Contract Type/Structure to pay nothing if results not achieved?

Seeking suggestions for how to structure a contract for the following:

A civilian program office needs to hire a federal employee for something mission-related. That program office wants the agency's HR office to post the job announcement to Usajobs. However, the program office also wants the HR office to hire a headhunter service contractor to also do its own search for qualified candidates. The program office has a set list of objective criteria it wants in the candidates (e.g., at least 10 years experience in such-and-such, education requirements, etc.). The program office wants the headhunter to seek candidates, submit the candidates to the HR office, and only if the names of the candidates submitted by the headhunter show up on the HR office's "qualified" list (HR has to review all candidates against the qualifications list), then the headhunter will get paid per qualified candidate it submits. If the headhunter submits candidates that are deemed NOT qualified, the program does not want the headhunter to get paid at all. So it would be X dollars unit price per each qualified candidate. The program office does not want to pay a "minimum" fee for the contract at all.

So how could the contracting officer structure such a contract? What contract type and incentives should be used?