Back with a bang

Number Theory Level pending

Our hero Batman likes to play with coins. He has \(n\) number of coins all of which are white on one side and black on the other. He puts all the coins on a straight line with white side up. Now he starts to flip the coins. First he flips every coins placed at position of multiple of \(1\), then at multiple of \(2\) and so on till the multiple of \(n\). He wants you to guess the last position of the coin whose black side is up if \(n\) is given to be 1000000007.

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