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 search(int index, int depth, unsigned long long K, vector<int> *vec) {
  int rtn = 0;
  if (depth > K) {
    rtn = 1;
    for (auto &i : vec[index]) {
      rtn += search(i, 2, K, vec);
    }
    return rtn;
  }
  int candidate = 0;
  for (auto &i : vec[index]) {
    candidate += search(i, 1, K, vec);
  }
  for (auto &i : vec[index]) {
    rtn += search(i, depth + 1, K, vec);
  }
  if (rtn > candidate) return candidate + 1;
  return rtn;
}
int main(int argc, char **argv) {
  int N;
  int ans = 0;
  unsigned long long K;
  vector<int> next[100001];
  cin >> N >> K;
  int a_in;
  cin >> a_in;
  if (a_in != 1) ans++;
  for (int i = 2; i <= N; i++) {
    cin >> a_in;
    next[a_in].push_back(i);
  }
  for (auto i : next[1]) {
    ans += search(i, 1, K, next);
  }
  cout << ans;
  return 0;
}
