We study the star-forming (SF) population of galaxies within a sample of 209 IR-selected galaxy clusters at 0.3$,leq,z,leq,$1.1 in the ELAIS-N1 and XMM-LSS fields, exploiting the first HSC-SSP data release. The large area and depth of these data allows us to analyze the dependence of the SF fraction, $f_{SF}$, on stellar mass and environment separately. Using $R/R_{200}$ to trace environment, we observe a decrease in $f_{SF}$ from the field towards the cluster core, which strongly depends on stellar mass and redshift. The data show an accelerated growth of the quiescent population within the cluster environment: the $f_{SF}$ vs. stellar mass relation of the cluster core ($R/R_{200},leq,$0.4) is always below that of the field (4$,leq,R/R_{200},<,$6). Finally, we find that environmental and mass quenching efficiencies depend on galaxy stellar mass and distance to the center of the cluster, demonstrating that the two effects are not separable in the cluster environment. We suggest that the increase of the mass quenching efficiency in the cluster core may emerge from an initial population of galaxies formed ``in situ. The dependence of the environmental quenching efficiency on stellar mass favors models in which galaxies exhaust their reservoir of gas through star formation and outflows, after new gas supply is truncated when galaxies enter the cluster.
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