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 \(n_1 + n_2 + (n_1)(n_2)\).

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