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) {
  }
}