{-# LANGUAGE BangPatterns #-}
{-# OPTIONS_GHC -O2 #-}

module Main where

import Control.Monad (replicateM, replicateM_)
import Data.ByteString.Char8 qualified as BS
import Data.Maybe (fromJust)

tuplify2 (x : y : _) = (x, y)
tuplify2 _ = undefined

-- Input functions with ByteString
readInt = fst . fromJust . BS.readInteger

readIntTuple = tuplify2 . map readInt . BS.words

readIntList = map readInt . BS.words

getInt = readInt <$> BS.getLine

getIntList = readIntList <$> BS.getLine

getIntNList n = map readIntList <$> replicateM (fromIntegral n) BS.getLine

getIntMatrix = map readIntList . BS.lines <$> BS.getContents

getIntTuple = readIntTuple <$> BS.getLine

getIntNTuples n = map readIntTuple <$> replicateM (fromIntegral n) BS.getLine

getIntTuples = map readIntTuple . BS.lines <$> BS.getContents

-- |
-- mwf(n,m,a,b,c,d) = max_{0 <= x < n} a*x + b*floor((c*x + d)/m) について、
-- mwf(n,m,a,b,c,d) <= z かどうかを判定して Bool を返す。
--
-- 前提:
--   - z,n,m,a,b,c,d は整数
--   - n > 0, m > 0
--
-- 計算量/メモリ:
--   - 時間: O(log m)（ユークリッド互除法的再帰による構造縮約）
--   - 追加メモリ: O(1)
mwfLeq :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Bool
mwfLeq z n0 m0 a0 b0 c0 d0 = loop n0 m0 a0 b0 c0 d0 (-z)
  where
    loop :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Bool
    loop !n !m !a !b !c !d !s =
      let (q1, c') = c `divMod` m
          !a1 = a + b * q1
          (q2, d') = d `divMod` m
          !sum_acc = s + b * q2
       in ( sum_acc <= 0
              && ( (a1 <= 0 && b <= 0)
                     || ( let !ymax = (c' * (n - 1) + d') `div` m
                           in if ymax == 0
                                then sum_acc + a1 * (n - 1) <= 0
                                else
                                  if a1 >= 0
                                    then
                                      ((sum_acc + a1 * (n - 1) + b * ymax) <= 0) && ((b >= 0) || loop ymax c' b a1 m (m - d' - 1) sum_acc)
                                    else loop ymax c' b a1 m (m - d' - 1) (sum_acc + a1 + b)
                        )
                 )
          )

-- |
-- max_{l <= x < r} a*x + b*floor((c*x + d)/m) <= z かどうかを返す述語版。
mwfLrLeq ::
  Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Bool
mwfLrLeq z l r m a b c d =
  let !n = r - l
      (q, d') = (c * l + d) `divMod` m
   in mwfLeq (z - a * l - b * q) n m a b c d'

-- |
-- Δ(D,A,B,x) = floor(x/D) - floor( (floor(x/A) * floor(A*B/D)) / B ) において、
-- u_min(D,A,B,K) = min { u >= 0 | Δ(D,A,B,u*D) > K } を半開区間二分探索 [0, A'BK+2) で求め、
-- x_min(D,A,B,K) = min { x >= 0 | Δ(D,A,B,x) > K } = u_min(D,A,B,K)*D を返す（解なしは -1）。
--
-- 前提:
--   * D > 0, A > 0, B > 0, K >= 0（整数）
computeXminLeq :: Integer -> Integer -> Integer -> Integer -> Integer
computeXminLeq d a b k =
  let g = gcd d a
      !d' = d `div` g
      !a' = a `div` g
      (m', r') = (a' * b) `divMod` d'
      !tdelta = b * k
   in -- 解なし判定
      if r' == 0 && d' * k + 1 >= a'
        then (-1)
        else
          let lo0 = if r' == 0 then k + 1 else max ((a' * b * k + r' - (a' - 1) * m') `div` r') (k + 1)
              hi0 = if r' == 0 then a' else ((a' * b * k + r') `div` r') + 1
              -- 二分探索で u_min を求める（F(u) <= T_Δ を満たす最大の u）
              loop lo hi
                | lo + 1 >= hi = d * lo
                | otherwise =
                    let mid = (lo + hi) `div` 2
                        ok = mwfLrLeq tdelta lo mid a' b (-m') d' 0
                     in if ok then loop mid hi else loop lo mid
           in loop lo0 hi0

-- |
-- 検算用 Δ(D,A,B,x)。
deltaVal :: Integer -> Integer -> Integer -> Integer -> Integer
deltaVal d a b x =
  let p = x `div` d
      m = a * b `div` d
      q = x `div` a * m `div` b
   in p - q

-- |
-- 入出力（複数ケース）
solve :: IO ()
solve = do
  t <- getInt
  replicateM_ (fromIntegral t :: Int) $ do
    [d, a, b, k] <- getIntList
    print (computeXminLeq d a b k)

main :: IO ()
main = solve