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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EDivisorPaths solver = new EDivisorPaths();
        solver.solve(1, in, out);
        out.close();
    }

    static class EDivisorPaths {
        long[] fac;
        long[] invfac;
        ArrayList<Long> primes;
        final static long mod = 998244353l;

        long nCr(long n, long r) {
            long up = fac[(int) n];
            long down = (invfac[(int) (n - r)] * invfac[(int) r]) % mod;
            return (up * down) % mod;
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            fac = new long[1000005];
            invfac = new long[1000005];
            fac[0] = fac[1] = 1;
            for (int i = 2; i < fac.length; i++) fac[i] = (fac[i - 1] * i) % mod;
            for (int i = 0; i < invfac.length; i++) invfac[i] = CodeX.modinv(fac[i], mod);


            long d = in.scanLong();
            primes = new ArrayList<>();

            for (long i = 2; i * i <= d; i++) {
                if (d % i == 0) primes.add(i);
                while (d % i == 0) d /= i;
            }
            if (d != 1) primes.add(d);

            int q = in.scanInt();
            while (q-- > 0) {
                long X = in.scanLong();
                long Y = in.scanLong();
                long gcd = CodeX.GCD(X, Y);
                long ans = (findIT(X, gcd) * findIT(Y, gcd)) % mod;
                out.println(ans);
            }


        }

        long findIT(long a, long b) {
            long pos = 0;
            long ans = 1;
            for (long p : primes) {
                int countA = 0;
                int countB = 0;
                while (a % p == 0) {
                    countA++;
                    a /= p;
                }
                while (b % p == 0) {
                    countB++;
                    b /= p;
                }
                long dif = Math.abs(countA - countB);
                ans = (ans * nCr(dif + pos, pos)) % mod;
                pos += dif;

            }
            return ans;
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

        public long scanLong() {
            long I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

    }

    static class CodeX {
        public static long GCD(long A, long B) {
            if (B == 0)
                return A;
            else
                return GCD(B, A % B);
        }

        public static long power(long x, long y, long p) {
            long res = 1;
            x = x % p;
            while (y > 0) {

                if ((y & 1) != 0)
                    res = (res * x) % p;
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

        public static long modinv(long k, long mod) {
            return power(k, mod - 2, mod);
        }

    }
}