Description

Let x1, x2, ..., xm be real numbers satisfying the following conditions:

for some integers a and b (a > 0).

Determine the maximum value of x₁^p

+ x

₂^p

+ … + x

_m^p

for some even positive integer p.

Input

Each input line contains four integers: m, p, a, b (m <= 2000, p <= 12, p is even). Input is correct, i.e. for each input numbers there exists x1, x2, …, xm satisfying the given conditions.

Output

For each input line print one number – the maximum value of expression, given above. The answer must be rounded to the nearest integer.

1997 12 3 -318
10 2 4 -1

189548
6

Source

Southeastern Europe 2006