A16437. Blueprint for Seating

The first line contains an integer $t$ — the number of test cases you need to solve ( $1 \le t \le 10^5$ ).

For each of the test cases, there is a single line containing $n$ and $k$ — the number of seats, and the number of aisles in a row ( $2 \le n \le 10^9$ ; $1 \le k \le 10^5$ ; $k < n$ ).

The total sum of $k$ in all $t$ given test cases does not exceed $10^6$ .

For each test case print two integers — the minimum inconvenience among all possible layouts, and the number of layouts with the minimum inconvenience modulo $998\,244\,353$ .

In the last test case of 9 2 the possible layouts with the minimum inconvenience of 6 are 3-4-2, 2-4-3, and 2-5-2.

In the last test case of 9 2 the possible layouts with the minimum inconvenience of 6 are 3-4-2, 2-4-3, and 2-5-2.