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Can someone explain me the task? What do p and q mean? And why does the answer exist(what if on every step they both roll neither 1 nor m?)
From where the 675 and 44 are came from?
Imagine a circle and person1 and person2 who have the dice and are sitting exactly opposite to each other on the left and write side of the circle. The probability of person1 rolling 1 and person2 rolling m, is equal to the probability of person1 rolling m and person2 rolling 1. That means the probability of each moving one step in the upper half of the circle (and therefore reducing the distance by two units) is equal to the probability of them doing the same thing in the lower half. And the same is true for other types of move (no passing and one to the right or left). Imho, the average is infinite.
The only problem is that I don't know how the hell is 675/44 = 113636380 (mod 10^9 + 9).
Could anyone give me an example about how to magically turn 675 and 44 into 113636380?