Problem: 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: 

<image>

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). 

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;

public class CP {
    static ArrayList<Long> list;
    static long fact[],infact[],M;
    static long gcd(long a,long b){
        if(b==0)
            return a;
        return gcd(b,a%b);
    }
    static long pow(long a,long b){
        if(b==0)
            return 1;
        long ans=pow(a,b/2);
        ans=(ans*ans)%M;
        if(b%2==1)
            ans=(ans*a)%M;
        return ans;

    }
    static long count(long x){
        long ans=1;
        int tot=0;
        for(long z:list){
            if(x%z==0){
                int c=0;
                while(x%z==0){
                    x=x/z;
                    c++;
                }
                tot+=c;
                ans=(ans*infact[c])%M;
            }
        }
        ans=(ans*fact[tot])%M;
        return ans;
    }
    public static void main(String[] args) throws Exception{
        FastReader in=new FastReader(System.in);
        StringBuilder sb=new StringBuilder();
        int i,j;
        M=998244353;
        fact=new long[1000];
        infact=new long[1000];
        fact[0]=infact[0]=1;
        for(i=1;i<1000;i++){
            fact[i]=(fact[i-1]*i)%M;
            infact[i]=pow(fact[i],M-2);
        }
        long d=in.nextLong();
        list=new ArrayList<>();
        long m=2;
        while(m*m<=d){
            if(d%m==0){
                while(d%m==0)
                    d=d/m;
                list.add(m);
            }
            m++;
        }
        if(d!=1)
            list.add(d);
        int q=in.nextInt();
        while(q-->0){
            long x=in.nextLong();
            long y=in.nextLong();
            long gcd=gcd(x,y);
            long ans=(count(x/gcd)*count(y/gcd))%M;
            sb.append(ans).append("\n");
        }
        System.out.print(sb);

    }
}
class FastReader {

    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;

    FastReader(InputStream is) {
        in = is;
    }

    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }

    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }

    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }

    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}