write a go solution for Description:
You are given a positive integer D. Let's build the following graph from it:

- each vertex is a divisor of D (not necessarily prime, 1 and D itself are also included);
- two vertices x and y (x>y) have an undirected edge between them if x is divisible by y and fracxy is a prime;
- the weight of an edge is the number of divisors of x that are not divisors of y.

For example, here is the graph for D=12:

Edge (4,12) has weight 3 because 12 has divisors [1,2,3,4,6,12] and 4 has divisors [1,2,4]. Thus, there are 3 divisors of 12 that are not divisors of 4 — [3,6,12].

There is no edge between 3 and 2 because 3 is not divisible by 2. There is no edge between 12 and 3 because 12/3=4 is not a prime.

Let the length of the path between some vertices v and u in the graph be the total weight of edges on it. For example, path [(1,2),(2,6),(6,12),(12,4),(4,2),(2,6)] has length 1+2+2+3+1+2=11. The empty path has length 0.

So the shortest path between two vertices v and u is the path that has the minimal possible length.

Two paths a and b are different if there is either a different number of edges in them or there is a position i such that a_i and b_i are different edges.

You are given q queries of the following form:

- v u — calculate the number of the shortest paths between vertices v and u.

The answer for each query might be large so print it modulo 998244353.

Input Format:
The first line contains a single integer D (1<=D<=10^15) — the number the graph is built from.

The second line contains a single integer q (1<=q<=3*10^5) — the number of queries.

Each of the next q lines contains two integers v and u (1<=v,u<=D). It is guaranteed that D is divisible by both v and u (both v and u are divisors of D).

Output Format:
Print q integers — for each query output the number of the shortest paths between the two given vertices modulo 998244353.

Note:
In the first example:

- The first query is only the empty path — length 0;
- The second query are paths [(12,4),(4,2),(2,1)] (length 3+1+1=5), [(12,6),(6,2),(2,1)] (length 2+2+1=5) and [(12,6),(6,3),(3,1)] (length 2+2+1=5).
- The third query is only the path [(3,1),(1,2),(2,4)] (length 1+1+1=3).. Output only the code with no comments, explanation, or additional text.