Exhibition

The city government is preparing an exhibition and is collecting industrial products. There are $n$ candidate products, and the government chooses $k$ of them. It wants the total price of the chosen products to be small, and it also takes their sizes and weights into account. Product $i$ has price $x_i$, size $y_i$ and weight $z_i$. The government picks $k$ different products $i_1, \dots, i_k$ that minimize the evaluation value

$e = \left(\sum_{j=1}^{k} x_{i_j}\right)\left(\sum_{j=1}^{k} y_{i_j}\right)\left(\sum_{j=1}^{k} z_{i_j}\right)$

If two or more choices reach the minimum, the government picks one of them uniformly at random.

You work for the company that makes product 1. The company will cut the price, the size and the weight of product 1 so that the government may pick it, that is, so that the probability of picking product 1 becomes positive. Cutting the price to $(1-\alpha)x_1$, the size to $(1-\beta)y_1$ and the weight to $(1-\gamma)z_1$, where $0 \le \alpha, \beta, \gamma \le 1$, costs $\alpha A + \beta B + \gamma C$ million yen. The price, the size and the weight after the cut do not have to be integers, and the government evaluates product 1 with the cut values. Compute the smallest investment that makes it possible for the government to choose product 1. Every other company leaves its product unchanged.

The input is a single test case in the following format.

n k A B C
x1 y1 z1
x2 y2 z2
...
xn yn zn

The first line has five integers. $n$ ($1 \le n \le 50$) is the number of products, $k$ ($1 \le k \le n$) is how many products the government chooses, and $A$, $B$, $C$ ($1 \le A, B, C \le 100$) fix the cost of cutting the price, the size and the weight of product 1. Each of the next $n$ lines has three integers $x_i$, $y_i$, $z_i$ ($1 \le x_i, y_i, z_i \le 100$), the price, the size and the weight of product $i$.

Print the smallest investment in million yen on one line, rounded to exactly six digits after the decimal point.