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 $$$998\,244\,353$$$.

Input format:
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 $$$10^5$$$.
Output format:
For each test case, output $$$k$$$ space-separated integers on a new line: the number of arrays for $$$x=1,2,\ldots,k$$$, modulo $$$998\,244\,353$$$.
Example Input 0:
3
2 2
4 3
10 6969420

Example Output 0:
2 3
3 6 6 10
6969420 124188773 124188773 729965558 124188773 337497990 124188773 50981194 729965558 337497990

Notes:
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 $$$2$$$:

- $$$[2]$$$
- $$$[1,2]$$$
- $$$[2,1]$$$

Example input:
3
2 2
4 3
10 6969420


Example output:
2 3
3 6 6 10
6969420 124188773 124188773 729965558 124188773 337497990 124188773 50981194 729965558 337497990