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 int;
const ll INF = 1e9;
template <typename Monoid>
struct SegmentTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int sz;
  vector<Monoid> seg;
  const F f;
  const Monoid M1;
  SegmentTree(int n, const F f, const Monoid &M1) : f(f), M1(M1) {
    sz = 1;
    while (sz < n) sz <<= 1;
    seg.assign(2 * sz, M1);
  }
  void set(int k, const Monoid &x) { seg[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  void update(int k, const Monoid &x) {
    k += sz;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
    }
  }
  Monoid query(int a, int b) {
    Monoid L = M1, R = M1;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) const { return seg[k + sz]; }
};
int main() {
  int n, x;
  cin >> n >> x;
  vector<ll> a(n);
  SegmentTree<ll> seg(
      n * 2, [](ll a, ll b) { return min(a, b); }, INF);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    seg.update(i, a[i]);
    seg.update(i + n, a[i]);
  }
  ll ans = INF;
  for (int k = 0; k < n; k++) {
    ll val = 0;
    for (int i = 0; i < n; i++) {
      val += seg.query(i - k, i + 1);
    }
    ans = min(ans, val + x * k);
  }
  cout << ans << endl;
  return 0;
}
