From Naturals To Naturals!

Number Theory Level 4

The function $f:\mathbb{N}\to\mathbb{N}$ satisfies: $m^2+f(n)\mid mf(m)+n ~~~\forall ~(m,n)\in\mathbb{N}^2.$ Let the sum of all possible values of $f(2014)$ be $N$ . Find the value of $N\bmod{1000}$ .