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.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

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

    static class EDivisorPaths {
        static int mod = 998244353;
        static long[] fac;
        static long[] modInvOfFac;
        static ArrayList<Long> primes;

        public void solve(int testNumber, FastReader s, PrintWriter out) {
            long d = s.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 = s.nextInt();
            while (q-- > 0) {
                long u = s.nextLong(), v = s.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;
                out.println(ans);
            }
        }

        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 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;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}