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# Problem 619

## Square subsets

For a set of positive integers ${a,a+1,a+2,\ldots,b}$, 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 $C(1000,1234)\text{ mod }1000000007=975523611$.

Find $C(1000000,1234567)\text{ mod }1000000007$.