Divisor Paths

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 \frac x y 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

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

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

Examples

Input

12 3 4 4 12 1 3 4

Output

1 3 1

Input

1 1 1 1

Output

1

Input

288807105787200 4 46 482955026400 12556830686400 897 414 12556830686400 4443186242880 325

Output

547558588 277147129 457421435 702277623

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).

inputFormat

Input

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).

outputFormat

Output

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

Examples

Input

12 3 4 4 12 1 3 4

Output

1 3 1

Input

1 1 1 1

Output

1

Input

288807105787200 4 46 482955026400 12556830686400 897 414 12556830686400 4443186242880 325

Output

547558588 277147129 457421435 702277623

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).

样例

12
3
4 4
12 1
3 4

1
3
1

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