Product of phi

Given two positive integers $n$ and $k$, define function $$T(n,k)=\prod _{a_1=1}^k\prod _{a_2=1}^k\cdots \prod _{a_n=1}^k\phi (\prod _{i=1}^n{a}_i)$$ where $\phi (x)$ is Euler's totient function.

For example, $T(2,3)$ = $\phi (1\times 1)$ $\phi (1\times 2)$ $\phi (1\times 3)$ $\phi (2\times 1)$ $\phi (2\times 2)$ $\phi (2\times 3)$ $\phi (3\times 1)$ $\phi (3\times 2)$ $\phi (3\times 3)$ = $192$. And you are given $T(10,10)mod1000000007=7103300$.

Find $T({10}^7,{10}^7)mod1000000007$.

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Thanks to C_K_Yang for the idea.