Campriani, a 28-year-old, three-time Olympian and 2012 silver medalist, established an Olympic record of 630.2 in the qualifying round and his competition score also now qualifies as an Olympic record. There had not been a comparable previous record due to a rule change.
Kulish, 23, shot a 204.6 in the final round of his second Olympic appearance and took silver.
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Russia's Vladimir Maslennikov, 21, took bronze on his Olympic debut with a score of 184.2.
India's Abhinav Bindra, a 33-year-old who in 2008 became the only individual athlete from his nation to win gold, took fourth with 163.8 after losing a shoot-off with Kulish after the pair exited the seventh round tied.
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Almaktoum's historic Olympic gold in Athens 2004