Hide all extra excel columns with Apache-POI

Question

This is my aim:

I am generating an xlsx file using Apache POI. I would like to hide all the unused columns to the right of the columns I am using. In Excel, this is a relatively simple operation: I can select all the extraneous columns and tell them all to hide in one action. In Apache POI, the only option I seem to have is sheet.setColumnHidden(index, true). If I try to do this for every extraneous column:

for (int i = myLastColumn+1; i < 16384; ++i) {
    sheet.setColumnHidden(i, true);
}

then the library tries to create over 16 thousand columns in order to hide them, which is impractical: it gets slower and slower as it goes, and never finishes. There doesn't seem to be a setColumnRangeHidden or anything like that.

Is there a way to hide nearly all the columns in Apache POI?