Testing the Addition of M3814 (Peposertib) to Radiation Therapy for Patients With Advanced Head and Neck Cancer Who Cannot Take Cisplatin

Inclusion Criteria: * Pathologically (histologically) proven diagnosis of HNSCC of the oral cavity, oropharynx, larynx, or hypopharynx prior to registration; * Patients with oropharynx cancer need p16 determination by immunohistochemistry (where positive is defined as greater than 70% strong nuclear or nuclear and cytoplasmic staining of tumor cells), Note: Institutions must screen patients using a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory. A rigorous laboratory accreditation process similar to the United States (U.S.) CLIA certification, such as the provincial accreditation status offered by the Ontario Laboratory Accreditation (OLA) Program in Canada, the College of American Pathologists (CAP), or an equivalent accreditation in other countries, is acceptable. The p16 results must be reported on the pathology report being submitted; * Oral cavity, larynx, hypopharynx, or p16-negative oropharynx cancer must be stages T1-2N2-3 or T3N1-3 or T4N0-3 (American Joint Committee on Cancer \[AJCC\] version 8); * p16-positive oropharynx cancer patients, stages T4N0-3 or T1-3N2-3 (AJCC version 8); * The patient has measurable disease as defined by the presence of at least one measurable lesion per RECIST 1.1; * Please note: A histological or pathological specimen from cervical lymph nodes with well-defined primary site documented clinically or radiologically is acceptable * Clinical stage noted above should be based upon following diagnostic work…