Step 1: Understand the "OK" sign. Making the "OK" sign requires flexion of the distal interphalangeal (DIP) joint of the index finger and the interphalangeal (IP) joint of the thumb so their pulps oppose to form a rounded "O". Inability to do this and forming a flattened pinch is the classic sign of anterior interosseous nerve (AIN) palsy.
Step 2: Identify the muscles needed. The anterior interosseous nerve supplies flexor pollicis longus (FPL), flexor digitorum profundus (FDP) to the index (and middle) finger, and pronator quadratus. DIP-joint flexion of the index finger is produced specifically by the flexor digitorum profundus.
Step 3: Why option B (FDP) is correct. Loss of distal flexion of the index finger - needed to round the fingertip in the "OK" sign - is due to weakness of the flexor digitorum profundus (together with FPL); among the listed options FDP is the muscle responsible for index DIP flexion.
Step 4: Why the other options are wrong. Flexor digitorum superficialis (FDS, option A) flexes the proximal interphalangeal (PIP) joint, not the DIP, so it cannot account for the failed "OK" sign. "FIC" (option C) is not a muscle that controls index DIP flexion. Option D is not a valid muscle.
Final answer: B (FDP).