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++14 (GCC 5.4.1) (judge verdict: Accepted)

//include
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <climits>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <queue>
#include <random>
#include <cctype>
#include <complex>
#include <regex>
#include <unordered_map>


using namespace std;

//typedef
//------------------------------------------
typedef long long LL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<char> VC;
typedef vector<double> VD;
typedef vector<string> VS;
typedef vector<LL> VLL;
typedef vector<VI> VVI;
typedef vector<VB> VVB;
typedef vector<VS> VVS;
typedef vector<VLL> VVLL;
typedef vector<VVI> VVVI;
typedef vector<VVLL> VVVLL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<int, string> PIS;
typedef pair<string, int> PSI;
typedef pair<string, string> PSS;
typedef vector<PII> VPII;
typedef vector<PLL> VPLL;
typedef vector<VPII> VVPII;
typedef vector<VPLL> VVPLL;
typedef vector<VS> VVS;
typedef map<int, int> MII;
typedef map<LL, LL> MLL;
typedef map<string, int> MSI;
typedef map<int, string> MIS;

//数値・文字列
//------------------------------------------
inline int toInt(string s) {
    int v;
    istringstream sin(s);
    sin >> v;
    return v;
}

inline LL toLongLong(string s) {
    LL v;
    istringstream sin(s);
    sin >> v;
    return v;
}

template<class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}

inline VC toVC(string s) {
    VC data(s.begin(), s.end());
    return data;
}

template<typename List>
void SPRIT(const std::string &s, const std::string &delim, List &result) {
    result.clear();
    string::size_type pos = 0;
    while (pos != string::npos) {
        string::size_type p = s.find(delim, pos);
        if (p == string::npos) {
            result.push_back(s.substr(pos));
            break;
        } else {
            result.push_back(s.substr(pos, p - pos));
        }
        pos = p + delim.size();
    }
}

vector<string> SPRIT(const std::string &s, const std::string &delim) {
    vector<string> result;
    string::size_type pos = 0;
    while (pos != string::npos) {
        string::size_type p = s.find(delim, pos);
        if (p == string::npos) {
            result.push_back(s.substr(pos));
            break;
        } else {
            result.push_back(s.substr(pos, p - pos));
        }
        pos = p + delim.size();
    }
    return result;
}

string TRIM(const string &str, const char *trimCharacterList = " \t\v\r\n") {
    string result;
    string::size_type left = str.find_first_not_of(trimCharacterList);
    if (left != string::npos) {
        string::size_type right = str.find_last_not_of(trimCharacterList);
        result = str.substr(left, right - left + 1);
    }
    return result;
}

string REPLACE_STRING(const string source, const string find, const string alt) {
    string result = source;
    string::size_type pos = 0;
    while (pos = result.find(find, pos), pos != string::npos) {
        result.replace(pos, find.length(), alt);
        pos += alt.length();
    }
    return result;
}

template<typename T>
bool VECTOR_EXISTS(vector<T> vec, T data) {
    auto itr = std::find(vec.begin(), vec.end(), data);
    size_t index = distance(vec.begin(), itr);
    if (index != vec.size())return true;
    else return false;
}

template<typename T>
vector<T> VECTOR_UNIQUE_ERASE(vector<T> vec) {
    sort(vec.begin(), vec.end());
    vec.erase(unique(vec.begin(), vec.end()), vec.end());
    return vec;
}

template<typename T>
void VECTOR_REMOVE_VALUE_ALL(vector<T> &vec, T data) {
    vec.erase(remove(vec.begin(), vec.end(), data), vec.end());
}

template<typename T>
vector<T> VECTOR_REMOVE_VALUE_ALL_FAST(vector<T> vec, T data) {
    vector<T> vec2;
    for (auto &x: vec) if (x != data) vec2.push_back(x);
    return vec2;
}

bool REG_MATCH(string const &text, regex const &re) {
    bool result = regex_match(text, re);
    return result;
}

bool REG_MATCH(string const &text, smatch &match, regex const &re) {
    bool result = regex_match(text, match, re);
    return result;
}

smatch REG_SEARCH(string const &text, regex const &re) {
    smatch m;
    regex_search(text, m, re);
    return m;
}

vector<smatch> REG_ALL_SEARCH(string const &text, regex const &re) {
    vector<smatch> matchs;
    sregex_iterator iter(text.cbegin(), text.cend(), re);
    sregex_iterator end;
    for (; iter != end; iter++) matchs.push_back(*iter);
    return matchs;
}

string REG_REPLACE(string const &text, regex const &re, string const &replace) {
    string result = regex_replace(text, re, replace, regex_constants::format_first_only);
    return result;
}

string REG_ALL_REPLACE(string const &text, regex const &re, string const &replace) {
    string result = regex_replace(text, re, replace);
    return result;
}

template<typename T, typename U, typename V, typename W>
auto operator+(const std::pair<T, U> &l, const std::pair<V, W> &r) -> std::pair<decltype(l.first + r.first), decltype(
l.second + r.second)> {
    return {l.first + r.first, l.second + r.second};
}

template<typename T, typename U, typename V, typename W>
auto operator-(const std::pair<T, U> &l, const std::pair<V, W> &r) -> std::pair<decltype(l.first - r.first), decltype(
l.second - r.second)> {
    return {l.first - r.first, l.second - r.second};
}

#define UPPER(s) transform((s).begin(), (s).end(), (s).begin(), ::toupper)
#define LOWER(s) transform((s).begin(), (s).end(), (s).begin(), ::tolower)



//四捨五入 nLen=小数点第n位にする
//------------------------------------------

//切り上げ
double ceil_n(double dIn, int nLen) {
    double dOut;
    dOut = dIn * pow(10.0, nLen);
    dOut = (double) (long long) (dOut + 0.9);
    return dOut * pow(10.0, -nLen);
}

//切り捨て
double floor_n(double dIn, int nLen) {
    double dOut;
    dOut = dIn * pow(10.0, nLen);
    dOut = (double) (long long) (dOut);
    return dOut * pow(10.0, -nLen);
}

//四捨五入
double round_n(double dIn, int nLen) {
    double dOut;
    dOut = dIn * pow(10.0, nLen);
    dOut = (double) (long long) (dOut + 0.5);
    return dOut * pow(10.0, -nLen);
}

//n桁目の数の取得
int take_a_n(LL num, int n) {
    string str = toString(num);
    return str[str.length() - n] - '0';
}

//整数を2進数表記したときの1の個数を返す
LL bitcount64(LL bits) {
    bits = (bits & 0x5555555555555555) + (bits >> 1 & 0x5555555555555555);
    bits = (bits & 0x3333333333333333) + (bits >> 2 & 0x3333333333333333);
    bits = (bits & 0x0f0f0f0f0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f0f0f0f0f);
    bits = (bits & 0x00ff00ff00ff00ff) + (bits >> 8 & 0x00ff00ff00ff00ff);
    bits = (bits & 0x0000ffff0000ffff) + (bits >> 16 & 0x0000ffff0000ffff);
    return (bits & 0x00000000ffffffff) + (bits >> 32 & 0x00000000ffffffff);
}



//comparison
//------------------------------------------
#define C_MAX(a, b) ((a)>(b)?(a):(b))
#define C_MIN(a, b) ((a)<(b)?(a):(b))
#define C_ABS(a, b) ((a)<(b)?(b)-(a):(a)-(b))

template<typename T1, typename T2>
inline void S_MAX(T1 &a, T2 b) { a = C_MAX(a, b); };

template<typename T1, typename T2>
inline void S_MIN(T1 &a, T2 b) { a = C_MIN(a, b); };


//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define EACH(i, arr) for(typeof((arr).begin()) i=(arr).begin(); i!=(arr).end(); ++i)
#define EXIST(str, e) ((str).find(e)!=(str).end())
#define COUNT(arr, v) count((arr).begin(), (arr).end(), v)
#define SEARCH(v, w) search((v).begin(), (v).end(), (w).begin(), (w).end())
#define B_SEARCH(arr, v) binary_search((arr).begin(), (arr).end(), v)
#define SORT(c) sort((c).begin(),(c).end())
#define RSORT(c) sort((c).rbegin(),(c).rend())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define ROTATE_LEFT(arr, c) rotate((arr).begin(), (arr).begin()+(c), (arr).end())
#define ROTATE_RIGHT(arr, c) rotate((arr).rbegin(), (arr).rbegin() + (c), (arr).rend())
#define SUMI(arr) accumulate((arr).begin(), (arr).end(), 0)
#define SUMD(arr) accumulate((arr).begin(), (arr).end(), 0.)
#define SUMLL(arr) accumulate((arr).begin(), (arr).end(), 0LL)
#define SUMS(arr) accumulate((arr).begin(), (arr).end(), string())
#define UB(arr, n) upper_bound((arr).begin(), (arr).end(), n)
#define LB(arr, n) lower_bound((arr).begin(), (arr).end(), n)
#define OF_ALL(arr, func) all_of((arr).begin(), (arr).end(), (func))
#define OF_NONE(arr, func) none_of((arr).begin(), (arr).end(), (func))
#define OF_ANY(arr, func) any_of((arr).begin(), (arr).end(), (func))
#define PB push_back
#define MP make_pair
#define ft first
#define sd second



//input output
//------------------------------------------
#define GL(s) getline(cin, (s))
#define INIT() std::ios::sync_with_stdio(false);std::cin.tie(0);
#define OUT(d) std::cout<<(d)
#define OUT_L(d) std::cout<<(d)<<endl
#define FOUT(n, data) std::cout<<std::fixed<<std::setprecision(n)<<(data)
#define FOUT_L(n, data) std::cout<<std::fixed<<std::setprecision(n)<<(data)<<"\n"
#define EL() printf("\n")
#define SHOW_VECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOW_MAP(v) {std::cerr << #v << endl; for(const auto& xxx: v){std::cerr << xxx.first << " " << xxx.second << "\n";}}
#define Yes() printf("Yes\n")
#define No() printf("No\n")
#define YES() printf("YES\n")
#define NO() printf("NO\n")


template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}

template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}




//repetition
//------------------------------------------
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n)  FOR(i,0,n)
#define RREP(i, n) for(int i = n-1;i >= 0;i--)
#define FORLL(i, a, b) for(LL i=LL(a);i<LL(b);++i)
#define RFORLL(i, a, b) for(LL i=LL(b)-1;i>=LL(a);--i)
#define REPLL(i, n) for(LL i=0;i<LL(n);++i)
#define RREPLL(i, n) for(LL i=LL(n)-1;i>=0;--i)
#define FOREACH(x, arr) for(auto &(x) : (arr))
#define FORITER(x, arr) for(auto (x) = (arr).begin(); (x) != (arr).end(); ++(x))


//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};


//math
//--------------------------------------------

//min <= aim <= max
template<typename T>
inline bool BETWEEN(const T aim, const T min, const T max) {
    if (min <= aim && aim <= max) {
        return true;
    } else {
        return false;
    }
}

template<typename T1, typename T2>
inline bool IS_OUT(const T1 toY, const T1 toX, const T2 H, const T2 W) {
    return (toY < 0 || toY >= H || toX < 0 || toX >= W);
}

template<class T>
inline T SQR(const T x) { return x * x; }

template<class T1, class T2>
inline T1 POW(const T1 x, const T2 y) {
    if (!y)return 1;
    else if ((y & 1) == 0) {
        return SQR(POW(x, y >> 1));
    } else return POW(x, y ^ 1) * x;
}


template<typename T>
constexpr T ABS(T x) {
    return x < 0 ? -x : x;
}

//partial_permutation nPr 順列
//first・・最初の数
//middle・・r(取り出す数)
//last・・n(全体数)
template<class Iter>
bool next_partial_permutation(Iter first, Iter middle, Iter last) {
    reverse(middle, last);
    return next_permutation(first, last);
}

//combination nCr 組み合わせ
//first1・・最初の数
//last1==first2・・r(取り出す数)
//last2・・n(全体数)
template<class Iter>
bool next_combination(Iter first1, Iter last1, Iter first2,
                      Iter last2) {
    if ((first1 == last1) || (first2 == last2)) {
        return false;
    }
    Iter m1 = last1;
    Iter m2 = last2;
    --m2;
    while (--m1 != first1 && !(*m1 < *m2)) {
    }
    bool result = (m1 == first1) && !(*first1 < *m2);
    if (!result) {
        while (first2 != m2 && !(*m1 < *first2)) {
            ++first2;
        }
        first1 = m1;
        std::iter_swap(first1, first2);
        ++first1;
        ++first2;
    }
    if ((first1 != last1) && (first2 != last2)) {
        m1 = last1;
        m2 = first2;
        while ((m1 != first1) && (m2 != last2)) {
            std::iter_swap(--m1, m2);
            ++m2;
        }
        std::reverse(first1, m1);
        std::reverse(first1, last1);
        std::reverse(m2, last2);
        std::reverse(first2, last2);
    }
    return !result;
}




//numeric_law
//--------------------------------------------

template<typename T>
constexpr bool ODD(T x) {
    return x % 2 != 0;
}

template<typename T>
constexpr bool EVEN(T x) {
    return x % 2 == 0;
}

//最大公約数
template<class T>
inline T GCD(const T x, const T y) {
    if (x < 0)return GCD(-x, y);
    if (y < 0)return GCD(x, -y);
    return (!y) ? x : GCD(y, x % y);
}

//最小公倍数
template<class T>
inline T LCM(const T x, const T y) {
    if (x < 0)return LCM(-x, y);
    if (y < 0)return LCM(x, -y);
    return x * (y / GCD(x, y));
}

//ax + by = 1
//x,yが変数に格納される
template<class T>
inline T EXTGCD(const T a, const T b, T &x, T &y) {
    if (a < 0) {
        T d = EXTGCD(-a, b, x, y);
        x = -x;
        return d;
    }
    if (b < 0) {
        T d = EXTGCD(a, -b, x, y);
        y = -y;
        return d;
    }
    if (!b) {
        x = 1;
        y = 0;
        return a;
    } else {
        T d = EXTGCD(b, a % b, x, y);
        T t = x;
        x = y;
        y = t - (a / b) * y;
        return d;
    }
}

//素数
template<class T>
inline bool ISPRIME(const T x) {
    if (x <= 1)return false;
    for (T i = 2; i * i <= x; i++)if (x % i == 0)return false;
    return true;
}

//素数をtrueとして返す
template<class T>
VB ERATOSTHENES(const T n) {
    VB arr(n + 1, true);
    arr[0] = arr[1] = false;
    for (LL i = 2; i * i <= n; i++) {
        if (arr[i]) {
            for (LL j = i * 2LL; j <= n; j += i) {
                arr[j] = false;
            }
        }
    }
    return arr;
}

// a <= x < b の素数を返す
template<typename T>
VB ERATOSTHENES(const T a, const T b) {
    VB small = ERATOSTHENES(b);
    VB prime(b - a, true);

    for (LL i = 2; i * i <= b; i++) {
        if (small[i]) {
            for (LL j = max(2LL, (a + i - 1) / i) * i; j < b; j += i) {
                prime[j - a] = false;
            }
        }
    }

    return prime;
}

//nの約数
template<typename T>
vector<T> DIVISOR(T n) {
    vector<T> v;
    for (LL i = 1; i * i <= n; ++i) {
        if (n % i == 0) {
            v.push_back(i);
            if (i != n / i) {
                v.push_back(n / i);
            }
        }
    }
    sort(v.begin(), v.end());
    return v;
}

//nまでのすべての約数
template<typename T>
vector<vector<T>> DIVISOR_ALL(T n) {
    vector<vector<T>> res(n + 1);
    for (LL i = 1; i <= n; i++) {
        for (LL j = i; j <= n; j += i) {
            res[j].push_back(i);
        }
    }
    return res;
}

//素因数分解
template<typename T>
vector<pair<T, LL>> FACTORIZATION(T x) {
    vector<pair<T, LL>> ans;
    for (LL i = 2; i * i <= x; i++) {
        if (x % i == 0) {
            LL count = 0;
            while (x % i == 0) {
                count++;
                x /= i;
            }
            ans.push_back(MP(i, count));
        }
    }
    if (x != 1) ans.push_back(MP(x, 1));
    return ans;
}

//N^P (mod M)
LL POW_MOD(LL N, LL P, LL M) {
    if (P == 0) return 1LL;
    if (P % 2 == 0) {
        LL ret = POW_MOD(N, P / 2, M);
        return ret * ret % M;
    }
    return N * POW_MOD(N, P - 1, M) % M;
}

//組み合わせ個数
template<typename T>
inline T NCR(T n, T r) {
    if (r > n - r) r = n - r;
    T ans = 1;
    REPLL(i, r) {
        ans = ans * (n - i) / (i + 1);
    }
    return ans;
}

//組み合わせ個数 (mod M)
LL NCR_MOD(LL n, LL r, LL M) {
    if (r > n - r) return NCR_MOD(n, n - r, M);
    LL numerator = 1LL; //分子
    LL denominator = 1LL; //分母
    for (LL i = 0; i < r; i++) {
        numerator *= (n - i);
        numerator %= M;
        denominator *= (i + 1);
        denominator %= M;
    }
    return numerator * POW_MOD(denominator, M - 2, M) % M;
}

//confirmation
//--------------------------------------------

//clear memory
#define CLR(arr, d) memset((arr), (d),sizeof(arr))

//debug
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " "  << endl;


/*
 *
 *
 *       Below My Answer
 *       _(＾～＾ ｣ ∠)_
 *
 *
 */

LL INF = 1e14;

int main() {

    LL A, B, Q;
    cin>> A >> B >> Q;

    VLL s(A + 1);
    s[0] = -INF;
    for(int i = 0;i <A;i++) cin >> s[i + 1];
    s.push_back(INF);
    s.push_back(INF);

    VLL t(B + 1);
    t[0] = -INF;
    for(int i = 0;i<B;i++) cin >> t[i + 1];
    t.push_back(INF);
    t.push_back(INF);

    while(Q--){
        LL x;
        cin >> x;

        auto ss = lower_bound(s.begin(), s.end(), x);
        auto tt = lower_bound(t.begin(), t.end(), x);

        LL ans = INF;
        for(int i = -1;i<=1;i++){
            auto sss = ss + i;
            if(abs(*sss) == INF) continue;
            for(int j = -1;j<=1;j++){
                auto ttt = tt + j;
                if(abs(*ttt) == INF) continue;
                LL d = INF;
                if(*sss <= x && *ttt <= x){
                    d = min(d, x - min(*sss, *ttt));
                }else if(*sss >= x && *ttt >= x){
                    d = min(d, max(*sss, *ttt) - x);
                }else{
                    LL d1 = min(abs(*sss - x), abs(*ttt - x));
                    LL d2 = max(abs(*sss - x), abs(*ttt - x));
                    d = min(d, 2 * d1 + d2);
                }
                ans = min(ans, d);
            }
        }
        cout << ans << endl;
    }

    return 0;
}