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;
using ll = long long;
using ld = long double;
template <typename T>
T &chmin(T &a, const T &b) {
  return a = min(a, b);
}
template <typename T>
T &chmax(T &a, const T &b) {
  return a = max(a, b);
}
template <typename T>
T inf() {
  assert(false);
}
template <>
constexpr int inf<int>() {
  return 1e9;
}
template <>
constexpr ll inf<ll>() {
  return 1e18;
}
template <>
constexpr ld inf<ld>() {
  return 1e30;
}
int main() {
  ll n, x;
  cin >> n >> x;
  vector<ll> a(n);
  for (ll &i : a) cin >> i;
  ll res = inf<ll>();
  for (int i = 0; i < (int)(n); i++) {
    chmin(res, accumulate((a).begin(), (a).end(), 0) + x * i);
    vector<ll> b = a;
    chmin(b[(i + 1) % n], a[i]);
    a = b;
  }
  cout << res << endl;
  return 0;
}
