Note

This problem has a strict execution time limit, so using a fast language is recommended. (It has been confirmed that the writer's solution gets TLE in Python3 and AC in PyPy3.)

Problem Statement

Sushi Toruna-kun uses an SNS called $Tbutter$.
Currently, Sushi Toruna-kun has $N$ tbeets. The $i$-th tbeet of Sushi Toruna-kun has $A_i$ likes. Not wanting to become a Tbutter addict, Sushi Toruna-kun has decided to delete tbeets so that his number of tbeets becomes $M$ or less.
Since merely deleting tbeets would be boring, Sushi Toruna-kun also wants to make the average number of likes equal to $Z$.
Tbeets with $Y$ or fewer likes are boring, so Sushi Toruna-kun always deletes them. Tbeets with $X$ or more likes are interesting, so he cannot delete them. For all other tbeets, he may freely decide whether to delete them or not. However, at least $1$ tbeet must remain.
Output the number of ways in which the number of remaining tbeets is $M$ or less and the average number of likes is $Z$. However, if the number of tbeets cannot be made $M$ or less no matter how he deletes them, output Handicapped.

Input

$N\ M\ X\ Y\ Z$
$A_1\ A_2\ A_3\ ... A_N$

Constraints
$1\leq M\leq N\leq 50$
$0\leq Y < X\leq 50$
$0\leq Z\leq 50$
$0\leq A_i\leq 50$ ($1 ≤ i ≤ N$)
There exists at least $1$ index $i$ such that $Y < A_i$
All inputs are integers

Output

Depending on whether Sushi Toruna-kun can make his number of tbeets $M$ or less:
・if he cannot, print Handicapped;
・if he can, print the number of ways in which the number of remaining tbeets is $M$ or less and the average number of likes is $Z$,
on $1$ line. Print a newline at the end.

Sample

9 6 8 2 7
1 3 2 5 4 7 6 8 9

4

5 2 3 0 2
0 4 3 6 50

Handicapped

6 3 6 2 4
2 2 3 5 1 1

1

5 2 3 2 1
1 2 1 3 1

0