Given that T at 1 and move by 1 step, H at 2 and move by 2 steps at a time

After 49 steps, T at 50, H at 100

After 25 steps, T at 75, H at 50

After 13 steps, T at 88, H at 76

After 7 steps, T at 95, H at 90

After 4 steps, T at 99, H at 98

After 1 steps, T at 100, H at 100

Total steps : 49+25+13+7+4+1 = 99