Given a collection of stones. The mass of each stone is $≤ 2 kg$ and their total mass is equal to $100 kg$. We selected a set of stones whose total mass differs from $10 kg$ by the least possible for this set number d. What is the greatest value of d for every admissible collection of stones? The original answer is in $\frac{m}{n}$ format, please give the value of $m + n$.

Let's think step by step and output the final answer within \boxed{}.
user