P5171 Earthquake

Given $a,\,b,\,c$, find the number of non-negative integer solutions that satisfy the inequality $ax+by \leqslant c$.

Input three integers $a,\,b,\,c$.

Output one integer representing the answer.

**Sample Explanation:** Let $(x,\,y)$ represent a valid solution. The sample has the following $12$ valid solutions: $(0,\,0)$, $(0,\,1)$, $(0,\,2)$, $(0,\,3)$, $(1,\,0)$, $(1,\,1)$, $(1,\,2)$, $(2,\,0)$, $(2,\,1)$, $(3,\,0)$, $(3,\,1)$, $(4,\,0)$. **Constraints:** |||| |:-:|:-:|:-:| |Test point ID|$a,\,b$|$c$| |$1 \sim 5$|$\leqslant 10$|$\leqslant 10$| |$6 \sim 10$|$\leqslant 10^5$|$\leqslant 10^9$| |$11 \sim 25$|$\leqslant 10^9$|$\leqslant 10^{18}$| For all testdata, $1 \leqslant a,\,b \leqslant 10^9,\ 0 \leqslant c \leqslant \min(a,\,b) \times 10^9$. Translated by ChatGPT 5