Tracking Segments
Description
You are given an array $a$ consisting of $n$ zeros. You are also given a set of $m$ not necessarily different segments. Each segment is defined by two numbers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le n$) and represents a subarray $a_{l_i}, a_{l_i+1}, \dots, a_{r_i}$ of the array $a$.
Let's call the segment $l_i, r_i$ beautiful if the number of ones on this segment is strictly greater than the number of zeros. For example, if $a = [1, 0, 1, 0, 1]$, then the segment $[1, 5]$ is beautiful (the number of ones is $3$, the number of zeros is $2$), but the segment $[3, 4]$ is not is beautiful (the number of ones is $1$, the number of zeros is $1$).
You also have $q$ changes. For each change you are given the number $1 \le x \le n$, which means that you must assign an element $a_x$ the value $1$.
You have to find the first change after which at least one of $m$ given segments becomes beautiful, or report that none of them is beautiful after processing all $q$ changes.
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 $m$ ($1 \le m \le n \le 10^5$) — the size of the array $a$ and the number of segments, respectively.
Then there are $m$ lines consisting of two numbers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le n$) —the boundaries of the segments.
The next line contains an integer $q$ ($1 \le q \le n$) — the number of changes.
The following $q$ lines each contain a single integer $x$ ($1 \le x \le n$) — the index of the array element that needs to be set to $1$. It is guaranteed that indexes in queries are distinct.
It is guaranteed that the sum of $n$ for all test cases does not exceed $10^5$.
For each test case, output one integer — the minimum change number after which at least one of the segments will be beautiful, or $-1$ if none of the segments will be beautiful.
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 $m$ ($1 \le m \le n \le 10^5$) — the size of the array $a$ and the number of segments, respectively.
Then there are $m$ lines consisting of two numbers $l_i$ and $r_i$ ($1 \le l_i \le r_i \le n$) —the boundaries of the segments.
The next line contains an integer $q$ ($1 \le q \le n$) — the number of changes.
The following $q$ lines each contain a single integer $x$ ($1 \le x \le n$) — the index of the array element that needs to be set to $1$. It is guaranteed that indexes in queries are distinct.
It is guaranteed that the sum of $n$ for all test cases does not exceed $10^5$.
Output
For each test case, output one integer — the minimum change number after which at least one of the segments will be beautiful, or $-1$ if none of the segments will be beautiful.
6
5 5
1 2
4 5
1 5
1 3
2 4
5
5
3
1
2
4
4 2
1 1
4 4
2
2
3
5 2
1 5
1 5
4
2
1
3
4
5 2
1 5
1 3
5
4
1
2
3
5
5 5
1 5
1 5
1 5
1 5
1 4
3
1
4
3
3 2
2 2
1 3
3
2
3
1
3
-1
3
3
3
1
Note
In the first case, after first 2 changes we won't have any beautiful segments, but after the third one on a segment $[1; 5]$ there will be 3 ones and only 2 zeros, so the answer is 3.
In the second case, there won't be any beautiful segments.