Let $B(n)$ be the smallest number larger than $n$ that can be formed by rearranging digits of $n$, or $0$ if no such number exists. For example, $B(245)=254$ and $B(542)=0$.

Define ${\displaystyle T(N)=\sum _{n=1}^{N}B(n^2)}$. You are given $T(10)=270$ and $T(100)=335316$.

Find $T({10}^{16})$. Give your answer modulo ${10}^9+7$.