Let $T(n,m)$ be the number of $m$-tuples of positive integers such that the sum of any two neighbouring elements of the tuple is $\le n$.

For example, $T(3,4)=8$, via the following eight $4$-tuples:
$(1,1,1,1)$
$(1,1,1,2)$
$(1,1,2,1)$
$(1,2,1,1)$
$(1,2,1,2)$
$(2,1,1,1)$
$(2,1,1,2)$
$(2,1,2,1)$

You are also given that $T(5,5)=246$, $T(10,{10}^2)\equiv 862820094(\mathrm{mod}1000000007)$ and $T({10}^2,10)\equiv 782136797(\mathrm{mod}1000000007)$.

Find $T(5000,{10}^{12})mod1000000007$.