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 N = 1000000;
const int mod = 998244353;
const long long INF = 1 << 30;
int main() {
  long long ans = 0, n, x, v[2010], ct = 0, t = 0;
  cin >> n >> x;
  for (long long i = (long long)0; i < (long long)n; ++i) cin >> v[i];
  for (long long i = (long long)0; i < (long long)n; ++i) {
    long long mn = INF, num = 0;
    long long t2 = 0;
    for (long long j = (long long)0; j < (long long)n; ++j) {
      if (mn > v[j] + x * ((i + n - j) % n))
        mn = v[j] + x * ((i + n - j) % n), t2 = (i + n - j) % n, num = v[j];
    }
    t = max(t, t2);
    ct += num;
  }
  cout << t * x + ct << endl;
  return 0;
}
