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The cyclone, named Sitrang by Thailand, is likely to make landfall between Tinkona island and Sandwip in Bangladesh on Tuesday morning, it said.
At 5.30 pm on Sunday, the cyclone was 580 km south of Sagar Island in West Bengal and 740 km south-southwest of Barisal in Bangladesh, it said.
Under its impact, parts of Odisha and West Bengal are likely to receive heavy rainfall, the IMD said.