Divisible by this year??? (Part 6: These are what my true love sent to me)

Assume that I continued the song "Twelve Days of Christmas" infinitely. Let $n_1$ and $n_2$ be the smallest and second smallest positive integers such that in the $n_1^{th}$ and $n_2^{th}$ day of Christmas, the total number of gifts (that is when you get the sum of all your gifts from the 1^{st} day up to the $n_1^{th}$ or $n_2^{th}$ day ) in both days is divisible by $2014$ . Find $n_1 + n_2 + (n_1)(n_2)$ .