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 main() {
  unsigned int N, x;
  cin >> N >> x;
  vector<int> a;
  vector<int> r;
  a.reserve(N);
  r.resize(N, 0);
  for (int i = 0; i < N; i++) {
    int n;
    cin >> n;
    a.push_back(n);
  }
  int maxRot = 0;
  for (int i = 0; i < N; i++) {
    unsigned long long minCos = a[i];
    unsigned long long rot = 0;
    for (int j = 0; j < N; j++) {
      unsigned long long cost = x * j + a[(i - j + N) % N];
      if (minCos > cost) {
        minCos = cost;
        rot = j;
      }
    }
    r[i] = a[(i - rot + N) % N];
    if (maxRot < rot) {
      maxRot = rot;
    }
  }
  unsigned long long ans = x * maxRot;
  for (int i = 0; i < N; i++) {
    ans += r[i];
  }
  cout << ans << endl;
  return 0;
}
