Two bluetooth receivers to one wireless keyboard?

I have two PCs at work and each has its own wireless keyboard/mouse. I want to be able able to type with just one keyboard and that same input be sent to both PCs. Rewording: I want to be able to type on one of the wireless keyboards, and i want that keyboard to send the signal to both wireless receiver that are connected to the PCs. That way whatever im typing, gets recorded on both pcs at the same time. Is it possible? maybe by pairing the two bluetooth receivers to the same keyboard or something like that... i need hardware options not software, the IT admin will not let me install any software.