Problem:
Score : 300 points

Problem Statement

A railroad running from west to east in Atcoder Kingdom is now complete.

There are N stations on the railroad, numbered 1 through N from west to east.

Tomorrow, the opening ceremony of the railroad will take place.

On this railroad, for each integer i such that 1≤i≤N-1, there will be trains that run from Station i to Station i+1 in C_i seconds. No other trains will be operated.

The first train from Station i to Station i+1 will depart Station i S_i seconds after the ceremony begins. Thereafter, there will be a train that departs Station i every F_i seconds.

Here, it is guaranteed that F_i divides S_i.

That is, for each Time t satisfying S_i≤t and t％F_i=0, there will be a train that departs Station i t seconds after the ceremony begins and arrives at Station i+1 t+C_i seconds after the ceremony begins, where A％B denotes A modulo B, and there will be no other trains.

For each i, find the earliest possible time we can reach Station N if we are at Station i when the ceremony begins, ignoring the time needed to change trains.

Constraints

1≤N≤500

1≤C_i≤100

1≤S_i≤10^5

1≤F_i≤10

S_i％F_i=0

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
C_1 S_1 F_1
:
C_{N-1} S_{N-1} F_{N-1}

Output

Print N lines. Assuming that we are at Station i (1≤i≤N) when the ceremony begins, if the earliest possible time we can reach Station N is x seconds after the ceremony begins, the i-th line should contain x.

Sample Input 1

3
6 5 1
1 10 1

Sample Output 1

12
11
0

We will travel from Station 1 as follows:

5 seconds after the beginning: take the train to Station 2.

11 seconds: arrive at Station 2.

11 seconds: take the train to Station 3.

12 seconds: arrive at Station 3.

We will travel from Station 2 as follows:

10 seconds: take the train to Station 3.

11 seconds: arrive at Station 3.

Note that we should print 0 for Station 3.

Sample Input 2

4
12 24 6
52 16 4
99 2 2

Sample Output 2

187
167
101
0

Sample Input 3

4
12 13 1
44 17 17
66 4096 64

Sample Output 3

4162
4162
4162
0

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Control.Applicative
import Data.List
import qualified Data.Map as Map
import Data.Array
import qualified Data.ByteString.Char8 as BC
import Data.Maybe
import qualified Data.Set as Set
import qualified Data.Sequence as Sq
import qualified Data.IntMap as IMap
import qualified Data.Vector as V
import Data.Sequence (ViewL(..),ViewR(..),(><),(<|),(|>),Seq)

bsreadInt :: BC.ByteString -> Int
bsreadInt = fst . fromJust . BC.readInt

sqleft :: Seq a -> a
sqleft q = sqleft_(Sq.viewl q)
sqleft_ :: ViewL a -> a
sqleft_ (x :< xs) = x
sqright :: Seq a -> a
sqright q = sqright_(Sq.viewr q)
sqright_ :: ViewR a -> a
sqright_ (xs :> x) = x

-----------------------------------------------------------
stepa :: Int -> Int -> [V.Vector Int] -> Int
stepa t i csfs = head [s + f * j + c | j <- [0..] , s + f * j >= t]
                 where csf = (csfs !! (i-1))
                       c = (V.!) csf 0
                       s = (V.!) csf 1
                       f = (V.!) csf 2

step :: Int -> Int -> Int -> [V.Vector Int] -> Int
step i n t csfs = if (i==n)
                  then t
                  else step (i+1) n (stepa t i csfs) csfs

main = do
    n <- readLn :: IO Int
    csfin <- map ((map bsreadInt . BC.words)) <$> replicateM (n-1) BC.getLine
    let csfs = map (V.fromList) csfin
    mapM_ print $ [step i n 0 csfs | i <- [1..(n-1)]] ++ [0]