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>
long long mod(long long a, long long b) { return ((a % b) + b) % b; }
int main(void) {
  const long long INF = 1000000001;
  long long N, x;
  std::vector<long long> a;
  long long result = 0;
  long long maxminj = -1;
  std::cin >> N >> x;
  for (long long i = 0; i < N; ++i) {
    long long t;
    std::cin >> t;
    a.push_back(t);
  }
  for (long long i = 0; i < N; ++i) {
    long long minimum = INF;
    long long minj = -1;
    for (long long j = 0; j < N; ++j) {
      long long t = a[mod(i - j, N)] + x * j;
      if (t < minimum) {
        minimum = t;
        minj = j;
      }
    }
    if (maxminj < minj) {
      maxminj = minj;
    }
    result += a[mod(i - minj, N)];
  }
  result += x * maxminj;
  std::cout << result << '\n';
  return 0;
}
