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D. Cleaning the Phone

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp often uses his smartphone. He has already installed $$$n$$$ applications on it. Application with number $$$i$$$ takes up $$$a_i$$$ units of memory.

Polycarp wants to free at least $$$m$$$ units of memory (by removing some applications).

Of course, some applications are more important to Polycarp than others. He came up with the following scoring system — he assigned an integer $$$b_i$$$ to each application:

- $$$b_i = 1$$$ — regular application;
- $$$b_i = 2$$$ — important application.

According to this rating system, his phone has $$$b_1 + b_2 + \ldots + b_n$$$ convenience points.

Polycarp believes that if he removes applications with numbers $$$i_1, i_2, \ldots, i_k$$$, then he will free $$$a_{i_1} + a_{i_2} + \ldots + a_{i_k}$$$ units of memory and lose $$$b_{i_1} + b_{i_2} + \ldots + b_{i_k}$$$ convenience points.

For example, if $$$n=5$$$, $$$m=7$$$, $$$a=[5, 3, 2, 1, 4]$$$, $$$b=[2, 1, 1, 2, 1]$$$, then Polycarp can uninstall the following application sets (not all options are listed below):

- applications with numbers $$$1, 4$$$ and $$$5$$$. In this case, it will free $$$a_1+a_4+a_5=10$$$ units of memory and lose $$$b_1+b_4+b_5=5$$$ convenience points;
- applications with numbers $$$1$$$ and $$$3$$$. In this case, it will free $$$a_1+a_3=7$$$ units of memory and lose $$$b_1+b_3=3$$$ convenience points.
- applications with numbers $$$2$$$ and $$$5$$$. In this case, it will free $$$a_2+a_5=7$$$ memory units and lose $$$b_2+b_5=2$$$ convenience points.

Help Polycarp, choose a set of applications, such that if removing them will free at least $$$m$$$ units of memory and lose the minimum number of convenience points, or indicate that such a set does not exist.

Input

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

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le 10^9$$$) — the number of applications on Polycarp's phone and the number of memory units to be freed.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the number of memory units used by applications.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le 2$$$) — the convenience points of each application.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output on a separate line:

- -1, if there is no set of applications, removing which will free at least $$$m$$$ units of memory;
- the minimum number of convenience points that Polycarp will lose if such a set exists.

Example

Input

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

Output

2 -1 6 4 3

Note

In the first test case, it is optimal to remove applications with numbers $$$2$$$ and $$$5$$$, freeing $$$7$$$ units of memory. $$$b_2+b_5=2$$$.

In the second test case, by removing the only application, Polycarp will be able to clear only $$$2$$$ of memory units out of the $$$3$$$ needed.

In the third test case, it is optimal to remove applications with numbers $$$1$$$, $$$2$$$, $$$3$$$ and $$$4$$$, freeing $$$10$$$ units of memory. $$$b_1+b_2+b_3+b_4=6$$$.

In the fourth test case, it is optimal to remove applications with numbers $$$1$$$, $$$3$$$ and $$$4$$$, freeing $$$12$$$ units of memory. $$$b_1+b_3+b_4=4$$$.

In the fifth test case, it is optimal to remove applications with numbers $$$1$$$ and $$$2$$$, freeing $$$5$$$ units of memory. $$$b_1+b_2=3$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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