Problem: There are n castles in the Lannister's Kingdom and some walls connect two castles, no two castles are connected by more than one wall, no wall connects a castle to itself. 

Sir Jaime Lannister has discovered that Daenerys Targaryen is going to attack his kingdom soon. Therefore he wants to defend his kingdom. He has k liters of a strange liquid. He wants to distribute that liquid among the castles, so each castle may contain some liquid (possibly zero or non-integer number of liters). After that the stability of a wall is defined as follows: if the wall connects two castles a and b, and they contain x and y liters of that liquid, respectively, then the strength of that wall is x·y.

Your task is to print the maximum possible sum of stabilities of the walls that Sir Jaime Lannister can achieve.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 40, 1 ≤ k ≤ 1000).

Then n lines follows. The i-th of these lines contains n integers ai, 1, ai, 2, ..., ai, n (<image>). If castles i and j are connected by a wall, then ai, j = 1. Otherwise it is equal to 0.

It is guaranteed that ai, j = aj, i and ai, i = 0 for all 1 ≤ i, j ≤ n.

Output

Print the maximum possible sum of stabilities of the walls that Sir Jaime Lannister can achieve.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

3 1
0 1 0
1 0 0
0 0 0


Output

0.250000000000


Input

4 4
0 1 0 1
1 0 1 0
0 1 0 1
1 0 1 0


Output

4.000000000000

Note

In the first sample, we can assign 0.5, 0.5, 0 liters of liquid to castles 1, 2, 3, respectively, to get the maximum sum (0.25).

In the second sample, we can assign 1.0, 1.0, 1.0, 1.0 liters of liquid to castles 1, 2, 3, 4, respectively, to get the maximum sum (4.0)

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
namespace std {
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_set = std::unordered_set<_Key, _Hash>;
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_mset = std::unordered_multiset<_Key, _Hash>;
template <typename _Key, typename _Val, typename _Hash = std::hash<_Key>>
using hash_map = std::unordered_map<_Key, _Val, _Hash>;
template <typename _Key, typename _Hash = std::hash<_Key>>
using hash_mmap = std::unordered_multimap<_Key, _Hash>;
template <typename _Key, typename _Cmp = std::less<_Key>>
using mset = std::multiset<_Key, _Cmp>;
template <typename _Key, typename _Val, typename _Cmp = std::less<_Key>>
using mmap = std::multimap<_Key, _Val, _Cmp>;
template <typename _Key>
using rset = std::set<_Key, std::greater<_Key>>;
template <typename _Key>
using rmset = std::multiset<_Key, std::greater<_Key>>;
template <typename _Key, typename _Val>
using rmap = std::map<_Key, std::greater<_Key>>;
template <typename _Key, typename _Val>
using rmmap = std::multimap<_Key, _Val, std::greater<_Key>>;
static std::ostream& fdeb = cerr;
struct NullOstream {};
template <typename T>
NullOstream& operator<<(NullOstream& out, const T&) {
  return out;
}
NullOstream& operator<<(NullOstream& out, std::ostream& (*)(std::ostream&)) {
  return out;
}
static NullOstream deb;
static NullOstream debl;
template <int _Ind, typename... _Args>
struct __TuplePrinter {
  static void print(ostream& out, const tuple<_Args...>& t) {
    __TuplePrinter<_Ind - 1, _Args...>::print(out, t);
    out << ' ' << get<_Ind>(t);
  }
};
template <typename... _Args>
struct __TuplePrinter<0, _Args...> {
  static void print(ostream& out, const tuple<_Args...>& t) {
    out << '(' << get<0>(t);
  }
};
template <typename... _Args>
ostream& operator<<(ostream& out, const tuple<_Args...>& t) {
  __TuplePrinter<sizeof...(_Args) - 1, _Args...>::print(out, t);
  out << ')';
  return out;
}
template <typename _T1, typename _T2>
ostream& operator<<(ostream& out, const pair<_T1, _T2>& p) {
  return out << '(' << p.first << ' ' << p.second << ')';
}
using uchar = unsigned char;
using ushort = unsigned short;
using uint = unsigned int;
using lld = long long;
using ulld = unsigned long long;
static const int MOD = 1e9 + 7;
static const int INF = MOD;
static const lld HASHP = 37;
}  // namespace std
using namespace std;
int kerbosh(const std::vector<std::uint64_t>& g, std::uint64_t candidates,
            std::uint64_t banned = 0ULL, std::uint64_t cresult = 0ULL,
            int depth = 0) {
  if (candidates == 0) {
    return depth;
  }
  debl << std::hex << std::showbase << "depth: " << depth << " " << candidates
       << " " << banned << " " << cresult;
  int best_result = depth;
  ++depth;
  int abi = 0;
  for (std::uint64_t i = 0, ii = 1; i < g.size(); ++i, ii <<= 1) {
    if ((candidates | banned) & ii) {
      abi = i;
      break;
    }
  }
  std::uint64_t z = candidates & ~g[abi];
  for (std::uint64_t ci = 0, c = 1ULL; ci < g.size(); ++ci, c <<= 1) {
    if ((z & c) == 0) {
      continue;
    }
    best_result = std::max(
        best_result,
        kerbosh(g, candidates & g[ci], banned & g[ci], cresult | c, depth));
    candidates &= ~c;
    banned |= c;
  }
  return best_result;
}
int main() {
  int N, K;
  cin >> N >> K;
  vector<std::uint64_t> g(N);
  for (auto& v : g) {
    v = 0;
    for (int i = 0; i < N; ++i) {
      long long vv;
      std::cin >> vv;
      v |= (vv << i);
    }
  }
  std::uint64_t max_click = kerbosh(g, (1ULL << g.size()) - 1);
  debl << max_click;
  std::cout << std::fixed << std::setprecision(8)
            << (0.5 * K * K * (max_click - 1) / max_click) << std::endl;
  return 0;
}