#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  bool f = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  x = f ? -x : x;
}
const long long N = 3e5;
const long long mod = 998244353;
long long n;
long long d, q;
long long p[20];
long long fac[60];
long long inv[60];
inline long long qw(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = (ans * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return ans;
}
long long now[20];
long long nn = 1;
inline void pre() {
  inv[0] = inv[1] = fac[0] = fac[1] = 1;
  for (long long i = (2); i <= (52); ++i) fac[i] = (i * fac[i - 1]) % mod;
  inv[52] = qw(fac[52], mod - 2);
  for (long long i = 51; i >= 2; --i) inv[i] = inv[i + 1] * (i + 1) % mod;
  long long h = d;
  long long hhh = sqrt(d);
  for (long long i = (2); i <= (hhh); ++i) {
    if (!(h % i)) {
      p[++n] = i;
      while (!(h % i)) h /= i;
    }
  }
  if (h > 1) p[++n] = h;
}
inline long long query(long long x) {
  long long sum = 0;
  long long ans = 1;
  for (long long i = 1; i <= n; ++i) {
    long long siz = 0;
    while (!(x % p[i])) ++siz, x /= p[i];
    ans = (ans * inv[siz]) % mod;
    sum += siz;
  }
  ans = (ans * fac[sum]) % mod;
  return ans;
}
long long gcd(long long u, long long v) { return v ? gcd(v, u % v) : u; }
int main() {
  read(d);
  read(q);
  pre();
  while (q--) {
    long long u, v;
    read(u);
    read(v);
    if (u < v) swap(u, v);
    long long w = gcd(u, v);
    long long ans = query(u / w) * query(v / w) % mod;
    cout << ans << endl;
  }
  return 0;
}
