If the sum $1 + 2 + 3 + \cdots + K$ is a perfect square $N^2$ and if $N$ is less than $100$, find all possible values for $K$. The original answer is in the form of $k_1, k_2, k_3$. Please give the sum of $k_1, k_2, k_3$.

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