For a set of positive integers $\{a,a+1,a+2,\dots ,b\}$, let $C(a,b)$ be the number of non-empty subsets in which the product of all elements is a perfect square.

For example $C(5,10)=3$, since the products of all elements of $\{5,8,10\}$, $\{5,8,9,10\}$ and $\{9\}$ are perfect squares, and no other subsets of $\{5,6,7,8,9,10\}$ have this property.

You are given that $C(40,55)=15$, and $C(1000,1234)mod1000000007=975523611$.

Find $C(1000000,1234567)mod1000000007$.