Measurements of the $\pi ^\pm $ , $K^\pm $ , and proton double differential yields emitted from the surface of the 90- $\hbox {cm}$ -long carbon target (T2K replica) were performed for the incoming $31\,$ $\hbox {GeV}\!/\!c$ protons with the NA61/SHINE spectrometer at the CERN SPS using data collected during 2010 run. The double differential $\pi ^\pm $ yields were measured with increased precision compared to the previously published NA61/SHINE results, while the $K^\pm $ and proton yields were obtained for the first time. A strategy for dealing with the dependence of the results on the incoming proton beam profile is proposed. The purpose of these measurements is to reduce significantly the (anti)neutrino flux uncertainty in the T2K long-baseline neutrino experiment by constraining the production of (anti)neutrino ancestors coming from the T2K target.