CF1912B.Blueprint for Seating

普及/提高-

通过率：0%

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题目描述

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 $10^6$ .

输入格式

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

输出格式

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.

输入输出样例

输入#1

8
4 1
3 2
4 2
5 2
6 1
6 2
1000000000 1
9 2

输出#1

2 1
0 1
0 1
1 3
6 1
2 4
249999999500000000 1
6 3

说明/提示

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.

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