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binary search

brute force

greedy

math

*1900

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D. Black Cells

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are playing with a really long strip consisting of $$$10^{18}$$$ white cells, numbered from left to right as $$$0$$$, $$$1$$$, $$$2$$$ and so on. You are controlling a special pointer that is initially in cell $$$0$$$. Also, you have a "Shift" button you can press and hold.

In one move, you can do one of three actions:

- move the pointer to the right (from cell $$$x$$$ to cell $$$x + 1$$$);
- press and hold the "Shift" button;
- release the "Shift" button: the moment you release "Shift", all cells that were visited while "Shift" was pressed are colored in black.

Your goal is to color at least $$$k$$$ cells, but there is a restriction: you are given $$$n$$$ segments $$$[l_i, r_i]$$$ — you can color cells only inside these segments, i. e. you can color the cell $$$x$$$ if and only if $$$l_i \le x \le r_i$$$ for some $$$i$$$.

What is the minimum number of moves you need to make in order to color at least $$$k$$$ cells black?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$; $$$1 \le k \le 10^9$$$) — the number of segments and the desired number of black cells, respectively.

The second line contains $$$n$$$ integers $$$l_1, l_2, \dots, l_n$$$ ($$$1 \le l_1 < l_2 < \dots < l_n \le 10^9$$$), where $$$l_i$$$ is the left border of the $$$i$$$-th segment.

The third line contains $$$n$$$ integers $$$r_1, r_2, \dots, r_n$$$ ($$$1 \le r_i \le 10^9$$$; $$$l_i \le r_i < l_{i + 1} - 1$$$), where $$$r_i$$$ is the right border of the $$$i$$$-th segment.

Additional constraints on the input:

- every cell belongs to at most one segment;
- the sum of $$$n$$$ doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print the minimum number of moves to color at least $$$k$$$ cells black, or $$$-1$$$ if it's impossible.

Example

Input

42 31 31 44 2010 13 16 1911 14 17 202 31 31 102 499 999999999100 1000000000

Output

8 -1 7 1000000004

Note

In the first test case, one of the optimal sequences of operations is the following:

- Move right: pointer is moving into cell $$$1$$$;
- Press Shift;
- Release Shift: cell $$$1$$$ is colored black;
- Move right: pointer is moving into cell $$$2$$$;
- Move right: pointer is moving into cell $$$3$$$;
- Press Shift;
- Move right: pointer is moving into cell $$$4$$$;
- Release Shift: cells $$$3$$$ and $$$4$$$ are colored in black.

In the second test case, we can color at most $$$8$$$ cells, while we need $$$20$$$ cell to color.

In the third test case, one of the optimal sequences of operations is the following:

- Move right: pointer is moving into cell $$$1$$$;
- Move right: pointer is moving into cell $$$2$$$;
- Move right: pointer is moving into cell $$$3$$$;
- Press Shift;
- Move right: pointer is moving into cell $$$4$$$;
- Move right: pointer is moving into cell $$$5$$$;
- Release Shift: cells $$$3$$$, $$$4$$$ and $$$5$$$ are colored in black.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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