The logical-OR of two bits is $0$ if both bits are $0$, otherwise it is $1$.
The bitwise-OR of two positive integers performs a logical-OR operation on each pair of corresponding bits in the binary expansion of its inputs.

For example, the bitwise-OR of $10$ and $6$ is $14$ because $10={1010}_2$, $6={0110}_2$ and $14={1110}_2$.

Let $T(n,k)$ be the number of $k$-tuples $(x_1,x_2,\cdots ,x_k)$ such that

• every $x_i$ is a prime $\le n$
• the bitwise-OR of the tuple is a prime $\le n$

For example, $T(5,2)=5$. The five $2$-tuples are $(2,2)$, $(2,3)$, $(3,2)$, $(3,3)$ and $(5,5)$.

You are given $T(100,3)=3355$ and $T(1000,10)\equiv 2071632(\mathrm{mod}1000000007)$.

Find $T({10}^6,999983)$. Give your answer modulo $1000000007$.