  A K-matrix re-analysis of the K-pi S-wave is performed in the mass region
900-2100 MeV, and solutions which describe the data well are found. The
solution with two resonances in the (IJ^P=1/2 0^+)-wave has poles at (1415 pm
25)- i(165 pm 25) MeV and (1820 pm 40) -i(125 pm 50) MeV, close to the previous
result of D. Aston et al., Nucl.Phys., B296 (1988) 493. The corresponding bare
states, which are the subjects of a qqbar classification, are:
K_0^{bare}(1220^{+50}_{-60}) and K_0^{bare}(1885^{+50}_{-80}). Within the
restored bare states, a construction of the 1^3P_0 qqbar and 2^3P_0 qqbar
nonets is completed. The three resonance solutions are analysed as well, the
corresponding bare states are found, and the qqbar-nonet classification is
suggested. In all variants of our qqbar-classification, the resonances a_0(980)
and f_0(980) (or their bare counterparts) are non-exotic, and an extra
scalar/isoscalar state exists in the mass region 1300-1700 MeV, being a good
candidate for the lightest scalar glueball.
