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

module Main where

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

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

{-|
Max Weighted Floor (mwf)
  mwf(n,m,a,b,c,d) = max_{0 <= x < n} a*x + b*floor((c*x + d)/m)
を返す非再帰（反復）実装。

前提:
  - 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)
-}
mwf :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer
mwf n0 m0 a0 b0 c0 d0 =
  let !sum0 = 0
      !max0 = b0 * (d0 `div` m0)     -- x = 0 のとき
  in go n0 m0 a0 b0 c0 d0 sum0 max0
  where
    go :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer
       -> Integer -> Integer -> Integer
    go !n !m !a !b !c !d !sumAcc !maxAcc =
      let (q1, c') = c `divMod` m
          !a'      = a + b * q1
          (q2, d') = d `divMod` m
          !sum'    = sumAcc + b * q2
          !max'    = max maxAcc sum'
          !ymax    = (c' * (n - 1) + d') `div` m
      in if ymax == 0
           then max max' (sum' + a' * (n - 1))
           else
             if a' >= 0
               then
                 let !max'' = max max' (sum' + a' * (n - 1) + b * ymax)
                 in  go ymax c' b a' m (m - d' - 1) sum' max''
               else
                 let !sum'' = sum' + a' + b
                 in  go ymax c' b a' m (m - d' - 1) sum'' max'

{-|
mwf(n,m,a,b,c,d) <= z かどうかを判定して Bool を返す。
（上の mwf と同じ前提・計算量）
-}
mwfLeq :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Bool
mwfLeq z n0 m0 a0 b0 c0 d0 =
  go n0 m0 a0 b0 c0 d0 (-z)
  where
    go :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Bool
    go !n !m !a !b !c !d !sumAcc =
      let (q1, c') = c `divMod` m
          !a'      = a + b * q1
          (q2, d') = d `divMod` m
          !sum'    = sumAcc + b * q2
      in ((sum' <= 0) && (let !ymax = (c' * (n - 1) + d') `div` m
                          in if ymax == 0
                               then (sum' + a' * (n - 1)) <= 0
                               else (sum' + max 0 (a' * (n - 1)) + max 0 (b * ymax) <= 0) || (if a' >= 0
                                             then
                                               ((sum' + a' * (n - 1) + b * ymax) <= 0) && go ymax c' b a' m (m - d' - 1) sum'
                                             else
                                               let !sum'' = sum' + a' + b
                                               in  go ymax c' b a' m (m - d' - 1) sum'')))

{-|
max_{l <= x < r} a*x + b*floor((c*x + d)/m) を返す。

既存の mwf(n,m,...)（0 <= x < n）を用いる。
前提: l < r, m > 0
-}
mwfLr :: Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer -> Integer
mwfLr l r m a b c d =
  let !n        = r - l
      (q, d')   = (c * l + d) `divMod` m
  in  a * l + b * q + mwf n m a b c d'

{-|
max_{L <= x < R} (...) <= 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
      -- 解なし判定
  in if r' == 0 && d' * k + 1 >= a'
       then (-1)
       else
         let hi0 = a' * b * k + 2  -- [0, hi) の上限
             -- 二分探索で u_min を求める（F(u) <= T_Δ を満たす最大の u）
             go 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 go mid hi else go lo mid
         in go 0 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