Erroneous Results with random two state benchmark

I ran this code for a preliminary benchmark, which compares the time taken to generate a certain number of random states using the scale a double random value and using a Bernoulli distribution. The code is below:

int main()
{

  std::random_device s;
  std::mt19937 engine(s());
  std::bernoulli_distribution bernp50(0.5000000000000000);
  std::uniform_real_distribution<double> d;
  
  long int limit = 10000000000; //10^10
  int counter[2] = {0};


  {
      Timer bernstate("Bern Two States");
      for(int i = limit; i>0; i--)
      {
              int tmp = bernp50(engine); 
              //Implicit bool to int conversion
              counter[tmp]++;
      }
  }
  cout << " Bern Two States - 0,1 \n\nCounter:\n" << "0: " << 
  counter[0] <<"\n1: " << counter[1]<<"\n"
  << "Counter additions:  " << counter[0] + counter[1] << "\n\n"
  << "\n0:  " << (double)((double)counter[0]*100/(double)limit) << "%" 
  << "\n1:  " << (double)((double)counter[1]*100/(double)limit) << "%"
  << "\n\n" << endl;
  
  counter[0]=0;
  counter[1]=0;

  {
      Timer double_comp("Two State - Double");
      for(int i = limit; i>0; i--)
      {
              double temp = d(engine)*2;
              if(temp < 1)
              {
                  counter[0]++;
              }
              else
              {
                  counter[1]++;
              }
      }
  }

  cout << " Double Two States - 0,1 \n\nCounter:\n" << "0: " << 
  counter[0] <<"\n1: " << counter[1]<<"\n"
  << "Counter additions:  " << counter[0] + counter[1] << "\n\n"
  << "\n0:  " << (double)((double)counter[0]*100/(double)limit) << "%" 
  << "\n1:  " << (double)((double)counter[1]*100/(double)limit) << "%"
  << "\n\n" << endl;

} //End of Main()

For limit = 10^10 I get the result, where the counter additions is greater than the limit variable. Same for 10^11:

Timer Object: Bern Two States Timer Object Destroyed: Bern Two States Duration Elapsed:  85.9409 s

 Bern Two States - 0,1

Counter: 0: 705044031 1: 705021377 Counter additions:  1410065408


0:  7.05044% 1:  7.05021%


Timer Object: Two State - Double Timer Object Destroyed: Two State - Double Duration Elapsed:  87.6082 s

 Double Two States - 0,1

Counter: 0: 705029886 1: 705035522 Counter additions:  1410065408


0:  7.0503% 1:  7.05036%

However, for limit = 10^9, the results are fine:

Timer Object: Bern Two States
Timer Object Destroyed: Bern Two States
Duration Elapsed:  62.5088 s

 Bern Two States - 0,1

Counter:
0: 500005067
1: 499994933
Counter additions: 1000000000


0:  50.0005%
1:  49.9995%


Timer Object: Two State - Double
Timer Object Destroyed: Two State - Double
Duration Elapsed:  62.6709 s

 Double Two States - 0,1

Counter:
0: 500015398
1: 499984602
Counter additions: 1000000000


0:  50.0015%
1:  49.9985%