Lots of presents!

Santa is going on two trips to deliver presents.

For the first trip, he needs to separate $2013$ distinct presents into $2$ bags, where the bags are the same as each other and each one has at least $1$ present. Let the number of ways he can do this be $c_1$ .

For the second trip, he needs to separate $2012$ distinct presents into $2$ bags, where the bags are the same as each other and each one has at least $1$ present. Let the number of ways he can do this be $c_2$ .

What is $2c_2-c_1+4$ ?