Did Israel once support Hamas?

Occasionally on Twitter I get a smart arse who triumphantly tells me that Israel used to support Hamas. 

Occasionally they say Israel created Hamas but I tend to ignore people who are that stupid.

In answer to the first group:

Israel used to support the Muslim Brotherhood (MB) back when it was focused on bringing religious piety into the public sphere but before it added the mission violent opposition to Israel. Later, a separate Islamic organization, Palestinian Islamic JIHAD (PIJ) , started up and was focused on violent opposition to Israel. So as not to lose support to PIJ, the MB created a subsidiary organization that would focus on violence against Israel, that new organization being Hamas. Israel's support for the MB stopped soon afterwards.

OK, got it?