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 ll = long long;
using namespace std;
const ll MOD = 1e9 + 7;
const double pi = acos(-1);
bool operator<(const pair<int, int> &a, const pair<int, int> &b) {
  if (a.first == b.first) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
ll a[2010];
ll r[2010];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N, x;
  cin >> N >> x;
  ll minV = 1000000000;
  for (int i = 1; i <= N; i++) {
    cin >> a[i];
  }
  for (int i = 1; i <= N; ++i) {
    r[i] = r[i - 1] + a[i];
  }
  for (int i = 1; i <= N; ++i) {
    for (int j = i; j <= N; ++j) {
      minV = min(minV, r[j] - r[i - 1] + (N - j + i - 1) * a[j] +
                           ((N - j) * x + (i - 1) * x));
    }
    for (int j = 1; j < i; ++j) {
      minV = min(minV, r[N] - r[i - 1] + r[j] + a[j] * (i - j) + (i - j) * x);
    }
  }
  cout << minV << endl;
  return 0;
}
