Why did Spartak go north and why did he turn when he was already at the border of Italy?

In the 1st century BC, an uprising broke out in the Roman Republic, which soon gained significant momentum. Tens of thousands of slaves were led by the Thracian Spartacus. He wanted to free as many slaves as possible, and then cross the Alps. True, difficulties soon arose, namely: significant funds were needed to cross the Alps, and there was also a shortage of provisions; some of the slaves wanted to stay in Italy – because of this, Spartacus was forced to turn to the south of Italy.