 0;
}
