A10724 | Servers

There are $n$ servers in a laboratory, each of them can perform tasks. Each server has a unique id — integer from $1$ to $n$ .

It is known that during the day $q$ tasks will come, the $i$ -th of them is characterized with three integers: $t_{i}$ — the moment in seconds in which the task will come, $k_{i}$ — the number of servers needed to perform it, and $d_{i}$ — the time needed to perform this task in seconds. All $t_{i}$ are distinct.

To perform the $i$ -th task you need $k_{i}$ servers which are unoccupied in the second $t_{i}$ . After the servers begin to perform the task, each of them will be busy over the next $d_{i}$ seconds. Thus, they will be busy in seconds $t_{i},t_{i}+1,...,t_{i}+d_{i}-1$ . For performing the task, $k_{i}$ servers with the smallest ids will be chosen from all the unoccupied servers. If in the second $t_{i}$ there are not enough unoccupied servers, the task is ignored.

Write the program that determines which tasks will be performed and which will be ignored.

The first line contains two positive integers $n$ and $q$ ( $1<=n<=100$ , $1<=q<=10^{5}$ ) — the number of servers and the number of tasks.

Next $q$ lines contains three integers each, the $i$ -th line contains integers $t_{i}$ , $k_{i}$ and $d_{i}$ ( $1<=t_{i}<=10^{6}$ , $1<=k_{i}<=n$ , $1<=d_{i}<=1000$ ) — the moment in seconds in which the $i$ -th task will come, the number of servers needed to perform it, and the time needed to perform this task in seconds. The tasks are given in a chronological order and they will come in distinct seconds.

Print $q$ lines. If the $i$ -th task will be performed by the servers, print in the $i$ -th line the sum of servers' ids on which this task will be performed. Otherwise, print -1.