CF839E.Mother of Dragons

There are n castles in the Lannister's Kingdom and some walls connect two castles, no two castles are connected by more than one wall, no wall connects a castle to itself.

Sir Jaime Lannister has discovered that Daenerys Targaryen is going to attack his kingdom soon. Therefore he wants to defend his kingdom. He has k liters of a strange liquid. He wants to distribute that liquid among the castles, so each castle may contain some liquid (possibly zero or non-integer number of liters). After that the stability of a wall is defined as follows: if the wall connects two castles a and b, and they contain x and y liters of that liquid, respectively, then the strength of that wall is x·y.

Your task is to print the maximum possible sum of stabilities of the walls that Sir Jaime Lannister can achieve.

兰尼斯特王国中有 $n$ 座城堡，若干堵墙连接着这些城堡，任意两座城堡之间至多只有一堵墙相连，且不存在连接某座城堡与其自身的墙。

詹姆·兰尼斯特爵士发现丹妮莉丝·坦格利安即将进攻他的王国。因此，他希望加强王国的防御。他拥有 $k$ 升某种奇异液体。他打算将该液体分配到各座城堡中（每座城堡可分配任意非负实数升液体，包括零升）。

随后，一堵墙的稳定性定义如下：若某堵墙连接城堡 $a$ 和 $b$，且这两座城堡中分别含有 $x$ 升和 $y$ 升该液体，则该墙的强度为 $x \cdot y$。

你的任务是输出詹姆·兰尼斯特爵士所能达到的墙壁稳定性总和的最大可能值。

The first line of the input contains two integers n and k (1 ≤ n ≤ 40, 1 ≤ k ≤ 1000).

Then n lines follows. The i-th of these lines contains n integers a__i, 1, a__i, 2, ..., a__i, n (). If castles i and j are connected by a wall, then a__i, j = 1. Otherwise it is equal to 0.

It is guaranteed that a__i, j = a__j, i and a__i, i = 0 for all 1 ≤ i, j ≤ n.

输入的第一行包含两个整数 $n$ 和 $k$（$1 \leq n \leq 40$，$1 \leq k \leq 1000$）。

接下来是 $n$ 行。其中第 $i$ 行包含 $n$ 个整数 $a_{i,1},\ a_{i,2},\ \dots,\ a_{i,n}$（）。若城堡 $i$ 与城堡 $j$ 之间有城墙相连，则 $a_{i,j} = 1$；否则 $a_{i,j} = 0$。

保证对所有 $1 \leq i, j \leq n$，均有 $a_{i,j} = a_{j,i}$ 且 $a_{i,i} = 0$。

Print the maximum possible sum of stabilities of the walls that Sir Jaime Lannister can achieve.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if .

输出瑟曦·兰尼斯特爵士所能达到的墙壁稳定性之和的最大可能值。

若您的答案的绝对或相对误差不超过 $10^{-6}$，则视为正确。

即：假设您的答案为 $a$，而裁判组的答案为 $b$。当满足 时，校验程序将判定您的答案正确。

In the first sample, we can assign 0.5, 0.5, 0 liters of liquid to castles 1, 2, 3, respectively, to get the maximum sum (0.25).

In the second sample, we can assign 1.0, 1.0, 1.0, 1.0 liters of liquid to castles 1, 2, 3, 4, respectively, to get the maximum sum (4.0)

在第一个样例中，我们可以分别为城堡 1、2、3 分配 $0.5$、$0.5$、$0$ 升液体，从而获得最大总和（$0.25$）。

在第二个样例中，我们可以分别为城堡 1、2、3、4 分配 $1.0$、$1.0$、$1.0$、$1.0$ 升液体，从而获得最大总和（$4.0$）。