Let n be a positive integer and let En be the set of n-tuples of strictly positive integers.
For u=(u1,⋯,un) and v=(v1,⋯,vn) two elements of En, we define:
Let Rn(M) be the sum of u⋆v over all ordered pairs (u,v) in En such that ⟨u,v⟩=M. For example: R1(10)=36, R2(100)=1873044, R2(100!)≡446575636mod109+7.
Find R6(10000!). Give your answer modulo 109+7.