Codeforces Global Round 3 |
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Finished |

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binary search

brute force

two pointers

*1600

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B. Born This Way

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputArkady bought an air ticket from a city A to a city C. Unfortunately, there are no direct flights, but there are a lot of flights from A to a city B, and from B to C.

There are $$$n$$$ flights from A to B, they depart at time moments $$$a_1$$$, $$$a_2$$$, $$$a_3$$$, ..., $$$a_n$$$ and arrive at B $$$t_a$$$ moments later.

There are $$$m$$$ flights from B to C, they depart at time moments $$$b_1$$$, $$$b_2$$$, $$$b_3$$$, ..., $$$b_m$$$ and arrive at C $$$t_b$$$ moments later.

The connection time is negligible, so one can use the $$$i$$$-th flight from A to B and the $$$j$$$-th flight from B to C if and only if $$$b_j \ge a_i + t_a$$$.

You can cancel at most $$$k$$$ flights. If you cancel a flight, Arkady can not use it.

Arkady wants to be in C as early as possible, while you want him to be in C as late as possible. Find the earliest time Arkady can arrive at C, if you optimally cancel $$$k$$$ flights. If you can cancel $$$k$$$ or less flights in such a way that it is not possible to reach C at all, print $$$-1$$$.

Input

The first line contains five integers $$$n$$$, $$$m$$$, $$$t_a$$$, $$$t_b$$$ and $$$k$$$ ($$$1 \le n, m \le 2 \cdot 10^5$$$, $$$1 \le k \le n + m$$$, $$$1 \le t_a, t_b \le 10^9$$$) — the number of flights from A to B, the number of flights from B to C, the flight time from A to B, the flight time from B to C and the number of flights you can cancel, respectively.

The second line contains $$$n$$$ distinct integers in increasing order $$$a_1$$$, $$$a_2$$$, $$$a_3$$$, ..., $$$a_n$$$ ($$$1 \le a_1 < a_2 < \ldots < a_n \le 10^9$$$) — the times the flights from A to B depart.

The third line contains $$$m$$$ distinct integers in increasing order $$$b_1$$$, $$$b_2$$$, $$$b_3$$$, ..., $$$b_m$$$ ($$$1 \le b_1 < b_2 < \ldots < b_m \le 10^9$$$) — the times the flights from B to C depart.

Output

If you can cancel $$$k$$$ or less flights in such a way that it is not possible to reach C at all, print $$$-1$$$.

Otherwise print the earliest time Arkady can arrive at C if you cancel $$$k$$$ flights in such a way that maximizes this time.

Examples

Input

4 5 1 1 2 1 3 5 7 1 2 3 9 10

Output

11

Input

2 2 4 4 2 1 10 10 20

Output

-1

Input

4 3 2 3 1 1 999999998 999999999 1000000000 3 4 1000000000

Output

1000000003

Note

Consider the first example. The flights from A to B depart at time moments $$$1$$$, $$$3$$$, $$$5$$$, and $$$7$$$ and arrive at B at time moments $$$2$$$, $$$4$$$, $$$6$$$, $$$8$$$, respectively. The flights from B to C depart at time moments $$$1$$$, $$$2$$$, $$$3$$$, $$$9$$$, and $$$10$$$ and arrive at C at time moments $$$2$$$, $$$3$$$, $$$4$$$, $$$10$$$, $$$11$$$, respectively. You can cancel at most two flights. The optimal solution is to cancel the first flight from A to B and the fourth flight from B to C. This way Arkady has to take the second flight from A to B, arrive at B at time moment $$$4$$$, and take the last flight from B to C arriving at C at time moment $$$11$$$.

In the second example you can simply cancel all flights from A to B and you're done.

In the third example you can cancel only one flight, and the optimal solution is to cancel the first flight from A to B. Note that there is still just enough time to catch the last flight from B to C.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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