Sorry for the wrong link, seem like the M331 is not using Unifying USB dongle according to the list.
The only option left for you is to find another identical USB dongle for M331 and use Logitech Reconnect Software to pair them together.
My laptop is using M325 given by a friend who lost the USB dongle, I use a spare Unifying dongle to successfully paired them using Logitech Unifying Software
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