Lian, who was really bored on a very certain day involving the number "$14$", thought of the polynomial-

$$1 - x + x^2 - x^3 + \dots +x^{12} - x^{13} + x^{14} $$

he noticed that it can be rewritten in the form

$$a_0 + a_1y + a_2y^2 + \dots + a_{13}y^{13} + a_{14}y^{14}$$

where $x = y + 1$.

Find $a_7$.