A9813. Mean Requests

The first line contains integer $n$ ( $1<=n<=2·10^{5}$ ), integer $T$ ( $1<=T<=n$ ) and real number $c$ ( $1<c<=100$ ) — the time range when the resource should work, the length of the time range during which we need the mean number of requests and the coefficient $c$ of the work of approximate algorithm. Number $c$ is given with exactly six digits after the decimal point.

The next line contains $n$ integers $a_{t}$ ( $1<=a_{t}<=10^{6}$ ) — the number of queries to the service at each moment of time.

The next line contains integer $m$ ( $1<=m<=n$ ) — the number of moments of time when we are interested in the mean number of queries for the last $T$ seconds.

The next line contains $m$ integers $p_{j}$ ( $T<=p_{j}<=n$ ), representing another moment of time for which we need statistics. Moments $p_{j}$ are strictly increasing.

Print $m$ lines. The $j$ -th line must contain three numbers $real$ , $approx$ and $error$ , where:

-  is the real mean number of queries for the last $T$ seconds;
- $approx$ is calculated by the given algorithm and equals $mean$ at the moment of time $t=p_{j}$ (that is, after implementing the $p_{j}$ -th iteration of the cycle);
-  is the relative error of the approximate algorithm.

The numbers you printed will be compared to the correct numbers with the relative or absolute error $10^{-4}$ . It is recommended to print the numbers with at least five digits after the decimal point.

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