10546: ABC119 —— D - Lazy Faith
[Creator : ]
Description
Along a road running in an east-west direction, there are $A$ shrines and $B$ temples. The $i$-th shrine from the west is located at a distance of $s_i$ meters from the west end of the road, and the $i$-th temple from the west is located at a distance of $t_i$ meters from the west end of the road.
Answer the following $Q$ queries:
- Query $i$ ($1 \leq i \leq Q$): If we start from a point at a distance of $x_i$ meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required.)
Answer the following $Q$ queries:
- Query $i$ ($1 \leq i \leq Q$): If we start from a point at a distance of $x_i$ meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required.)
Input
Input is given from Standard Input in the following format:
```
$A$ $B$ $Q$
$s_1$
$:$
$s_A$
$t_1$
$:$
$t_B$
$x_1$
$:$
$x_Q$
```
```
$A$ $B$ $Q$
$s_1$
$:$
$s_A$
$t_1$
$:$
$t_B$
$x_1$
$:$
$x_Q$
```
Output
Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.
Constraints
- $1 \leq A, B \leq 10^5$
- $1 \leq Q \leq 10^5$
- $1 \leq s_1 < s_2 < ... < s_A \leq 10^{10}$
- $1 \leq t_1 < t_2 < ... < t_B \leq 10^{10}$
- $1 \leq x_i \leq 10^{10}$
- $s_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q$ are all different.
- All values in input are integers.
- $1 \leq Q \leq 10^5$
- $1 \leq s_1 < s_2 < ... < s_A \leq 10^{10}$
- $1 \leq t_1 < t_2 < ... < t_B \leq 10^{10}$
- $1 \leq x_i \leq 10^{10}$
- $s_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q$ are all different.
- All values in input are integers.
Sample 1 Input
2 3 4
100
600
400
900
1000
150
2000
899
799
Sample 1 Output
350
1400
301
399
There are two shrines and three temples. The shrines are located at distances of 100,600 meters from the west end of the road, and the temples are located at distances of 400,900,1000 meters from the west end of the road.
- Query 1: If we start from a point at a distance of 150 meters from the west end of the road, the optimal move is first to walk 50 meters west to visit a shrine, then to walk 300 meters east to visit a temple.
- Query 2: If we start from a point at a distance of 2000 meters from the west end of the road, the optimal move is first to walk 1000 meters west to visit a temple, then to walk 400 meters west to visit a shrine. We will pass by another temple on the way, but it is fine.
- Query 3: If we start from a point at a distance of 899 meters from the west end of the road, the optimal move is first to walk 1 meter east to visit a temple, then to walk 300 meters west to visit a shrine.
- Query 4: If we start from a point at a distance of 799 meters from the west end of the road, the optimal move is first to walk 199 meters west to visit a shrine, then to walk 200 meters west to visit a temple.
Sample 2 Input
1 1 3
1
10000000000
2
9999999999
5000000000
Sample 2 Output
10000000000
10000000000
14999999998