Score : 300 points
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.
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}
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.
3 6 5 1 1 10 1
12 11 0
We will travel from Station 1 as follows:
We will travel from Station 2 as follows:
Note that we should print 0 for Station 3.
4 12 24 6 52 16 4 99 2 2
187 167 101 0
4 12 13 1 44 17 17 66 4096 64
4162 4162 4162 0