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D. Segment Intersections

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given two lists of segments $$$[al_1, ar_1], [al_2, ar_2], \dots, [al_n, ar_n]$$$ and $$$[bl_1, br_1], [bl_2, br_2], \dots, [bl_n, br_n]$$$.

Initially, all segments $$$[al_i, ar_i]$$$ are equal to $$$[l_1, r_1]$$$ and all segments $$$[bl_i, br_i]$$$ are equal to $$$[l_2, r_2]$$$.

In one step, you can choose one segment (either from the first or from the second list) and extend it by $$$1$$$. In other words, suppose you've chosen segment $$$[x, y]$$$ then you can transform it either into $$$[x - 1, y]$$$ or into $$$[x, y + 1]$$$.

Let's define a total intersection $$$I$$$ as the sum of lengths of intersections of the corresponding pairs of segments, i.e. $$$\sum\limits_{i=1}^{n}{\text{intersection_length}([al_i, ar_i], [bl_i, br_i])}$$$. Empty intersection has length $$$0$$$ and length of a segment $$$[x, y]$$$ is equal to $$$y - x$$$.

What is the minimum number of steps you need to make $$$I$$$ greater or equal to $$$k$$$?

Input

The first line contains the single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — 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 length of lists and the minimum required total intersection.

The second line of each test case contains two integers $$$l_1$$$ and $$$r_1$$$ ($$$1 \le l_1 \le r_1 \le 10^9$$$) — the segment all $$$[al_i, ar_i]$$$ are equal to initially.

The third line of each test case contains two integers $$$l_2$$$ and $$$r_2$$$ ($$$1 \le l_2 \le r_2 \le 10^9$$$) — the segment all $$$[bl_i, br_i]$$$ are equal to initially.

It's guaranteed that the sum of $$$n$$$ doesn't exceed $$$2 \cdot 10^5$$$.

Output

Print $$$t$$$ integers — one per test case. For each test case, print the minimum number of step you need to make $$$I$$$ greater or equal to $$$k$$$.

Example

Input

3 3 5 1 2 3 4 2 1000000000 1 1 999999999 999999999 10 3 5 10 7 8

Output

7 2000000000 0

Note

In the first test case, we can achieve total intersection $$$5$$$, for example, using next strategy:

- make $$$[al_1, ar_1]$$$ from $$$[1, 2]$$$ to $$$[1, 4]$$$ in $$$2$$$ steps;
- make $$$[al_2, ar_2]$$$ from $$$[1, 2]$$$ to $$$[1, 3]$$$ in $$$1$$$ step;
- make $$$[bl_1, br_1]$$$ from $$$[3, 4]$$$ to $$$[1, 4]$$$ in $$$2$$$ steps;
- make $$$[bl_2, br_2]$$$ from $$$[3, 4]$$$ to $$$[1, 4]$$$ in $$$2$$$ steps.

In the second test case, we can make $$$[al_1, ar_1] = [0, 1000000000]$$$ in $$$1000000000$$$ steps and $$$[bl_1, br_1] = [0, 1000000000]$$$ in $$$1000000000$$$ steps.

In the third test case, the total intersection $$$I$$$ is already equal to $$$10 > 3$$$, so we don't need to do any steps.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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