#include<bits/stdc++.h>
#include<atcoder/all>
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define RD(T,...) T __VA_ARGS__;li(__VA_ARGS__)
#define LL(...) RD(ll,__VA_ARGS__)
#define VE(a,...) au a=vec(__VA_ARGS__)
#define JO(a,b) a##b
#define jo(a,b) JO(a,b)
#define uq_symbol(a) jo(a,__LINE__)
#define FE(v,e,...) for(au&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):v)
#define FO(n) for(ll uq_symbol(i)=n;uq_symbol(i)-->0;)
#define FOR(i,...) for(au[i,i##O,i##E]=rng(0,__VA_ARGS__);i<i##O;i+=i##E)
#define fe(v,...) FE(v,__VA_ARGS__)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define of(i,...) for(au[i,i##O,i##E]=rng(1,__VA_ARGS__);i>=i##O;i-=i##E)
#define I template
#define J class
#define au auto
#define rr return
using std::cin,std::cout,std::begin,std::end,std::rbegin;
using std::swap,std::move,std::abs,std::prev,std::next;
using std::tuple,std::array,std::bitset,std::minmax,std::get;
using vo=void;using bo=bool;
vo solve();
using is=std::istream;using os=std::ostream;
using dd=long double;using ll=long long;using ull=unsigned long long;
using lll=__int128_t;using ulll=__uint128_t;using str=std::string;
using namespace atcoder;using ml=modint;au&operator<<(os&o,const ml&x){rr o<<x.val();}
constexpr ll oo=3e18;
constexpr ll dx[]{-1,0,1,0,-1,1,1,-1},dy[]{0,-1,0,1,-1,-1,1,1};
constexpr char sp=32;
constexpr char nl=10;
au rng(bo s,ll a,ll b=oo,ll c=1){if(b==oo)b=a,(s?b:a)=0;rr tuple{a-s,b,c};}

ll pw2(ll n){rr 1LL<<n;}
I<J T>bo at2(T x,ll i){rr x>>i&1;}
I<J T>T zz(T x){rr x<0?-x:x;}
I<J T>ll len(const T&a){rr a.size();}
I<J T>bo amax(T&a,const T&b){rr a<b?a=b,1:0;}

struct edg{
  ll t,w;
  edg(){}
  edg(ll t,ll w=1):t(t),w(w){}
  friend os&operator<<(os&o,const edg&e){rr o<<e.t<<sp<<e.w;}
};

I<J A,J B=A>struct cp{
  A a={};B b={};
  cp(){}
  cp(A a,B b):a(a),b(b){}
  cp(std::pair<A,B>p):a(p.first),b(p.second){}
  bo operator==(const cp&c)const{rr a==c.a&&b==c.b;}
  bo operator<(const cp&c)const{rr a!=c.a?a<c.a:b<c.b;}
  bo operator>(const cp&c)const{rr a!=c.a?a>c.a:b>c.b;}

  friend is&operator>>(is&i,cp&c){rr i>>c.a>>c.b;}
  friend os&operator<<(os&o,const cp&c){rr o<<c.a<<sp<<c.b;}
};using cl=cp<ll>;
I<J A,J B=A,J C=A>struct tr{
  A a={};B b={};C c={};
  tr(){}
  tr(A a,B b,C c):a(a),b(b),c(c){}
  bo operator==(const tr&t)const{rr a==t.a&&b==t.b&&c==t.c;}

  au operator<(const tr&t)const{rr a!=t.a?a<t.a:b!=t.b?b<t.b:c<t.c;}
  friend is&operator>>(is&i,tr&t){rr i>>t.a>>t.b>>t.c;}
  friend os&operator<<(os&o,const tr&t){rr o<<t.a<<sp<<t.b<<sp<<t.c;}
};using tl=tr<ll>;

I<J T>decltype(au)rb(T&a){rr*rbegin(a);}
I<J T>au pot(T&a){au r=a.top();a.pop();rr r;}

I<J T,J U=T>using map=std::map<T,U>;
I<J T,J U>os&operator<<(os&o,const map<T,U>&m){fe(m,e)o<<e.first<<sp<<e.second<<nl;rr o;}

I<J T,J U=T>using umap=std::unordered_map<T,U>;
I<J T,J U>os&operator<<(os&o,const umap<T,U>&m){fe(m,e)o<<e.first<<sp<<e.second<<nl;rr o;}

I<J V>struct ve;
I<J V>constexpr bo isv=0;
I<J V>constexpr bo isv<ve<V>> =1;
I<J V>constexpr bo isv<std::vector<V>> =1;
I<J V>au rawv(V){if constexpr(isv<V>)rr rawv(V(1)[0]);else rr V();}

I<J V>struct ve:std::vector<V>{
  using std::vector<V>::vector;
  using T=decltype(rawv(V()));
  I<J U>ve(const std::vector<U>&v={}){fe(v,e)this->eb(e);}

  ve&operator+=(const ve&u){au&v=*this;fo(i,len(v))v[i]+=u[i];rr v;}
  ve&operator-=(const ve&u){au&v=*this;fo(i,len(v))v[i]-=u[i];rr v;}
  ve&operator^=(const ve&u){fe(u,e)this->eb(e);rr*this;}
  ve&operator+=(const T&x){au&v=*this;fe(v,e)e+=x;rr v;}
  ve&operator-=(const T&x){au&v=*this;fe(v,e)e-=x;rr v;}
  ve&operator*=(const T&x){au&v=*this;fe(v,e)e*=x;rr v;}
  I<size_t n>au&operator+=(const bitset<n>&a){fo(i,n)(*this)[i]+=a[i];rr*this;}
  I<size_t n>au&operator-=(const bitset<n>&a){fo(i,n)(*this)[i]-=a[i];rr*this;}

  ve operator+(const ve&u)const{rr ve(*this)+=u;}
  ve operator-(const ve&u)const{rr ve(*this)-=u;}
  ve operator^(const ve&u)const{rr ve(*this)^=u;}
  ve operator+(const T&x)const{rr ve(*this)+=x;}
  ve operator-(const T&x)const{rr ve(*this)-=x;}
  ve operator*(const T&x)const{rr ve(*this)*=x;}
  ve&operator++(){rr*this+=1;}
  ve&operator--(){rr*this-=1;}
  ve operator-()const{rr ve(*this)*=-1;}

  au lower_bound(const V&x)const{rr std::lower_bound(all(*this),x);}
  au upper_bound(const V&x)const{rr std::upper_bound(all(*this),x);}

};
I<J T=ll,size_t n,size_t i=0>au vec(const ll(&s)[n],T x={}){
  if constexpr(n==i+1)rr ve<T>(s[i],x);
  else{au X=vec<T,n,i+1>(s,x);rr ve<decltype(X)>(s[i],X);}
}
I<ll n,J...A>vo setsize(const ll(&l)[n],A&...a){((a=vec(l,rawv(a))),...);}
I<J T>using vve=ve<ve<T>>;using vl=ve<ll>;using vvl=vve<ll>;
using gl=ve<ve<ll>>;using ge=ve<ve<edg>>;

struct io{io(){cin.tie(0)->sync_with_stdio(0);
  cout<<std::fixed<<std::setprecision(15);std::cerr<<nl;}}io;
os&operator<<(os&o,const ulll&x){rr(x<10?o:o<<x/10)<<ll(x%10);}
os&operator<<(os&o,const lll&x){rr o<<str(x<0,'-')<<ulll(zz(x));}
I<size_t n>os&operator<<(os&o,const bitset<n>&b){fo(i,n)o<<b[i];rr o;}
I<J...A>os&operator<<(os&o,const tuple<A...>&t){
  apply([&](const au&...a){ll i=0;(((o<<a<<str(++i!=sizeof...(a),sp))),...);},t);rr o;}
I<J V>os&operator<<(os&o,const std::vector<V>&v){fe(v,e)o<<e<<str(&e!=&rb(v),isv<V>?nl:sp);rr o;}
I<char c=sp,J...A>vo pp(const A&...a){ll i=0;((cout<<a<<str(++i!=sizeof...(a),c)),...);cout<<nl;}
I<J V>is&operator>>(is&i,std::vector<V>&v){fe(v,e)i>>e;rr i;}
I<J...A>vo li(A&...a){(cin>>...>>a);}
I<J...A>vo vi(A&...a){fo(i,(len(a)&...))(cin>>...>>a[i]);}

I<J F>struct rec:F{rec(F&&f):F(std::forward<F>(f)){}I<J...A>decltype(au)operator()(A&&...a)const{rr F::operator()(*this,std::forward<A>(a)...);}};

int main(){ll T=1;fo(T)solve();}
vo solve(){
  LL(N,M);
  ve<dd>a(N),b(N),p(N);vi(a,b,p);

  VE(dp,{pw2(N),M+1},dd(-1));
  VE(used,{pw2(N),M+1});
  au f=rec([&](au&f,ll S,ll k)->dd{
    if(dp[S][k]!=-1)rr dp[S][k];

    dd res=0;
    fo(i,N){
      if(!at2(S,i)){
        amax(res,f(S|pw2(i),k)+1/a[i]);
        if(k)amax(res,1/p[i]*(f(S|pw2(i),k)+1/b[i])+(1-1/p[i])*f(S,k-1));
      }
    }
    rr dp[S][k]=res;
  });
  pp(f(0,M));
}