Kilk

Find the number of strings that consist of $x$ letters a and $y$ letters b, such that the length of the longest substring of equal letters is as small as possible among all such strings. Display the count modulo $998244353$.

The first line contains a single integer $t$ ($1 \le t \le 10^5$), the number of test cases. Each of the next $t$ lines contains two integers $x$ and $y$ ($1 \le x, y \le 2000$).

For each test case, print the required number.

In the first test case, the strings are abbabb, bababb, babbab, bbaabb, bbabab, and bbabba. Each of these strings has a longest run of equal letters of length 2, and no string with 2 letters a and 4 letters b has a smaller value.