Special Trains

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.

Examples

Input

3 6 5 1 1 10 1

Output

12 11 0

Input

4 12 24 6 52 16 4 99 2 2

Output

187 167 101 0

Input

4 12 13 1 44 17 17 66 4096 64

Output

4162 4162 4162 0

inputFormat

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}

outputFormat

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.

Examples

Input

3 6 5 1 1 10 1

Output

12 11 0

Input

4 12 24 6 52 16 4 99 2 2

Output

187 167 101 0

Input

4 12 13 1 44 17 17 66 4096 64

Output

4162 4162 4162 0

样例

3
6 5 1
1 10 1

12
11
0

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