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 ll = long long;
using P = std::pair<ll, ll>;
const ll MOD = 1e9 + 7;
int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);
  ll n, x, ans = MOD;
  std::cin >> n >> x;
  std::vector<ll> a(n);
  for (ll(i) = (0); i < (n); i++) std::cin >> a[i];
  std::vector<std::vector<ll>> min(n, std::vector<ll>(n));
  for (ll(i) = (0); i < (n); i++) {
    min[i][0] = a[i];
    for (ll(j) = (1); j < (n); j++)
      min[i][j] = std::min(min[i][j - 1], a[(i - j + n) % n]);
  }
  for (ll(i) = (0); i < (n); i++) {
    ll temp = 0;
    for (ll(j) = (0); j < (n); j++) temp += min[j][i];
    ans = std::min(ans, i * x + temp);
  }
  std::cout << ans;
  return 0;
}
