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;
unsigned long long inf = (1LL << 62);
long long mod = 998244353;
pair<long long, long long> dx[4] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
long long N, x;
vector<long long> a;
long long dist[2000][2000];
int main() {
  cin >> N >> x;
  a.resize(N);
  long long index = 0;
  long long mi = inf;
  for (int i = 0; i < (int)(N); i++) {
    cin >> a[i];
    if (mi > a[i]) {
      index = i;
      mi = a[i];
    }
  }
  long long sum = a[index];
  long long nindex = (index + 1) % N;
  while (nindex != index) {
    sum += min(a[index] + x, a[nindex]);
    nindex += 1;
    nindex %= N;
  }
  cout << sum << endl;
  return 0;
}
