Alice has \(N\) varieties chocolates with quantities \(A_1, A_2, ..., A_N\). But the problem with them is that if he eats one chocolate of some variety, then all the other chocolates of that variety vanishes. He also has a special type of chocolate with quantity \(A_0\), if he eats one chocolate of that type then all the chocolates of all the variety vanish.

What is the expected number of chocolates he will eat till all the chocolates of all the variety vanishes. Your answer would be considered correct if it has a precision of exactly 6 decimal places.

Constraints:
\( 1 <= N <= 3 * 10^{6} \)
\( 1 <= A_i <= 3 * 10^{6} \) for \( 0 <= i <= N \)

Format of the input file:
First line : Two space separated integers \(N\) and \(A_0\), as stated above.
Second line : \(N\) space separated integers i.e. \(A_1, A_2, ..., A_N\).

Format of the output file:
Print the answer.