import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } // floor(a / b) Int divFloor(Int)(Int a, Int b) { return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0); } // sum_{x=l}^r floor((a x + b) / m) // m > 0 long sumFloors(long m, long a, long b, long l, long r) in { assert(m > 0, "sumFloors: m > 0 must hold"); } do { long sum; for (; l <= r; ) { const q = divFloor(a, m); const aa = a - q * m; const ll = divFloor(aa * l + b, m) + 1; const rr = divFloor(aa * r + b, m); sum += q * ((r + 1) * r / 2 - l * (l - 1) / 2) + r * rr - (l - 1) * (ll - 1) + (rr - ll + 1); a = m; m = aa; l = -rr; r = -ll; } return sum; } void main() { try { for (; ; ) { const numCases = readInt; foreach (caseId; 0 .. numCases) { long P = readLong; long Q = readLong; const K = readLong; const G = gcd(P, Q); P /= G; Q /= G; long lo = -1, hi = min(P, Q) * K + 1; for (; lo + 1 < hi; ) { const mid = (lo + hi) / 2; // <= mid const num = sumFloors(Q, -P, mid + Q, 0, min(mid / P, Q - 1)); debug { writeln(" ", mid, ": ", num); } if(num>=2*10L^^18)assert(false); ((num >= K + 1) ? hi : lo) = mid; } long ans = hi; ans *= G; writeln(ans); debug { long[] ns; foreach (x; 0 .. K + 1) foreach (y; 0 .. K + 1) { ns ~= (P * x + Q * y); } ns = ns.sort.uniq.array; long brt = ns[cast(int)(K)]; brt *= G; writeln("brt = ", brt); assert(brt == ans); } } } } catch (EOFException e) { } }