Network Mask

题意翻译

## 题目背景 该问题使用了一个简化的TCP/IP地址模型，请确保您仔细阅读了该声明。 ## 题目描述 Polycarpus找到了一份工作，他是一名系统管理员。 有一天他偶然发现了n个IP地址。 每个IP地址是一个32位的数字，用4个8位数字(不带前导零)组成一组，用点分隔。 例如，记录0.255.1.123显示正确的IP地址，记录0.256.1.123和0.255.1.01不正确。 在这个问题中，由4个8位数字组成的任意组就是一个正确的IP地址。 Polycarpus作为一名管理员工作了一段时间，了解到如果您知道IP地址，您可以使用子网掩码来获得拥有该IP地址的网络地址。 子网掩码是一个IP地址，它有以下属性:如果我们把这个IP地址写为一个32位的字符串，它可以表示为“11…11000..000”。 换句话说，子网掩码首先有一个或多个1位，然后是一个或多个0位(总共有32位)。 例如，IP地址2.0.0.0不是一个正确的子网掩码，因为它的32位记录看起来是0000001000000000000000000000。 要得到IP地址的网络地址，需要执行IP地址和子网掩码的按位“与”操作。 例如，如果子网掩码是255.192.0.0,IP地址是192.168.1.2，则网络地址等于192.128.0.0。 在按位的“与”中，当且仅当两个操作数对应的位都等于1时，结果的位等于1。 现在Polycarpus想要找到他的IP地址所属的所有网络。 不幸的是Polycarpus丢失了子网掩码。 幸运的是，Polycarpus记得他的IP地址完全属于 $k$ 种不同的网络。 帮助Polycarpus找到子网掩码，这样他的IP地址将完全属于 $k$ 种不同的网络。 如果有多个子网掩码，则查找位记录中1个数最少的一个。 如果不存在这样的子网掩码，输出-1。 ## 输入格式 第一行包含两个整数，$n$ 和 $k$$（1<=k<=n<=10^{5}）$ 表示IP地址和网络的数量。接下来的 $n$ 行每行包含一条IP地址。保证所有IP地址都是不同的。 ## 输出格式 如果存在所需的子网掩码，则以语句中描述的格式在单行中输出子网掩码的IP地址。否则输出-1。

题目描述

The problem uses a simplified TCP/IP address model, please make sure you've read the statement attentively. Polycarpus has found a job, he is a system administrator. One day he came across $ n $ IP addresses. Each IP address is a 32 bit number, represented as a group of four 8-bit numbers (without leading zeroes), separated by dots. For example, the record 0.255.1.123 shows a correct IP address and records 0.256.1.123 and 0.255.1.01 do not. In this problem an arbitrary group of four 8-bit numbers is a correct IP address. Having worked as an administrator for some time, Polycarpus learned that if you know the IP address, you can use the subnet mask to get the address of the network that has this IP addess. The subnet mask is an IP address that has the following property: if we write this IP address as a 32 bit string, that it is representable as "11...11000..000". In other words, the subnet mask first has one or more one bits, and then one or more zero bits (overall there are 32 bits). For example, the IP address 2.0.0.0 is not a correct subnet mask as its 32-bit record looks as 00000010000000000000000000000000. To get the network address of the IP address, you need to perform the operation of the bitwise "and" of the IP address and the subnet mask. For example, if the subnet mask is 255.192.0.0, and the IP address is 192.168.1.2, then the network address equals 192.128.0.0. In the bitwise "and" the result has a bit that equals 1 if and only if both operands have corresponding bits equal to one. Now Polycarpus wants to find all networks to which his IP addresses belong. Unfortunately, Polycarpus lost subnet mask. Fortunately, Polycarpus remembers that his IP addresses belonged to exactly $ k $ distinct networks. Help Polycarpus find the subnet mask, such that his IP addresses will belong to exactly $ k $ distinct networks. If there are several such subnet masks, find the one whose bit record contains the least number of ones. If such subnet mask do not exist, say so.

输入输出格式

输入格式

The first line contains two integers, $ n $ and $ k $ $ (1<=k<=n<=10^{5}) $ — the number of IP addresses and networks. The next $ n $ lines contain the IP addresses. It is guaranteed that all IP addresses are distinct.

输出格式

In a single line print the IP address of the subnet mask in the format that is described in the statement, if the required subnet mask exists. Otherwise, print -1.

输入输出样例

输入样例 #1

5 3
0.0.0.1
0.1.1.2
0.0.2.1
0.1.1.0
0.0.2.3

输出样例 #1

255.255.254.0

输入样例 #2

5 2
0.0.0.1
0.1.1.2
0.0.2.1
0.1.1.0
0.0.2.3

输出样例 #2

255.255.0.0

输入样例 #3

2 1
255.0.0.1
0.0.0.2

输出样例 #3

-1