\(\bar{a}, \overline{\mathrm{~b}}, \overline{\mathrm{c}}\) are nonzero vectors such that \(\bar{a}\) is perpendicular to \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\), \(|\bar{a}|=1,|\bar{b}|=2,|\bar{c}|=1\) and \(\bar{b} \cdot \bar{c}=1\). There is nonzero vector \(\bar{d}\) coplanar with \(\bar{a}+\overline{\mathrm{b}}\) and \(2 \overline{\mathrm{~b}}-\overline{\mathrm{c}}\). If \(\overline{\mathrm{d}} \cdot \bar{a}=1\), then \(|\overline{\mathrm{d}}|^2=\)
(Note that \(x\) and \(y\) are parameters involved when we write \(d=x(a+b)+y(2 b-c))\)

1. A \(13 y^2+14 y+5\)
2. B \(y^2+14 y+5\)
3. C \(y^2-14 y-5\)
4. D \(y^2-14 y+5\)