Speed Reading

All $K$ ($1 \le K \le 1{,}000$) cows are taking part in Farmer John's annual reading contest. The contest is to read a single book of $N$ ($1 \le N \le 100{,}000$) pages as fast as possible while understanding it.

Cow $i$ has a reading speed of $S_i$ ($1 \le S_i \le 100$) pages per minute, a maximum continuous reading time of $T_i$ ($1 \le T_i \le 100$) minutes, and a minimum rest time of $R_i$ ($1 \le R_i \le 100$) minutes. The cow reads $S_i$ pages per minute, but she can read for at most $T_i$ minutes at a stretch. Once she stops to rest, she must rest for $R_i$ minutes before she can start reading again.

For each cow, determine the number of minutes (rounded up to the next whole minute) needed to read the entire book.

• Line 1: two space-separated integers $N$ and $K$.
• Lines 2 to $K+1$: line $i+1$ contains three space-separated integers $S_i$, $T_i$, and $R_i$.

• Lines 1 to $K$: line $i$ is the number of minutes (rounded up to the next whole minute) that cow $i$ needs to read the whole book.

Reading always happens in whole-minute units. A cow reads in bursts of at most $T_i$ minutes (covering at most $S_i \cdot T_i$ pages); if pages still remain afterward she rests $R_i$ minutes and reads again. No rest is needed after the final burst that finishes the book, and a partial last minute still counts as a full minute.

For example, for a 10-page book, a cow that reads 2 pages/min for up to 4 minutes and rests 1 minute reads 8 pages in 4 minutes, rests 1 minute, then reads the last 2 pages in 1 minute, for 6 minutes total.