#include <bits/stdc++.h>
inline long long read() {
  long long x = 0, f = 1;
  char c = getchar();
  for (; c > '9' || c < '0'; c = getchar()) {
    if (c == '-') f = -1;
  }
  for (; c >= '0' && c <= '9'; c = getchar()) {
    x = x * 10 + c - '0';
  }
  return x * f;
}
const int mod = 998244353;
std::vector<long long> divisor;
long long fac[100005] = {1}, inv[100005] = {1};
inline void divide(long long D) {
  for (long long i = 2; i * i <= D; i++) {
    if (D % i == 0) {
      divisor.push_back(i);
      for (; D % i == 0; D /= i)
        ;
    }
  }
  if (D > 1) divisor.push_back(D);
}
inline long long q_pow(long long x, int t) {
  long long s = 1;
  for (; t; t >>= 1) {
    if (t & 1) s = s * x % mod;
    x = x * x % mod;
  }
  return s;
}
inline long long count(long long u, long long v) {
  long long sum = 0, facinv = 1;
  for (auto i : divisor) {
    int cntu = 0, cntv = 0;
    for (; u % i == 0; u /= i) cntu++;
    for (; v % i == 0; v /= i) cntv++;
    if (cntu || cntv) {
      int dif = abs(cntu - cntv);
      facinv = facinv * inv[dif] % mod;
      sum += dif;
    }
  }
  return fac[sum] * facinv % mod;
}
long long gcd(long long a, long long b) { return !b ? a : gcd(b, a % b); }
inline void work() {
  long long D = read();
  divide(D);
  for (int i = 1; i <= 1000; i++) fac[i] = fac[i - 1] * i % mod;
  inv[1000] = q_pow(fac[1000], mod - 2);
  for (int i = 999; i; i--) inv[i] = inv[i + 1] * (i + 1) % mod;
  for (int q = read(); q; q--) {
    long long u = read(), v = read(), g = gcd(u, v);
    printf("%lld\n", count(u, g) * count(v, g) % mod);
  }
}
int main() {
  work();
  return 0;
}
