2a1+3a2+⋯+2003a20023a1+4a2+⋯+2004a20022003a1+2004a2+⋯+4004a2002=34=54⋮=40054
Given that real numbers a1,a2,…,a2002 satisfy the system of equations above, evaluate the following sum:
3a1+5a2+⋯+4005a2002.
If your answer is of the form nm, where m and n are coprime positive integers, submit m+n.