Can anyone help find optimal solution to find random number but with N that can increase?

The range of N is from 1-1000 And based on the number you guess the program will say higher or lower. But unlike ordinary high-low game, the N can increase by P if you guess a number lower than N, and the N can increase infinitely if you keep on guessing number lower than N. The range of P is from 1-200.

Can anyone suggest an optimal searching method to solve this problem ?