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.*;
import java.util.*;

public class Main{
	static int mod=998244353;
	static long fastpow(long n,long ti) {
		 if (ti == 0) 
		        return 1l;
		if(ti%2==0) {
			long y=fastpow(n, ti/2);
			long k=y*y;
			k%=mod;
			return k;
		}
		else {
			long y=fastpow(n, ti/2);
			long k=((n*y)%mod)*y;
			k%=mod;
			return k;
		}
	}
	static long modInv(long i) {
		return fastpow(i, mod-2);
	}
	static long gcd(long a, long b) {

		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
	static long[]fac,modInvOfFac;
	static ArrayList<Long>primes;
	static long count(long x) {
		int[]powers=new int[primes.size()];
		int allPrimes=0;
		for(int i=0;i<primes.size();i++) {
			long p=primes.get(i);
			while(x%p==0) {
				powers[i]++;
				allPrimes++;
				x/=p;
			}
		}
		long ways=fac[allPrimes];
		for(int power:powers) {
			ways=(ways*modInvOfFac[power])%mod;
		}
		return ways;
	}
	
	public static void main(String[] args) throws Exception{
		PrintWriter pw=new PrintWriter(System.out);
		MScanner sc = new MScanner(System.in);
		long d=sc.nextLong();
		fac=new long[200];
		
		fac[0]=1;
		for(int i=1;i<200;i++) {
			fac[i]=(fac[i-1]*i)%mod;
		}
		modInvOfFac=new long[200];
		for(int i=0;i<200;i++) {
			modInvOfFac[i]=modInv(fac[i]);
		}
		primes=new ArrayList<>();
		long x=d;
		for(long i=2;i*i<=x;i++) {
			if(x%i==0) {
				primes.add(i);
				while(x%i==0) {
					x/=i;
				}
			}
		}
		if(x>1)primes.add(x);
		
		int q=sc.nextInt();
		while(q-->0) {
			long u=sc.nextLong(),v=sc.nextLong();
			long gcd=gcd(u, v);
			long fromuToGcd=u/gcd;
			long fromGcdTov=v/gcd;
			
			long ans1=count(fromGcdTov),ans2=count(fromuToGcd);
			
			long ans=(ans1*ans2)%mod;
			pw.println(ans);
		}
		
		pw.flush();
	}
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		static void shuffle(int[]in) {
			for(int i=0;i<in.length;i++) {
				int idx=(int)(Math.random()*in.length);
				int tmp=in[i];
				in[i]=in[idx];
				in[idx]=tmp;
			}
		}
		static void shuffle(long[]in) {
			for(int i=0;i<in.length;i++) {
				int idx=(int)(Math.random()*in.length);
				long tmp=in[i];
				in[i]=in[idx];
				in[idx]=tmp;
			}
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void addX(int[]in,int x) {
		for(int i=0;i<in.length;i++)in[i]+=x;
	}
	static void addX(long[]in,int x) {
		for(int i=0;i<in.length;i++)in[i]+=x;
	}
}