\( \mathrm{X^{a+}} \) and \( \mathrm{Y^{b+}} \) are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers \( n = 1 \) and \( n = 2 \) of \( \mathrm{X^{a+}} \) is \( \lambda \). The wavelength of light absorbed during the transition between the states with principal quantum numbers \( n = 2 \) and \( n = 4 \) of \( \mathrm{Y^{b+}} \) is \( 9\lambda \). The lowest possible value of \( (a + b) \) is __________.
