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;
template <typename T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
using ll = int_fast64_t;
constexpr ll INF = (1e9);
constexpr ll MOD = (1e9 + 7);
ll b[2003][2003];
signed main() {
  ll n, x;
  cin >> n >> x;
  vector<ll> a(n);
  for (ll i = 0; i < (ll)n; ++i) cin >> a[i];
  for (ll i = 0; i < (ll)n; ++i) b[i][0] = a[i];
  for (ll i = 0; i < (ll)n; ++i)
    for (ll j = 1; j < (ll)n; ++j) {
      b[i][j] = min(b[i][j - 1], a[(i - j + n) % n]);
    }
  for (ll j = 0; j < (ll)n; ++j)
    for (ll i = 1; i < (ll)n; ++i) {
      b[i][j] += b[i - 1][j];
    }
  ll ans = INF;
  for (ll i = 0; i < (ll)n; ++i) {
    chmin(ans, i * x + b[n - 1][i]);
  }
  cout << ans << endl;
  return 0;
}
