Problem:
Score : 400 points

Problem Statement

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.)

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.

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

Output

Print Q lines. The i-th line should contain the answer to the i-th query.

Sample Input 1

2 3 4
100
600
400
900
1000
150
2000
899
799

Sample Output 1

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 Input 2

1 1 3
1
10000000000
2
9999999999
5000000000

Sample Output 2

10000000000
10000000000
14999999998

The road is quite long, and we may need to travel a distance that does not fit into a 32-bit integer.

Solution in Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

# debug
debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if debugFlag

# util functions
def find_posmin(arr)
  m = arr.max
  arr.each do |e_i|
    m = e_i if e_i > 0 and m > e_i
  end
  return m
end

# input
a, b, q = $stdin.gets.chomp.split(" ").map(&:to_i)
shrs = []
a.times do
  shrs << $stdin.gets.chomp.to_i
end

tmps = []
b.times do
  tmps << $stdin.gets.chomp.to_i
end

xs = []
q.times do
  xs << $stdin.gets.chomp.to_i
end

# input check
if debugFlag
  p "--- INPUT (begin) ---"
  p shrs
  p tmps
  p xs
  p "--- INPUT (end) ---"
  print "\n"
end

# body
if debugFlag
end

xs.each do |x_i|
  sw = nil
  se = nil
  tw = nil
  te = nil
  shrs.size.times do |j|
    if x_i <= shrs[j]
      sw = shrs[j - 1]  # can be nil
      se = shrs[j]
      break
    end
  end
  if se == nil
    sw = shrs[-1]
  elsif se == shrs[0]
    sw = nil
  end

  tmps.size.times do |j|
    if x_i <= tmps[j]
      tw = tmps[j - 1]  # can be nil
      te = tmps[j]
      break
    end
  end
  if te == nil
    tw = tmps[-1]
  elsif te == tmps[0]
    tw = nil
  end

  if debugFlag
    p x_i
    print "sw:"  
    p sw
    print "se:"    
    p se
    print "tw:"      
    p tw
    print "te:"        
    p te
  end

  cur = x_i
  costs = []
  [te, tw].each do |t|
    tmp_cost = 0
    next if t == nil
    tmp_cost += (cur - t).abs
    [se, sw].each do |s|
      next if s == nil
      costs << (t - s).abs + tmp_cost
    end
  end
  if te != nil and se != nil and te >= se
    costs << (cur - te).abs
  end
  if tw != nil and sw != nil and tw <= sw
    costs << (cur - tw).abs
  end

  cur = x_i
  [se, sw].each do |s|
    tmp_cost = 0
    next if s == nil
    tmp_cost += (cur - s).abs
    [te, tw].each do |t|
      next if t == nil
      costs << (s - t).abs + tmp_cost
    end
  end
  if te != nil and se != nil and te >= se
    costs << (cur - se).abs
  end
  if sw != nil and tw != nil and sw <= tw
    costs << (cur - sw).abs
  end
  #p costs
  #print "---"
  p costs.min
end