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 vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<long long>;
using vvl = vector<vl>;
using P = pair<int, int>;
using PP = pair<int, P>;
using Pl = pair<long long, long long>;
using PPl = pair<long long, Pl>;
using vs = vector<string>;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
const long long MOD = 1000000007LL;
const int INF = 1 << 30;
const long long LINF = 1LL << 60;
template <typename Monoid>
struct SegTree {
  using F = function<Monoid(Monoid, Monoid)>;
  int size;
  vector<Monoid> dat;
  const F func;
  const Monoid Mdef;
  SegTree(int sz, const F func, const Monoid &Mdef) : func(func), Mdef(Mdef) {
    size = 1;
    while (size < sz) {
      size *= 2;
    }
    dat.assign(size * 2, Mdef);
  }
  void set(int k, const Monoid &x) { dat[k + size - 1] = x; }
  void build() {
    for (int k = size - 2; k >= 0; k--) {
      dat[k] = func(dat[k * 2 + 1], dat[k * 2 + 2]);
    }
  }
  void update(int k, const Monoid &x) {
    int now = k + size - 1;
    dat[now] = x;
    while (now) {
      now = (now - 1) / 2;
      dat[now] = func(dat[now * 2 + 1], dat[now * 2 + 2]);
    }
  }
  Monoid _query(int a, int b, int k, int l, int r) {
    if (r < a || b < l) {
      return Mdef;
    }
    if (a <= l && b >= r) {
      return dat[k];
    }
    auto tl = _query(a, b, k * 2 + 1, l, (l + r) / 2);
    auto tr = _query(a, b, k * 2 + 2, (l + r) / 2 + 1, r);
    return func(tl, tr);
  }
  Monoid query(int l, int r) { return _query(l, r, 0, 0, size - 1); }
  Monoid operator[](const int &k) const { return dat[k + size - 1]; }
  void Debug() {
    for (int i = 0; i < size; i++) {
      cerr << " " << dat[i + size - 1];
    }
    cerr << endl;
  }
  int Size() { return size; }
};
long long rmq(SegTree<long long> &tr, int l, int r) {
  long long res;
  if (l <= r) {
    res = tr.query(l, r);
  } else {
    res = min(tr.query(l, tr.Size() - 1), tr.query(0, r));
  }
  return res;
}
int main() {
  int n, x;
  cin >> n >> x;
  SegTree<long long> tr(
      n, [](long long a, long long b) { return min(a, b); }, LINF);
  for (int i = (0); i < (n); i++) {
    long long t;
    cin >> t;
    tr.set(i, t);
  }
  tr.build();
  long long ans = LINF;
  for (int i = (0); i < (n); i++) {
    long long sum = x * i;
    for (int j = (0); j < (n); j++) {
      sum += rmq(tr, (j - i + n) % n, j);
    }
    chmin(ans, sum);
  }
  cout << ans << endl;
  return 0;
}
