Patrick calls a substring$$$^\dagger$$$ of a binary string$$$^\ddagger$$$ good if this substring contains exactly one 1.

Help Patrick count the number of binary strings $$$s$$$ such that $$$s$$$ contains exactly $$$n$$$ good substrings and has no good substring of length strictly greater than $$$k$$$. Note that substrings are differentiated by their location in the string, so if $$$s =$$$ 1010 you should count both occurrences of 10.

$$$^\dagger$$$ A string $$$a$$$ is a substring of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

$$$^\ddagger$$$ A binary string is a string that only contains the characters 0 and 1.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 2500$$$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 2500$$$, $$$1 \leq k \leq n$$$) — the number of required good substrings and the maximum allowed length of a good substring.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2500$$$.

Output

For each test case, output a single integer — the number of binary strings $$$s$$$ such that $$$s$$$ contains exactly $$$n$$$ good substrings and has no good substring of length strictly greater than $$$k$$$. Since this integer can be too large, output it modulo $$$998\,244\,353$$$.

Note

In the first test case, the only suitable binary string is 1. String 01 is not suitable because it contains a substring 01 with length $$$2 \gt 1$$$.

In the second test case, suitable binary strings are 011, 110 and 111.

In the third test case, suitable binary strings are 101, 0110, 0111, 1110, and 1111.

Counting Binary Strings

Examples