In a nonvolatile memory block that contains separately-selectable sets of NAND strings, a bit line current sensing unit is configured to sense bit line current for a separately-selectable set of NAND strings of the block. A bit line voltage adjustment unit is configured to apply a first and second bit line voltages to separately-selectable sets of NAND strings that have bit line currents greater and less than the minimum current respectively, the second bit line voltage being greater than the first bit line voltage.