#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) x1*y2-x2*y1 #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) x1*y2*z3+x2*y3*z1+x3*y1*z2-z1*y2*x3-z2*y3*x1-z3*y1*x2 #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = ll; val op(val a, val b) { return a + b; } val e() { return 0; } val mp(func f, val a) { if (f == -1) return a; return f; } func comp(func f, func g) { if (f == -1) return g; return f; } func id() { return -1; } ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; void solve() { ll n, m; cin >> n >> m; auto [a, b, p] = read_tuple(n); ll ch = m - n; if (ch <= 0) { SORT(a); double ans = 0; REP(i, m) { ans += 1.0 / a[i]; } printf("%.10f\n", ans); return; } vector> bap(n); REP(i, n) { bap[i].first = (1.0 / b[i] - 1.0 / a[i]) / p[i]; bap[i].second = i; } SORT(bap); reverse(all(bap)); vector dp(n + 1, vector(ch + 1, 0.0)); dp[0][0] = 1.0; REP(i, n) { auto [t, ii] = bap[i]; REP(j, ch) { if (t <= 0.0) { dp[i][j + 1] += dp[i][j]; } else { // 成功 dp[i + 1][j] += dp[i][j] / p[ii]; // 失敗 dp[i][j + 1] += dp[i][j] * (1.0 - 1.0 / p[ii]); } } } vector sa(n + 1), sb(n + 1); REP(i, n) sb[i + 1] = sb[i] + 1.0 / b[bap[i].second]; PER(i, n) sa[i] = sa[i + 1] + 1.0 / a[bap[i].second]; double ans = 0; REP(i, n) { ans += dp[i].back() * (sb[i] + sa[i]); } REP(i, ch) { ans += dp[n][i] * sb[n]; } printf("%.10f\n", ans); } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }