Define $m=M(n,d)$ to be the smallest positive integer such that when $m^2$ is written in base $n$ it includes the base $n$ digit $d$. For example, $M(10,7)=24$ because if all the squares are written out in base 10 the first time the digit 7 occurs is in ${24}^2=576$. $M(11,10)=19$ as ${19}^2=361=2A{9}_{11}$.

Find ${\displaystyle \sum _{d=1}^{{10}^5}M(p,p-d)}$ where $p={10}^9+7$.