Identifying Special Customers

Zi provides a sequence of length ( n ) where the ( i)-th element corresponds to customer number ( i ). All ordinary customers are colored blue and all special customers are colored purple. It is known that there are ( m ) special customers with purple positions. Importantly, the purple positions are very few and are almost uniformly distributed at random.

The value ( a_i ) at position ( i ) is assigned according to the formula: [ a_i=\begin{cases} s & \text{if } i=1\ a_{i-1}+k & \text{if } i>1\end{cases} ]

Mistia can ask queries of the form l r to obtain the sum of the values ( a_i ) for all blue positions in the interval ( [l, r] ) (i.e. skipping the purple positions). If you are able to determine all the special customers (i.e. all purple positions), then you should output a line of the form -1 p1 p2 ... pm, where ( p_i ) are the indices of the special customers in non-decreasing order.

Note: After each operation (query or final answer), you should flush the output buffer. For example, in C++ use fflush(stdout) or cout.flush(); in C use fflush(stdout); in Java use System.out.flush(); in Python use stdout.flush(); in Pascal use flush(output); and please consult the relevant documentation for other languages.

inputFormat

The input consists of two lines:

• The first line contains four integers \( n \), \( m \), \( s \) and \( k \), where \( n \) is the length of the sequence, \( m \) is the number of special customers, \( s \) is the first term of the sequence, and \( k \) is the common difference.
• The second line contains \( m \) distinct integers representing the indices of the special (purple) customers. These indices are in the range \( [1,n] \) and may be given in any order.

Note that although the problem description mentions query operations, this offline version provides you with all the necessary input. You just need to output the special positions.

outputFormat

Output a single line that starts with -1 followed by the ( m ) special customer indices in non-decreasing order, separated by spaces.

sample

10 2 1 2
3 8

-1 3 8