You're given integers (k) and (n). For each integer (x) from (1) to (k), count the number of integer arrays (a) such that all of the following are satisfied: (1 \leq |a| \leq n) where (|a|) represents the length of (a). (1 \leq a_i \leq k) for all (1 \leq i \leq |a|). (a_1 \times a_2 \times \dots \times a_{|a|}=x) (i.e., the product of all elements is (x)). Note that two arrays (b) and (c) are different if either their lengths are different, or if there exists an index (1 \leq i \leq |b|) such that (b_i\neq c_i). Output the answer modulo (998\,244\,353). The first line contains an integer (t) ((1 \leq t\leq 10^3)) — the number of independent test cases. The only line of each test case contains two integers (k) and (n) ((1 \leq k \leq 10^5, 1\leq n \leq 9\cdot 10^8)). It is guaranteed that the sum of (k) over all test cases does not exceed (10^5). For each test case, output (k) space-separated integers on a new line: the number of arrays for (x=1,2,\ldots,k), modulo (998\,244\,353). In the first test case, there are (2) arrays (a) with (|a|\leq 2) and the product of elements equal to (1): (1) (1,1) There are (3) arrays (a) with (|a|\leq 2) and the product of elements equal to (2): (2) (1,2) (2,1)