I tried(trying...) to solve the SPOJ prime number problem [PRIME1][1] so i learned and implemented Segmented Sieve correctly but this program works in time for 10^8 but getting Time limit exceeded (TLE) for 10^9 input integer. can someone help me reduce complexity within my code please.

/*
 followed this tutorial
 https://medium.com/@agilanbtdw/prime-number-generation-in-java-using-segmented-sieve-of-eratosthenes-187af1dcd051
*/
#include <iostream>
#include <math.h>
#include <vector>
#include <fstream>
using std::cin;
using std::ifstream;
using std::vector;
using std::cout;
using std::ios_base;
int main() {
ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL); 
    //ifstream in("inp.txt");
  short int t;
  unsigned long int n ,q;
  cin >> t; 
  while(t--){
  cin >>q >> n;
  vector<bool> a(n,true);
  unsigned long int m = sqrt(n); 
  a[0] = false;
  a[1] = false;
  // find primes till sqrt
  for(unsigned long int i = 2 ; i <= m ; i++ ){
    if(a[i]){
      for(unsigned long int j = i*i ; j <= m ; j+=i ){
        a[j] = false;
      }
    }
  }
//  store the primes upto m
  vector<unsigned long int> primes;
  for(unsigned long int i = 2 ; i <= m ; i++ ){
      if(a[i]){ primes.push_back(i);}
  }

  unsigned long int temp;
  for (unsigned long int x : primes) {
        temp = q/x;
        temp*=x;
                // from primes arrays increment each prime with that num , set the index as false
        for(unsigned long int y = temp ; y <=n ; y+=x){
        a[y] = false;
        }
  }
// set the falsed indexes in previous primes arrays to true
  for(unsigned long int i = 0 ; i < primes.size() ;++i){
    a[primes[i]] = true;
  }
  for(unsigned long int i =q ; i <= n ; i++ ){
    if(a[i]) {cout << i << " ";}
  }
  cout << "\n";
  }
  return 0;
}

my repl link - https://repl.it/repls/UnrulyMotherlyTransformation [1]: https://www.spoj.com/problems/PRIME1/