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D. Cleaning the Phone
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Polycarp 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. $b_1+b_2=3$.