Let x1, x2, ..., xm be real numbers satisfying the following conditions:
for some integers a and b (a > 0).
Determine the maximum value of x
1p + x
2p + … + x
mp for some even positive integer p.
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.
For each input line print one number – the maximum value of expression, given above. The answer must be rounded to the nearest integer.