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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long mod = 998244353;
long long n, m, x, y, a[101], p[101], inv[101], cnt;
long long gcd(long long x, long long y) {
  if (!y)
    return x;
  else
    return gcd(y, x % y);
}
long long qpow(long long x, long long p) {
  long long ans = 1, ret = x;
  for (; p; p /= 2) {
    if (p % 2 == 1) ans = (ans * ret) % mod;
    ret = (ret * ret) % mod;
  }
  return ans;
}
long long get(long long x) {
  long long ans = 1, t = x, sum = 0;
  for (int i = 1; i <= cnt; i++)
    if (t % p[i] == 0) {
      long long num = 0;
      while (t % p[i] == 0) {
        t /= p[i];
        num++;
      }
      ans = (ans * inv[num]) % mod;
      sum += num;
    }
  ans = (ans * a[sum]) % mod;
  return ans;
}
int main() {
  scanf("%lld", &n);
  long long t = n;
  for (int i = 2; i <= (int)sqrt(n); i++)
    if (t % i == 0) {
      p[++cnt] = i;
      while (t % i == 0) t /= i;
    }
  if (t > 1) p[++cnt] = t;
  a[0] = 1;
  for (int i = 1; i <= 100; i++) {
    a[i] = (a[i - 1] * i) % mod;
    inv[i] = qpow(a[i], mod - 2);
  }
  scanf("%lld", &m);
  while (m--) {
    scanf("%lld%lld", &x, &y);
    long long k = gcd(x, y);
    x = x / k;
    y = y / k;
    long long ans = (get(x) * get(y)) % mod;
    printf("%lld\n", ans);
  }
  return 0;
}