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 C++ (GCC 9.2.1) (judge verdict: Accepted)

/*
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

#include <boost/rational.hpp>
*/
#include <bits/stdc++.h>
using namespace std;
#define _GLIBCXX_DEBUG
#define rep(i,t) for (ll i = (ll)(0); i < (ll)(t); i++)
#define rep2(i,s,t) for (ll i = (ll)(s); i < (ll)(t); i++)
#define rep3(i,t) for (ll i = (ll)(1); i <= (ll)(t); i++)
#define rep4(i,s,t) for (ll i = (ll)(s); i <= (ll)(t); i++)
#define repr(i,t) for (ll i = (t-1); i>=(0);i--)
#define repr2(i,s,t) for (ll i = (t-1); i>=(s);i--)
#define repr3(i,t) for (ll i = (t); i>=(1);i--)
#define repr4(i,s,t) for (ll i = (t); i>=(s);i--)
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc =pair<char,char>;
using pll = pair<ll,ll>;
using pii = pair<int,int>;
using pdd = pair<double,double>;
using tuplis = array<ll,3>;
template<class T> using pq = priority_queue<T,vector<T>,greater<T>>;
inline const ll LINF = 0x1fffffffffffffff;
inline const ll MINF = 0x7fffffffffff;
inline const int INF = 0x3fffffff;
inline const int mod=1000000007;
//inline const int mod=998244353;



inline const ld DINF = numeric_limits<ld>::infinity();
inline const ld EPS=1e-9;
inline const ld PI=acos(-1);
//const ll dx[] ={0,1,0,-1,1,-1,1,-1};
//const ll dy[] ={1,0,-1,0,1,1,-1,-1};
inline const bool grindin(const int i,const int j,const int H,const int W){return i>=0&&i<H&&j>=0&&j<W;}
inline const ll dx[] ={0,1,0,-1};
inline const ll dy[] ={1,0,-1,0};
#define is_low(c) ('a'<=c)&&(c<='z')
#define is_upp(c) ('A'<=c)&&(c<='Z')
#define each1(i,a) for(auto&& i:a)
#define each2(x,y,a) for(auto&& [x,y]:a)
#define each3(x,y,z,a) for(auto&& [x,y,z]:a)
#define rrep(n) for(ll i=(n);i--;)
#define stlen(s) ll s.size()-1
#define all(v) begin(v), end(v)
#define range(v,a) begin(v),begin(v)+a
#define range2(v,a,b) begin(v)+a,begin(v)+b
#define range3(v,a) begin(v)+1,begin(v)+a+1
#define range4(v,a,b) begin(v)+a+1,begin(v)+b+1
#define allr(v) rbegin(v), v.rend(v)
#define ranger(v,a) rbegin(v),rbegin(v)+a
#define ranger2(v,a,b) rbegin(v)+a,rbegin(v)+b
#define ranger3(v,a) rbegin(v)+1,rbegin(v)+a+1
#define ranger4(v,a,b) rbegin(v)+a+1,rbegin(v)+b+1
#define cout(n) cout<<std::fixed<<std::setprecision(n)
//#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a)); a.erase(unique(all(a))),end(a))
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size); in(name)
#define vv(type,name,h,...) vector<vector<type>> name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>> name(h,vector<type>(w)); in(name)
template<class T> inline const auto min(const T& a){ return *min_element(all(a));}
template<class T> inline const auto max(const T& a){ return *max_element(all(a));}
inline const ll popcnt(const ull a){return __builtin_popcountll(a);}
inline const ll gcd(ll a,ll b){while(b){ll c=b; b=a%b;a=c;}return a;}
inline const ll lcm(ll a,ll b){unless(a&&b) return 0;return a*b/gcd(a,b);}
inline const ll intpow(ll a,ll b){ll ans=1; while(b){if(b&1)ans*=a;a *=a; b/=2;}return ans;}
inline const ll modpow(ll a,ll b, ll p=mod){ll ans=1; while(b){if(b&1)(ans*=a)%=p;(a*=a)%=p;b/=2;}return ans;}
template<class T,class U>inline const bool chmin(T& a,const U& b){if(a>b){a=b;return 1;}return 0;}
template<class T,class U>inline const bool chmax( T& a,const U& b){if(a<b){a=b;return 1;}return 0;}
inline const vector<ll> iota(const ll n){vector<ll> a(n); iota(all(a),0);return a;}
inline const vector<pll> factor(ull x){vector<pll> ans; for(ull i=2;i*i<=x;i++)if(x%i==0){ans.push_back({i,1});while((x/=i)%i==0)ans.back().second++;}if(x!=1)ans.push_back({x,1});return ans;}
inline const map<ll,ll> factor_map(ull x){map<ll,ll> ans; for(ull i=2; i*i<=x;i++)if(x%i==0){ans[i]=1;while((x/=i)%i==0)ans[i]++;}if(x!=1)ans[x]=1;return ans;}
inline const vector<ll> divisor(ull x){vector<ll> ans; for(ull i=2;i*i<=x;i++)if(x%i==0)ans.push_back(i);rrep(ans.size()-(ans.back()*ans.back()==x))ans.push_back(x/ans[i]);return ans;}
inline const int scan() {return getchar();}
inline const void scan(int &a){scanf("%d", &a);}
inline const void scan(unsigned& a){scanf("%u",&a);}
inline const void scan(long& a){scanf("%ld",&a);}
inline const void scan(long long& a){scanf("%lld", &a);}
inline const void scan(char& a){ do{a=getchar();}while(a==' '||a=='\n');}
inline const void scan(float& a){ scanf("%f",&a);}
inline const void scan(double& a){ scanf("%lf",&a);}
inline const void scan(long double& a){ scanf("%Lf",&a);}
inline const void scan( string& a){cin>> a;}
template<class T>inline const void scan( vector<T>& a){for(auto&& i:a)scan(i);}
template<class T,size_t size>inline const void scan(array<T, size>& a){for(auto&& i:a)scan(i);}
template<class T,class L>inline const void scan( pair<T,L>&p){scan(p.first);scan(p.second);}
template<class T,size_t size>inline const void scan( T (&a)[size]){ for(auto&& i:a)scan(i);}
inline const void in(){}
template <class Head,class... Tail>inline const void in( Head& head, Tail&... tail){scan(head);in(tail...);}
inline const int ctoi(const char c){if(c>='a'&&c<='z'){return c-'a';} if(c>='A'&&c<='Z'){return c-'A';}return -1;}
inline const void print(){putchar(' ');}
inline const void print(const bool a){printf("%d", a);}
inline const void print(const int a){printf("%d",a);}
inline const void print(const unsigned a){ printf("%u",a);}
inline const void print(const long a){printf("%ld",a);}
inline const void print(const unsigned long long a){printf("%llu",a);}
inline const void print(const char a){ printf("%c",a);}
inline const void print(const double a){printf("%.15f",a);}
inline const void print(const long double a){printf("%.15Lf",a);}
inline const void print(const string&a){for(auto&&i :a)print(i);}
template<class T> inline const void print(const vector<T> &a){if(a.empty())return ;print(a[0]);for(auto i=a.begin();++i!=a.end();){putchar(' ');print(*i);}}
template<class T> inline const void print(const deque<T>&a ){if(a.empty())return;print(a[0]);for(auto i=a.begin(); ++i!=a.end();){putchar(' ');print(*i);}}
template<class T, size_t size>inline const void print(const T (&a)[size]){print(a[0]);for(auto i=a;++i!=end(a);){putchar(' ');print(*i);}}
template<class T>inline const void print(const T& a){cout<<a;}
inline const int out(){putchar('\n');return 0;}
template<class T> inline const int out(const T& t){print(t);putchar('\n');return 0;}
template<class Head,class... Tail>inline const int out(const Head& head,const Tail&... tail){print(head);putchar(' ');out(tail...);return 0;}
inline const int first(const bool i){return out(i?"first":"second");}
inline const int yes(const bool i){return out(i?"yes":"no");}
inline const int Yes(const bool i){return out(i?"Yes":"No");}
inline const int YES(const bool i){return out(i?"YES":"NO");}
inline const int possible(const bool i){return out(i?"possible":"impossible");}
inline const int Possible(const bool i){return out(i?"Possible":"Impossible");}
inline const int POSSIBLE(const bool i){return out(i?"POSSIBLE":"IMPOSSIBLE");}

 
using Graph = vector<vector<int>>;
using Graphw = vector<vector<pair<ll,ll>>>;
using mat = vector<vector<ll>>;
using vec = vector<ll>;

/*
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部長が32の浮動小数点数型
using Real32 = mp::number<mp::cpp_dec_float<32>>;
// 仮数部長が1024の浮動小数点数型
using Real1024 = mp::number<mp::cpp_dec_float<1024>>;
// 有理数型
using Rat = boost::rational<Bint>;
*/

signed main(){



INT(A,B);
INT(Q);
vector<pair<ll,int>> change;
ll s[A],t[B],x[Q];
map<ll,int> xtochange;


rep(i,A){
    cin>>s[i];
    change.push_back({s[i],0});
}
rep(i,B){
    cin>>t[i];
    change.push_back({t[i],1});
}
rep(i,Q){
    cin>>x[i];
    change.push_back({x[i],2});
}
Sort(change);

rep(i,change.size()){
    if(change[i].second==2){
        xtochange[change[i].first]=i;
    }

}
ll max_l[change.size()][2],min_r[change.size()][2];//0 神社 1 寺社
rep(i,change.size())rep(j,2){
 max_l[i][j]=-MINF; 
 min_r[i][j]=MINF;
}
rep(i,change.size()){
    if(i!=0){
        rep(j,2){
            chmax(max_l[i][j],max_l[i-1][j]);
            
        }
    }
    if(change[i].second!=2){
        chmax(max_l[i][change[i].second],change[i].first);
        
    }
}
repr(i,change.size()){
    if(i!=change.size()-1){
        rep(j,2){
            chmin(min_r[i][j],min_r[i+1][j]);
            
        }
    }
    if(change[i].second!=2){
        chmin(min_r[i][change[i].second],change[i].first);
        
    }
}
ll ans[Q];
rep(i,Q){
    int p=xtochange[x[i]];
    ans[i]=MINF;
    chmin(ans[i],max(min_r[p][0]-x[i],min_r[p][1]-x[i]));
    
    chmin(ans[i],min(min_r[p][0]-x[i]+min_r[p][0]-max_l[p][1],x[i]-max_l[p][1]+min_r[p][0]-max_l[p][1]));
    
    chmin(ans[i],min(min_r[p][1]-x[i]+min_r[p][1]-max_l[p][0],x[i]-max_l[p][0]+min_r[p][1]-max_l[p][0]));
    
    chmin(ans[i],max(x[i]-max_l[p][0],x[i]-max_l[p][1]));
    out(ans[i]);
    
}


}