All the $7$ digit numbers containing each of the digits $1, 2, 3, 4, 5, 6, 7$ exactly once and not divisible by $5$ are arranged in the increasing order. Then -

If $L=$ the number of ways in which these books are distributed between two students $X$ and $Y$ such that $X$ get $p$ books and $Y$ gets $q$ books.

$M=$ The number of ways in which these books are distributed between two students $X$ and $Y$ such that one of them gets $p$ books and another gets $q$ books.

$N=$ The number of ways in which these books are divided into two groups of $p$ books and $q$ books then -