ILL 1986 Problem 40

Find the maximum value that the quantity $2m+7n$ can have such that there exist distinct positive integers $x_i \ (1 \leq i \leq m), y_j \ (1 \leq j \leq n)$ such that the $x_i$ 's are even, the $y_j$ 's are odd, and $\sum_{i=1}^{m} x_i +\sum_{j=1}^{n} y_j=1986.$