B'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. Each test consists of multiple test cases. The first line contains a single integer t ( 1 <= q t <= q 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 <= q n <= q 2500 , 1 <= q k <= q 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 . 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 . 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 > 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. '...