import Control.Applicative
import Control.Monad
import Data.Int
import Data.List (sort)

getInts :: IO [Int64]
getInts = map (fromIntegral . read) . words <$> getLine

factor :: Int64 -> [(Int64, Int64)]
factor x = helper x 2
  where
    helper x y
      | y * y > x = if x /= 1 then [(x, 1)] else []
      | x `mod` y == 0 = let (n, x') = f x y 0
                         in (y, n) : helper x' (y+1)
      | otherwise = helper x (y+1)
    f x y a
      | x `mod` y == 0 = f (x`div`y) y (a+1)
      | otherwise = (a, x)
  
main = do
  q <- readLn
  query <- replicateM q getInts
  let
    m = 100000009
    count n x t
      | n `mod` x == 0 = count (n`div`x) x (t+1)
      | otherwise = t
    f x 0 = [x]
    f x n = x : (f x' (n-1))
      where
        x' = 1+(x*x`mod`m + x*12345`mod`m) `mod` m
    g [seed,n,k,b] = minimum $ map h fs
      where
        xs = f seed n
        fs = factor b
        h (p,q) = (`div`q) . sum . take (fromIntegral k) . sort $ map (\x -> count x p 0) xs
   in mapM (print . g) query