#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
const int inf = 0x3f3f3f3f;
const int mod = 998244353;
long long ans[maxn], fac[maxn], a[maxn];
long long pow_(long long a, long long b) {
  a %= mod;
  long long ans = 1;
  while (b) {
    if (b & 1) ans = (ans * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return ans;
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long C(long long n, long long m) {
  return (fac[n] * pow_(fac[n - m] * fac[m], mod - 2)) % mod;
}
long long cal(long long x) {
  long long ans = 1;
  int cnt = 0, all = 0;
  for (long long i = 2; i * i <= x; ++i) {
    int num = 0;
    while (x % i == 0) {
      ++num;
      x /= i;
    }
    all += num;
    if (num) a[++cnt] = num;
  }
  if (x > 1 || cnt == 0) a[++cnt] = 1, ++all;
  for (int i = 1; i <= cnt; ++i) {
    ans = (ans * C(all, a[i])) % mod;
    all -= a[i];
  }
  return ans;
}
int main() {
  long long d, u, v, q;
  map<long long, long long> mp;
  scanf("%lld %lld", &d, &q);
  fac[0] = fac[1] = 1;
  for (int i = 2; i < maxn; ++i) fac[i] = (fac[i - 1] * i) % mod;
  while (q--) {
    scanf("%lld %lld", &u, &v);
    long long g = gcd(u, v);
    if (mp[u / g] == 0) mp[u / g] = cal(u / g);
    if (mp[v / g] == 0) mp[v / g] = cal(v / g);
    printf("%lld\n", (mp[u / g] * mp[v / g] + mod) % mod);
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 int maxn = 1e5 + 5;
const int inf = 0x3f3f3f3f;
const int mod = 998244353;
long long ans[maxn], fac[maxn], a[maxn];
long long pow_(long long a, long long b) {
  a %= mod;
  long long ans = 1;
  while (b) {
    if (b & 1) ans = (ans * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return ans;
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long C(long long n, long long m) {
  return (fac[n] * pow_(fac[n - m] * fac[m], mod - 2)) % mod;
}
long long cal(long long x) {
  long long ans = 1;
  int cnt = 0, all = 0;
  for (long long i = 2; i * i <= x; ++i) {
    int num = 0;
    while (x % i == 0) {
      ++num;
      x /= i;
    }
    all += num;
    if (num) a[++cnt] = num;
  }
  if (x > 1 || cnt == 0) a[++cnt] = 1, ++all;
  for (int i = 1; i <= cnt; ++i) {
    ans = (ans * C(all, a[i])) % mod;
    all -= a[i];
  }
  return ans;
}
int main() {
  long long d, u, v, q;
  map<long long, long long> mp;
  scanf("%lld %lld", &d, &q);
  fac[0] = fac[1] = 1;
  for (int i = 2; i < maxn; ++i) fac[i] = (fac[i - 1] * i) % mod;
  while (q--) {
    scanf("%lld %lld", &u, &v);
    long long g = gcd(u, v);
    if (mp[u / g] == 0) mp[u / g] = cal(u / g);
    if (mp[v / g] == 0) mp[v / g] = cal(v / g);
    printf("%lld\n", (mp[u / g] * mp[v / g] + mod) % mod);
  }
  return 0;
}

```