#!/usr/bin/env nodejs

const gcd = (a, b) => {
  while (b != 0n) {
    [a, b] = [b, a % b];
  }
  return a;
};
const max = (a, b) => {
  return a < b ? b : a;
};
const euclid_divmod = (a, b) => {
  let [q, r] = [a / b, a % b];
  if (r < 0) {
    if (b > 0) {
      q = q - 1n;
      r = r + b;
    } else {
      q = q + 1n;
      r = r - b;
    }
  }
  return [q, r];
};
const mwf = (n, m, a, b, c, d) => {
  let sum_acc = 0n;
  let max_acc = b * euclid_divmod(d, m)[0];
  let q, y_max;
  while (true) {
    [q, c] = euclid_divmod(c, m);
    a = a + b * q;
    [q, d] = euclid_divmod(d, m);
    sum_acc = sum_acc + b * q;
    max_acc = max(max_acc, sum_acc);
    y_max = (c * (n - 1n) + d) / m;
    if (y_max == 0n) {
      return max(max_acc, sum_acc + a * (n - 1n));
    }
    if (a >= 0n) {
      max_acc = max(max_acc, sum_acc + a * (n - 1n) + b * y_max);
    } else {
      sum_acc = sum_acc + a + b;
    }
    [n, m, a, b, c, d] = [y_max, c, b, a, m, m - d - 1n];
  }
};
const mwf_lr = (l, r, m, a, b, c, d) => {
  let n = r - l;
  let q;
  [q, d] = euclid_divmod(c * l + d, m);
  return a * l + b * q + mwf(n, m, a, b, c, d);
};
const compute_xmin = (d, a, b, k) => {
  let gcd_da = gcd(d, a);
  let [dred, ared] = [d / gcd_da, a / gcd_da];
  let [mred, rred] = euclid_divmod(ared * b, dred);
  let tdelta = b * k;
  if (rred == 0n && dred * k + 1n >= ared) {
    return -1n;
  }
  let [lo, hi] = [0n, ared * b * k + 2n];
  while (lo + 1n < hi) {
    let mid = (lo + hi) / 2n;
    if (mwf(mid, ared, b, -mred, dred, 0n) <= tdelta) {
      lo = mid;
    } else {
      hi = mid;
    }
  }
  return d * lo;
};

let [t, ...inputs] = require("fs")
  .readFileSync("/dev/stdin", "utf8")
  .trim()
  .split(/\s+/);
t = Number(t);
for (let i = 0; i < t; i += 1) {
  let [d, a, b, k] = inputs.slice(i * 4, i * 4 + 4).map((s) => BigInt(s));
  console.log(compute_xmin(d, a, b, k).toString());
}