A 61-year-old postmenopausal nulliparous woman with a strong family history of ovarian cancer (mother and sister) presents with 4 months of progressive abdominal distension, early satiety, weight loss, and pelvic pressure. Transvaginal ultrasound reveals a 14 × 11 cm complex multiloculated adnexal mass with thick irregular septa (>3 mm), papillary projections (>3 mm), and solid components with high-velocity colour-Doppler flow (RI 0.34). CA-125 is 1560 U/mL, and staging CT shows peritoneal deposits and pleural effusion. The structure marked **A** in the diagram is highly suspicious for epithelial ovarian carcinoma. Which of the following is the most common histological subtype and carries the worst prognosis in this clinical presentation?