# Problem: Cats III: Off With Their Heads

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## Cats III: Off With Their Heads

**Input File:** `cats.in`

**Output File:** `cats.out`

**Time Limit:** 1 second

**Memory Limit:** 64 MB

You really don't like cats. Unfortunately this fact has escaped your aunt,
who has just given you the present of a lifetime: *Cats in a
Box*.

Cats in a Box is a fiendish feline puzzle with two different types of
pieces: heads and tails. There are *n* different heads and
*n* different
tails, which come in an assortment of loveable sizes and colours.
Any head and tail can be combined to create a unique cat (so there are
*n*^{2} different cats that you can make).
The size of the resulting cat is the size of the head plus the size of the
tail.

The box advertises that you can create "thousands of HUGE creations!"
As you don't trust cat-lovers in the slightest, you are rather
suspicious of their claims. You set out to determine precisely how large
these creations are. Specifically, given the sizes of each of the head
and tail pieces, your task is to calculate the size of the *k*th largest
cat that can be created.

### Input

The first line of the input will contain the single integer *n*
(1 <= *n* <= 100,000),
the number of heads and the number of tails in the
box. The second line of the input will contain the single integer *k*
(1 <= *k* <= *n*^{2} and
*k* <= 1,000,000,000), the number of possible
"huge" creations that are advertised.

Following this will be *n* additional lines containing the integers
*a*_{1}, *a*_{2}, ..., *a*_{n},
written one per line, where *a*_{i} is the size
of the *i*th head
(1 <= *a*_{i} <= 1,000,000).
This will be followed by another *n* lines containing the integers
*b*_{1}, *b*_{2}, ..., *b*_{n},
also one per line, where *b*_{i} is the size of
the *i*th tail
(1 <= *b*_{i} <= 1,000,000).
The heads and tails will be given in descending order, so that
*a*_{1} >= *a*_{2} >= ... >= *a*_{n}
and
*b*_{1} >= *b*_{2} >= ... >= *b*_{n}.

### Output

The output should consist of a single integer *s*, the size of the
*k*th largest cat that can be created.

### Sample Input

4
7
8
7
7
3
9
7
4
2

### Sample Output

12

### Explanation

In the sample data above we have heads of sizes 8, 7, 7 and 3, and tails
of sizes 9, 7, 4 and 2. You are asked to find the size of the seventh
largest cat.
The largest cats that can be created are:

Head |
*#1:* 8 |
*#2:* 7 |
*#3:* 7 |
*#1:* 8 |
*#2:* 7 |
*#3:* 7 |
*#1:* 8 |
... |

Tail |
*#1:* 9 |
*#1:* 9 |
*#1:* 9 |
*#2:* 7 |
*#2:* 7 |
*#2:* 7 |
*#3:* 4 |
... |

Cat size |
17 |
16 |
16 |
15 |
14 |
14 |
12 |
... |

The seventh largest cat therefore has size 12.

### Scoring

The score for each input scenario will be 100% if the correct answer is written to the
output file, and 0% otherwise.