#include <bits/stdc++.h>
using namespace std;
const long long INF(0x3f3f3f3f3f3f3f3fll);
const long long inf(0x3f3f3f3f);
template <typename T>
void read(T &res) {
  bool flag = false;
  char ch;
  while (!isdigit(ch = getchar())) (ch == '-') && (flag = true);
  for (res = ch - 48; isdigit(ch = getchar());
       res = (res << 1) + (res << 3) + ch - 48)
    ;
  flag && (res = -res);
}
template <typename T>
void Out(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) Out(x / 10);
  putchar(x % 10 + '0');
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
long long pow_mod(long long x, long long n, long long mod) {
  long long res = 1;
  while (n) {
    if (n & 1) res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}
long long fact_pow(long long n, long long p) {
  long long res = 0;
  while (n) {
    n /= p;
    res += n;
  }
  return res;
}
long long mult(long long a, long long b, long long p) {
  a %= p;
  b %= p;
  long long r = 0, v = a;
  while (b) {
    if (b & 1) {
      r += v;
      if (r > p) r -= p;
    }
    v <<= 1;
    if (v > p) v -= p;
    b >>= 1;
  }
  return r;
}
long long quick_pow(long long a, long long b, long long p) {
  long long r = 1, v = a % p;
  while (b) {
    if (b & 1) r = mult(r, v, p);
    v = mult(v, v, p);
    b >>= 1;
  }
  return r;
}
bool CH(long long a, long long n, long long x, long long t) {
  long long r = quick_pow(a, x, n);
  long long z = r;
  for (long long i = 1; i <= t; i++) {
    r = mult(r, r, n);
    if (r == 1 && z != 1 && z != n - 1) return true;
    z = r;
  }
  return r != 1;
}
bool Miller_Rabin(long long n) {
  if (n < 2) return false;
  if (n == 2) return true;
  if (!(n & 1)) return false;
  long long x = n - 1, t = 0;
  while (!(x & 1)) {
    x >>= 1;
    t++;
  }
  srand(time(NULL));
  long long o = 8;
  for (long long i = 0; i < o; i++) {
    long long a = rand() % (n - 1) + 1;
    if (CH(a, n, x, t)) return false;
  }
  return true;
}
void exgcd(long long a, long long b, long long &x, long long &y) {
  if (!b) {
    x = 1, y = 0;
    return;
  }
  exgcd(b, a % b, x, y);
  long long t = x;
  x = y, y = t - (a / b) * y;
}
long long inv(long long a, long long b) {
  long long x, y;
  return exgcd(a, b, x, y), (x % b + b) % b;
}
long long crt(long long x, long long p, long long mod) {
  return inv(p / mod, mod) * (p / mod) * x;
}
long long fac(long long x, long long a, long long b) {
  if (!x) return 1;
  long long ans = 1;
  for (long long i = 1; i <= b; i++)
    if (i % a) ans *= i, ans %= b;
  ans = pow_mod(ans, x / b, b);
  for (long long i = 1; i <= x % b; i++)
    if (i % a) ans *= i, ans %= b;
  return ans * fac(x / a, a, b) % b;
}
long long C(long long n, long long m, long long a, long long b) {
  long long N = fac(n, a, b), M = fac(m, a, b), Z = fac(n - m, a, b), sum = 0,
            i;
  for (i = n; i; i = i / a) sum += i / a;
  for (i = m; i; i = i / a) sum -= i / a;
  for (i = n - m; i; i = i / a) sum -= i / a;
  return N * pow_mod(a, sum, b) % b * inv(M, b) % b * inv(Z, b) % b;
}
long long exlucas(long long n, long long m, long long p) {
  long long t = p, ans = 0, i;
  for (i = 2; i * i <= p; i++) {
    long long k = 1;
    while (t % i == 0) {
      k *= i, t /= i;
    }
    ans += crt(C(n, m, i, k), p, k), ans %= p;
  }
  if (t > 1) ans += crt(C(n, m, t, t), p, t), ans %= p;
  return ans % p;
}
const long long N = 3e5 + 10;
const long long mod = 998244353;
map<long long, long long> cnt;
long long solve(long long now) {
  if (cnt.count(now)) return cnt[now] % mod;
  long long n = now, res = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res += solve(now / i) % mod;
      while (n % i == 0) n /= i;
    }
  }
  if (n > 1) res += solve(now / n) % mod;
  return cnt[now] = res % mod;
}
signed main() {
  long long d, q;
  read(d), read(q);
  cnt[1] = 1;
  while (q--) {
    long long u, v;
    read(u), read(v);
    long long gcdd = gcd(u, v);
    Out(solve(u / gcdd) * solve(v / gcdd) % mod);
    puts("");
  }
  return 0;
}

### Prompt

Create a solution in Cpp for the following 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). 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long INF(0x3f3f3f3f3f3f3f3fll);
const long long inf(0x3f3f3f3f);
template <typename T>
void read(T &res) {
  bool flag = false;
  char ch;
  while (!isdigit(ch = getchar())) (ch == '-') && (flag = true);
  for (res = ch - 48; isdigit(ch = getchar());
       res = (res << 1) + (res << 3) + ch - 48)
    ;
  flag && (res = -res);
}
template <typename T>
void Out(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) Out(x / 10);
  putchar(x % 10 + '0');
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
long long pow_mod(long long x, long long n, long long mod) {
  long long res = 1;
  while (n) {
    if (n & 1) res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}
long long fact_pow(long long n, long long p) {
  long long res = 0;
  while (n) {
    n /= p;
    res += n;
  }
  return res;
}
long long mult(long long a, long long b, long long p) {
  a %= p;
  b %= p;
  long long r = 0, v = a;
  while (b) {
    if (b & 1) {
      r += v;
      if (r > p) r -= p;
    }
    v <<= 1;
    if (v > p) v -= p;
    b >>= 1;
  }
  return r;
}
long long quick_pow(long long a, long long b, long long p) {
  long long r = 1, v = a % p;
  while (b) {
    if (b & 1) r = mult(r, v, p);
    v = mult(v, v, p);
    b >>= 1;
  }
  return r;
}
bool CH(long long a, long long n, long long x, long long t) {
  long long r = quick_pow(a, x, n);
  long long z = r;
  for (long long i = 1; i <= t; i++) {
    r = mult(r, r, n);
    if (r == 1 && z != 1 && z != n - 1) return true;
    z = r;
  }
  return r != 1;
}
bool Miller_Rabin(long long n) {
  if (n < 2) return false;
  if (n == 2) return true;
  if (!(n & 1)) return false;
  long long x = n - 1, t = 0;
  while (!(x & 1)) {
    x >>= 1;
    t++;
  }
  srand(time(NULL));
  long long o = 8;
  for (long long i = 0; i < o; i++) {
    long long a = rand() % (n - 1) + 1;
    if (CH(a, n, x, t)) return false;
  }
  return true;
}
void exgcd(long long a, long long b, long long &x, long long &y) {
  if (!b) {
    x = 1, y = 0;
    return;
  }
  exgcd(b, a % b, x, y);
  long long t = x;
  x = y, y = t - (a / b) * y;
}
long long inv(long long a, long long b) {
  long long x, y;
  return exgcd(a, b, x, y), (x % b + b) % b;
}
long long crt(long long x, long long p, long long mod) {
  return inv(p / mod, mod) * (p / mod) * x;
}
long long fac(long long x, long long a, long long b) {
  if (!x) return 1;
  long long ans = 1;
  for (long long i = 1; i <= b; i++)
    if (i % a) ans *= i, ans %= b;
  ans = pow_mod(ans, x / b, b);
  for (long long i = 1; i <= x % b; i++)
    if (i % a) ans *= i, ans %= b;
  return ans * fac(x / a, a, b) % b;
}
long long C(long long n, long long m, long long a, long long b) {
  long long N = fac(n, a, b), M = fac(m, a, b), Z = fac(n - m, a, b), sum = 0,
            i;
  for (i = n; i; i = i / a) sum += i / a;
  for (i = m; i; i = i / a) sum -= i / a;
  for (i = n - m; i; i = i / a) sum -= i / a;
  return N * pow_mod(a, sum, b) % b * inv(M, b) % b * inv(Z, b) % b;
}
long long exlucas(long long n, long long m, long long p) {
  long long t = p, ans = 0, i;
  for (i = 2; i * i <= p; i++) {
    long long k = 1;
    while (t % i == 0) {
      k *= i, t /= i;
    }
    ans += crt(C(n, m, i, k), p, k), ans %= p;
  }
  if (t > 1) ans += crt(C(n, m, t, t), p, t), ans %= p;
  return ans % p;
}
const long long N = 3e5 + 10;
const long long mod = 998244353;
map<long long, long long> cnt;
long long solve(long long now) {
  if (cnt.count(now)) return cnt[now] % mod;
  long long n = now, res = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res += solve(now / i) % mod;
      while (n % i == 0) n /= i;
    }
  }
  if (n > 1) res += solve(now / n) % mod;
  return cnt[now] = res % mod;
}
signed main() {
  long long d, q;
  read(d), read(q);
  cnt[1] = 1;
  while (q--) {
    long long u, v;
    read(u), read(v);
    long long gcdd = gcd(u, v);
    Out(solve(u / gcdd) * solve(v / gcdd) % mod);
    puts("");
  }
  return 0;
}

```