Multiple-ion coincidence momentum imaging experiments were carried out for K-shell (1s) excited Ar clusters containing about 130 atoms and Kr clusters containing about 30, 90, and 160 atoms. The time-of-flight spectra reveal that the major products of the Coulomb explosion are singly charged ions. With increasing the number of charges generated in clusters, the momentum of monomer ions such as Ar(+) and Kr(+) increases, while that of cluster ions such as Ar(3) (+), Kr(2) (+), and Kr(3) (+) decreases. This observation indicates the site-specific decay process that the heavier ions appear in the central part of clusters. We have also investigated the momentum distribution in various fragmentation channels and the branching ratio of each channel at the Coulomb explosion. When the number N(coin) of coincidently detected ions is four, for example, the most frequent channel from Kr clusters containing 30 atoms is to emit simply four Kr(+) ions, but Kr(2) (+) ions participate in the fragmentation from the larger Kr clusters. The fragmentation channel in which two Ar(2) (+) ions are emitted becomes dominant with increasing N(coin), and the average momentum of Ar(2) (+) ion in this channel is larger than that in the channels where only single Ar(2) (+) is emitted.