# Given L, s and d, which are positive real number, what is the probability that there exist integer k and k', such that $kd\in [k'(L+s)-s, k'(L+s)]$

Given $$L$$, $$s$$ and $$d$$, which are positive real numbers, is there always a pair of integers k and k', such that $$kd\in [k'(L+s)-s, k'(L+s)]$$. It is like there is a line which is painted red of length $$L$$ and painted blue of length $$s$$ next and so on. Suppose a man is walking with stepsize $$d$$. Whether the man will walk on the blue line at some time or not? We can suppose the blue line part is a closed set but the red line is an open set.