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 long long MAXN = (1 << 20);
const long long inf = (long long)1e18 + 42;
long long n, k;
long long a[MAXN];
void read() {
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) cin >> a[i];
}
long long opt[MAXN], cost[MAXN], val[MAXN];
void solve() {
  for (long long i = n + 1; i <= 2 * n; i++) a[i] = a[i - n];
  for (long long i = 1; i <= 2 * n; i++) {
    cost[i] = a[i];
    for (long long j = 1; j <= i; j++) {
      cost[i] = min(cost[i], a[j] + (i - j) * k);
      if (cost[i] == a[j] + (i - j) * k) opt[i] = (i - j), val[i] = a[j];
    }
  }
  for (long long i = 1; i <= n; i++)
    cost[i] = cost[i + n], opt[i] = opt[i + n], val[i] = val[i + n];
  long long ans = 0;
  for (long long i = 1; i <= n; i++) ans += val[i];
  long long mx = 0;
  for (long long i = 1; i <= n; i++) mx = max(mx, opt[i]);
  ans += mx * k;
  cout << ans << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  read();
  solve();
  return 0;
}
