Gentle Excavation Planning

Byteasar is stranded in the Byteotian Desert along the Dry River. With the river dry and his water supplies depleted, his only hope is to dig a well deep enough to reach the water level. However, he can only dig a limited amount before his strength fails. Moreover, he wants to keep the excavation slope as gentle as possible to avoid a deadly landslide.

You are given the depth of the water level D, his maximum digging capacity (strength) S, and a topographic map of the river bed indicating the elevation at N positions. At position i (1-indexed) the elevation is a_i. In order to reach water at position i, Byteasar must dig an amount equal to

\(d_i = D - a_i\)

provided \(a_i \leq D\).

The digging at position i is feasible only if \(d_i \leq S\). Among all feasible positions, Byteasar wishes to choose the one that minimizes \(d_i\) (i.e. where the excavation is as gentle as possible). If there are multiple positions with the same \(d_i\), choose the one with the smallest index. If no position can be excavated within his strength, output impossible.

Your task is to help Byteasar determine where he should dig. If a feasible position exists, output the 1-indexed position and the required digging amount separated by a space. Otherwise, output impossible.

inputFormat

The input consists of two lines.

The first line contains three integers:

• N (the number of positions in the topographic map),
• D (the water level depth), and
• S (the maximum amount Byteasar can dig).

The second line contains N integers \(a_1, a_2, \ldots, a_N\) representing the elevation at each position.

outputFormat

If there exists a position where the required digging amount \(d_i = D - a_i\) does not exceed \(S\), output two integers separated by a space: the 1-indexed position and \(d_i\). Otherwise, output the string impossible.

sample

5 10 5
6 8 4 9 7

4 1