Sideways information passing is a well-known technique for mitigating the impact of large build sides in a database query plan. As currently implemented in production systems, sideways information passing enables only a uni-directional information flow, as opposed to instance-optimal algorithms, such as Yannakakis'. On the other hand, the latter require an additional pass over the input, which hinders adoption in production systems. In this paper, we make a step towards enabling single-pass bidirectional information passing during query execution. We achieve this by statically analyzing between which tables the information flow is blocked and by leveraging precomputed join-induced fingerprint columns on FK-tables. On the JOB benchmark, Parachute improves DuckDB v1.2's end-to-end execution time without and with semi-join filtering by 1.54x and 1.24x, respectively, when allowed to use 15% extra space.