#line 2 "library/template/template.hpp" #include using namespace std; #line 2 "library/template/macro.hpp" #define rep(i, a, b) for (int i = (a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) #define YN(b) cout << ((b) ? "YES" : "NO") << "\n"; #define Yn(b) cout << ((b) ? "Yes" : "No") << "\n"; #define yn(b) cout << ((b) ? "yes" : "no") << "\n"; #line 6 "library/template/template.hpp" #line 2 "library/template/util.hpp" using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template S SUM(const vector& a) { return accumulate(ALL(a), S(0)); } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } template int popcnt(T x) { return __builtin_popcountll(x); } template int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } #line 8 "library/template/template.hpp" #line 2 "library/template/inout.hpp" struct Fast { Fast() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(15); } } fast; ostream& operator<<(ostream& os, __uint128_t x) { char buf[40]; size_t k = 0; while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10; if (k == 0) buf[k++] = '0'; while (k) os << buf[--k]; return os; } ostream& operator<<(ostream& os, __int128_t x) { return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x); } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream& os, const pair& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, vector& a) { for (auto& v : a) is >> v; return is; } template ostream& operator<<(ostream& os, const vector& a) { for (auto it = a.begin(); it != a.end();) { os << *it; if (++it != a.end()) os << " "; } return os; } template ostream& operator<<(ostream& os, const set& st) { os << "{"; for (auto it = st.begin(); it != st.end();) { os << *it; if (++it != st.end()) os << ","; } os << "}"; return os; } template ostream& operator<<(ostream& os, const map& mp) { os << "{"; for (auto it = mp.begin(); it != mp.end();) { os << it->first << ":" << it->second; if (++it != mp.end()) os << ","; } os << "}"; return os; } void in() {} template void in(T& t, U&... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T& t, const U&... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } namespace IO { namespace Graph { vector> unweighted(int n, int m, bool directed = false, int offset = 1) { vector> g(n); for (int i = 0; i < m; i++) { int u, v; cin >> u >> v; u -= offset, v -= offset; g[u].push_back(v); if (!directed) g[v].push_back(u); } return g; } template vector>> weighted(int n, int m, bool directed = false, int offset = 1) { vector>> g(n); for (int i = 0; i < m; i++) { int u, v; T w; cin >> u >> v >> w; u -= offset, v -= offset; g[u].push_back({v, w}); if (!directed) g[v].push_back({u, w}); } return g; } } // namespace Graph namespace Tree { vector> unweighted(int n, bool directed = false, int offset = 1) { return Graph::unweighted(n, n - 1, directed, offset); } template vector>> weighted(int n, bool directed = false, int offset = 1) { return Graph::weighted(n, n - 1, directed, offset); } vector> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) { vector> g(n); for (int i = 1; i < n; i++) { int p; cin >> p; p -= offset; if (to_root) g[i].push_back(p); if (to_leaf) g[p].push_back(i); } return g; } } // namespace Tree } // namespace IO #line 10 "library/template/template.hpp" #line 2 "library/template/debug.hpp" #ifdef LOCAL #define debug 1 #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define debug 0 #define show(...) true #endif template void _show(int i, T name) { cerr << '\n'; } template void _show(int i, const T1& a, const T2& b, const T3&... c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } #line 2 "main.cpp" #line 2 "library/math/util.hpp" namespace Math { template T safe_mod(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; a %= b; return a >= 0 ? a : a + b; } template T floor(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a >= 0 ? a / b : (a + 1) / b - 1; } template T ceil(T a, T b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a > 0 ? (a - 1) / b + 1 : a / b; } long long isqrt(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } // return g=gcd(a,b) // a*x+b*y=g // - b!=0 -> 0<=x<|b|/g // - b=0 -> ax=g template T ext_gcd(T a, T b, T& x, T& y) { T a0 = a, b0 = b; bool sgn_a = a < 0, sgn_b = b < 0; if (sgn_a) a = -a; if (sgn_b) b = -b; if (b == 0) { x = sgn_a ? -1 : 1; y = 0; return a; } T x00 = 1, x01 = 0, x10 = 0, x11 = 1; while (b != 0) { T q = a / b, r = a - b * q; x00 -= q * x01; x10 -= q * x11; swap(x00, x01); swap(x10, x11); a = b, b = r; } x = x00, y = x10; if (sgn_a) x = -x; if (sgn_b) y = -y; if (b0 != 0) { a0 /= a, b0 /= a; if (b0 < 0) a0 = -a0, b0 = -b0; T q = x >= 0 ? x / b0 : (x + 1) / b0 - 1; x -= b0 * q; y += a0 * q; } return a; } constexpr long long inv_mod(long long x, long long m) { x %= m; if (x < 0) x += m; long long a = m, b = x; long long y0 = 0, y1 = 1; while (b > 0) { long long q = a / b; swap(a -= q * b, b); swap(y0 -= q * y1, y1); } if (y0 < 0) y0 += m / a; return y0; } long long pow_mod(long long x, long long n, long long m) { x = (x % m + m) % m; long long y = 1; while (n) { if (n & 1) y = y * x % m; x = x * x % m; n >>= 1; } return y; } constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = x % m; if (y >= m) y += m; while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); }; // namespace Math #line 4 "main.cpp" void solve() { ll n, m, k; in(n, m, k); double ans = 0; ll l = Math::ceil(k, m); ans += 1.0 * (m - max(1ll, k - m * (n - 1))) / m * l / n; ans += 1.0 * (n - l) / n; out(ans); // f(n,m,k) // =(m-max(1,k-m*(n-1)))/n/m+(1-1/n)f(n-1,m,k-m) // =(m-max(1,k-m*(n-1)))/n/m+(m-max(1,k-m-m*(n-2)))/n/m+(1-1/n)(1-1/(n-1))f(n-2,m,k-2m) } int main() { int t = 1; in(t); while (t--) solve(); }