A.I.T.S Advanced level problem from Resonance

The numbers \[1000, 1001,....., 2999 \]have been written on a board. Each time, one is allowed to erase two numbers, say, a and b, and replace them by the number \(\frac {1}{2}min(a, b)\). After 1999 such operations, one obtains exactly one number c on the board, than which of them is correct

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