Transistor Repair

Interview

Time limit2sMemory limit1024 MB

Summary

Given n leg resistances, find three of them whose sum is A and product is B, or report -1 if none exist.

Level: Medium4 of 10
Topics: Number theory, Hash map, Brute force
Solved: No attempts yet

Problem

Papus is teaching Nolik how to repair transistors. A transistor consists of a base and three legs. Each leg has an integer resistance, and the values are known. Two numbers $A$ and $B$ are written on the base. The transistor works if the sum of the leg resistances is $A$ and their product is $B$ .

After Papus left, Nolik found a transistor base. To show that he can work on his own, he wants to repair this transistor.

Nolik has $n$ legs in his repair kit. He knows how to repair transistors, but choosing the right legs is hard. Help him find three legs that fit this base.

Input

The first line contains three integers $n$ , $A$ , $B$ ( $3 \le n \le 10^5$ , $1 \le A, B \le 10^5$ ): the number of legs in the kit, the required sum, and the required product.

The second line contains $n$ integers $a_i$ ( $1 \le a_i \le 10^5$ ), the resistances of the legs in the kit.

Output

Print three integers, the resistances of suitable legs. If there are several answers, print any of them. If no answer exists, print -1.

Examples3

Example 1
Input
```
5 11 40
1 2 3 4 5
```
Expected output
```
2 4 5
```
Example 2
Input
```
3 9 27
3 3 3
```
Expected output
```
3 3 3
```
Example 3
Input
```
3 9 27
3 2 3
```
Expected output
```
-1
```