Let \( a, b \) be two real numbers such that \( ab < 0 \). If the complex number \( \frac{1 + ai}{\, b + i \,} \) is of unit modulus and \( a + ib \) lies on the circle \( |z - 1| = |2z| \), then a possible value of \( \frac{1 + [a]}{4b} \), where \( [t] \) is greatest integer function, is:
