How to compute accumulated values in bilinear map accumulators
In your setting this is assumed to be hard. It is exactly the task of producing a forgery for message $s$ of the weakly secure Boneh-Boyen signature scheme (Sec. 3.1) under public key $g^{e_1}$ (note that the scheme is presented in the asymmetric setting but can equally be instantiated in the symmetric setting under the $q$-SDH assumption).

In other words, if you can do this, you can break the $1$-SDH problem.