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;
int n;
int x;
int a[3000];
long long int dp[2500];
long long int min(long long int a, long long int b) {
  if (a > b) return b;
  return a;
}
int main() {
  cin >> n >> x;
  long long int all = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    all += a[i];
  }
  sort(a, a + n);
  dp[0] = a[0];
  int cnt = 0;
  for (int i = 1; i < n; i++) {
    if (dp[i - 1] + x <= a[i]) {
      dp[i] = min(dp[i - 1] + x, a[i]);
      cnt++;
    } else
      dp[i] = dp[i - 1] + a[i];
  }
  if (all < dp[n - 1] + cnt * a[0]) {
    cout << all << endl;
  } else
    cout << dp[n - 1] + cnt * a[0] << endl;
  return 0;
}
