Minimal Segment Cover

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 2 \cdot 10^5$$$) — the number of intervals and the number of queries, respectively.

Each of the next $$$n$$$ lines contains two integer numbers $$$l_i$$$ and $$$r_i$$$ ($$$0 \le l_i < r_i \le 5 \cdot 10^5$$$) — the given intervals.

Each of the next $$$m$$$ lines contains two integer numbers $$$x_i$$$ and $$$y_i$$$ ($$$0 \le x_i < y_i \le 5 \cdot 10^5$$$) — the queries.

Output:

Print $$$m$$$ integer numbers. The $$$i$$$-th number should be the answer to the $$$i$$$-th query: either the minimal number of intervals you have to take so that every point (not necessarily integer) from $$$x_i$$$ to $$$y_i$$$ is covered by at least one of them or -1 if you can't choose intervals so that every point from $$$x_i$$$ to $$$y_i$$$ is covered.

Sample Input:

2 3
1 3
2 4
1 3
1 4
3 4

Sample Output:

1
2
1

Sample Input:

3 4
1 3
1 3
4 5
1 2
1 3
1 4
1 5

Sample Output:

1
1
-1
-1

Note:

In the first example there are three queries:

1. query $$$[1; 3]$$$ can be covered by interval $$$[1; 3]$$$;
2. query $$$[1; 4]$$$ can be covered by intervals $$$[1; 3]$$$ and $$$[2; 4]$$$. There is no way to cover $$$[1; 4]$$$ by a single interval;
3. query $$$[3; 4]$$$ can be covered by interval $$$[2; 4]$$$. It doesn't matter that the other points are covered besides the given query.

In the second example there are four queries:

1. query $$$[1; 2]$$$ can be covered by interval $$$[1; 3]$$$. Note that you can choose any of the two given intervals $$$[1; 3]$$$;
2. query $$$[1; 3]$$$ can be covered by interval $$$[1; 3]$$$;
3. query $$$[1; 4]$$$ can't be covered by any set of intervals;
4. query $$$[1; 5]$$$ can't be covered by any set of intervals. Note that intervals $$$[1; 3]$$$ and $$$[4; 5]$$$ together don't cover $$$[1; 5]$$$ because even non-integer points should be covered. Here $$$3.5$$$, for example, isn't covered.