Dose Ranging, Switch Study of Islatravir (MK-8591) and Ulonivirine (MK-8507) Once-Weekly in Virologically-Suppressed Adults With Human Immunodeficiency Virus Type 1 (HIV-1) [MK-8591-013]

Inclusion Criteria: * Is HIV-1 positive with plasma human immunodeficiency virus type 1 (HIV-1) RNA \<50 copies/mL at screening * Has been virologically suppressed on bictegravir/emtricitabine/tenofovir alafenamide (BIC/FTC/TAF) for ≥6 months * Has a screening CD4+ T-cell count \>200 cells/mm\^3 (completed by the central laboratory) * Is male or female, at least 18 years of age, at the time of signing the informed consent * Female participants are eligible to participate if not pregnant or breastfeeding, and at least one of the following conditions applies: * Is not a woman of childbearing potential (WOCBP) * Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) Exclusion Criteria: * Has HIV-2 infection * Has hypersensitivity or other contraindication to any of the components of the study interventions as determined by the investigator * Has active hepatitis C virus (HCV) coinfection (defined as detectable HCV RNA) or hepatitis B virus (HBV) coinfection (defined as hepatitis B surface antigen \[HBsAg\]-positive or HBV deoxyribonucleic acid \[DNA\] positive) * Has a current (active) diagnosis of acute hepatitis due to any cause * Has a history of malignancy ≤5 years prior to signing informed consent except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or cutaneous Kaposi's sarcoma * Has a history or current evidence of any condition (including active tuberculosis infection), therapy, laboratory abnormality or other circumstance (including drug or alcohol use or dependence) that might, in the opinion of the investigator, confound the results of the study or interfere with the participant's participation for the full duration of the study * Is taking or is anticipated to require systemic immunosuppressive therapy, immune modulators, or any prohibited therapies * Is currently participating in or has participated in a clinical study with an investigational compound or device from 45 days prior to Day 1 through the study treatment period * Has a documented or known virological resistance to ulonivirine or nucleoside/nucleotide reverse transcriptase inhibitors (NNRTI) * Is female and expecting to conceive or donate eggs at any time during the study