Problem:


Score: 400 points

Problem Statement

The Patisserie AtCoder sells cakes with number-shaped candles.
There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively.
Each cake has an integer value called deliciousness, as follows:

The deliciousness of the cakes with 1-shaped candles are A_1, A_2, ..., A_X.

The deliciousness of the cakes with 2-shaped candles are B_1, B_2, ..., B_Y.

The deliciousness of the cakes with 3-shaped candles are C_1, C_2, ..., C_Z.

Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.

There are X \times Y \times Z such ways to choose three cakes.

We will arrange these X \times Y \times Z ways in descending order of the sum of the deliciousness of the cakes.

Print the sums of the deliciousness of the cakes for the first, second, ..., K-th ways in this list.

Constraints

1 \leq X \leq 1 \ 000

1 \leq Y \leq 1 \ 000

1 \leq Z \leq 1 \ 000

1 \leq K \leq \min(3 \ 000, X \times Y \times Z)

1 \leq A_i \leq 10 \ 000 \ 000 \ 000

1 \leq B_i \leq 10 \ 000 \ 000 \ 000

1 \leq C_i \leq 10 \ 000 \ 000 \ 000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y Z K
A_1 \ A_2 \ A_3 \ ... \ A_X
B_1 \ B_2 \ B_3 \ ... \ B_Y
C_1 \ C_2 \ C_3 \ ... \ C_Z

Output

Print K lines. The i-th line should contain the i-th value stated in the problem statement.

Sample Input 1

2 2 2 8
4 6
1 5
3 8

Sample Output 1

19
17
15
14
13
12
10
8

There are 2 \times 2 \times 2 = 8 ways to choose three cakes, as shown below in descending order of the sum of the deliciousness of the cakes:

(A_2, B_2, C_2): 6 + 5 + 8 = 19

(A_1, B_2, C_2): 4 + 5 + 8 = 17

(A_2, B_1, C_2): 6 + 1 + 8 = 15

(A_2, B_2, C_1): 6 + 5 + 3 = 14

(A_1, B_1, C_2): 4 + 1 + 8 = 13

(A_1, B_2, C_1): 4 + 5 + 3 = 12

(A_2, B_1, C_1): 6 + 1 + 3 = 10

(A_1, B_1, C_1): 4 + 1 + 3 = 8

Sample Input 2

3 3 3 5
1 10 100
2 20 200
1 10 100

Sample Output 2

400
310
310
301
301

There may be multiple combinations of cakes with the same sum of the deliciousness. For example, in this test case, the sum of A_1, B_3, C_3 and the sum of A_3, B_3, C_1 are both 301.
However, they are different ways of choosing cakes, so 301 occurs twice in the output.

Sample Input 3

10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736

Sample Output 3

23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547

Note that the input or output may not fit into a 32-bit integer type.



Sample input:
2 2 2 8
4 6
1 5
3 8


Sample output:
19
17
15
14
13
12
10
8

Submission status: Runtime Error

Solution code:
//
//  2019/03/30 Ver1.10
//
//  Codeforces: ganariya
//  AtCoder: ganariya2525
//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMHBYYYWMMMM#BYYTTTYWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
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//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM9Olll=l======??????????>>>>>>;;;;;;;;;:;?TMMMMMMMMMMMMMMMMMMMMMMMMMMMM
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//  MMMMMMMMMMMMMMMMNOtXtdMMMMMNxzZMMNmgHyVVVVVW%..?/(.,(x-..........(HfffpffpffpffWHHffpffppfVyyWMMMMMM


//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;
typedef __int128 Lint;

//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;
}

Lint toLint(const string s) {
    Lint ret = 0;
    for (int i = 0; i < s.length(); i++)
        if ('0' <= s[i] && s[i] <= '9')
            ret = 10 * ret + s[i] - '0';
    return ret;
}

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;
}

vector<string> SPRIT(const string &s, const 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>
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>
vector<T> COMPRESS(vector<T> v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
    return v;
}

template<typename T>
pair<map<T, int>, map<int, T>> MAPPING(const vector<T> v) {
    map<T, int> zip;
    map<int, T> unzip;
    for (int i = 0; i < v.size(); i++) zip[v[i]] = i;
    for (int i = 0; i < v.size(); i++) unzip[i] = v[i];
    return make_pair(zip, unzip);
}

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};
}

ostream &operator<<(ostream &dest, __int128_t value) {
    ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char *d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(ios_base::badbit);
        }
    }
    return dest;
}


#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, long long 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, long long 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, long long 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';
}

int bitcount32(int bits) {
    bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
    bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
    bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
    bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
    return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
}

//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<class T1, class T2>
inline bool chmin(T1 &a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<class T1, class T2>
inline bool chmax(T1 &a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

//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 MULD(arr) accumulate((arr).begin(), (arr).end(), 1., multiplies<double>())
#define MULLL(arr) accumulate((arr).begin(), (arr).end(), 1LL, multiplies<long long>())
#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;
}

istream &operator>>(istream &in, Lint &d) {
    string s;
    cin >> s;
    Lint tmp = 0;
    for (int i = 0; i < s.length(); i++)if ('0' <= s[i] && s[i] <= '9')tmp = 10 * tmp + s[i] - '0';
    d = tmp;
    return in;
}

template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "\n";
    return out;
}


//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 = gcd(a, b)
//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;
    }
}

//mの世界でのaの逆元
//gce(a, m) = 1
template<class T>
inline T INV_MOD(const T a, const T m) {
    T x, y;
    EXTGCD(a, m, x, y);
    return (x + m) % m;
}

//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 (T i = 2; i * i <= n; i++) {
        if (arr[i]) {
            for (T 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 (T i = 2; i * i <= b; i++) {
        if (small[i]) {
            for (T 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 (T 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 (T i = 1; i <= n; i++) {
        for (T j = i; j <= n; j += i) {
            res[j].push_back(i);
        }
    }
    return res;
}

//素因数分解
template<typename T>
vector<pair<T, T>> FACTORIZATION(T x) {
    vector<pair<T, LL>> ans;
    for (T i = 2; i * i <= x; i++) {
        if (x % i == 0) {
            T 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) {
    LL ret = 1;
    while (P > 0) {
        if (P & 1LL) ret = (ret * N) % M;
        N = (N * N) % M;
        P >>= 1LL;
    }
    return ret;
}

//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 = 1LL;
    for (T i = 0; i < r; i++) {
        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;


//~~~~~~~~~~~~~~~~~~~~~_(＾～＾ ｣ ∠)_~~~~~~~~~~~~~~~~~~~~~

int main() {

    LL X, Y, Z, K;
    cin >> X >> Y >> Z >> K;

    VLL A(X), B(Y), C(Z);
    cin >> A >> B >> C;

    RSORT(A);
    RSORT(B);
    RSORT(C);

    VLL ans;
    for (LL i = 0; i < X; i++) {
        for (LL j = 0; j < Y; j++) {
            if (ans.size() > K && (i + 1) * (j + 1) > K) break;
            for (LL k = 0; k < Z; k++) {
                if (ans.size() > K && (i + 1) * (j + 1) * (k + 1) > K) break;
                ans.push_back(A[i] + B[j] + C[k]);
            }
        }
    }
    RSORT(ans);

    REP(i, K) cout << ans[i] << endl;

    return 0;
}

Submission status: Runtime Error

Solution code:
#include<iostream>
using namespace std;

long long s[200001];
long long bit[200001];

int main()
{
	cin.tie(0);
	ios::sync_with_stdio(false);
	long long n, k;
	cin >> n >> k;
	long long a;
	s[0] = 0;
	for (int j = 1; j <= n; ++j) {
		cin >> a;
		s[j] = s[j - 1] + a - k;
	}
	int ans;
	// c.f. 蟻本p.162（バブルソートの交換回数）
	// そのためにsを1-nまでの値にする必要あり
	// sをソートしたものを作り、そのインデックスを見ればよい

	cout << ans << endl;


	return 0;
}

Submission status: Runtime Error

Solution code:
#input
x,y,z,k=[int(i) for i in input().split()]
a=[int(i) for i in input().split()]
b=[int(i) for i in input().split()]
c=[int(i) for i in input().split()]

#sort
a=sorted(a,reverse=True)
b=sorted(b,reverse=True)
c=sorted(c,reverse=True)

q=[]
heappush(q,(-(a[0]+b[0]+c[0]),0,0,0))
s={(0,0,0)}

for n in range(k):
    p,h,i,j=heappop(q)
    
    if  (h+1<x) and ((h+1,i,j) not in s):
        heappush(q,(-(a[h+1]+b[i]+c[j]),h+1,i,j))
        s.add((h+1,i,j))
        
    if  (i+1<y) and ((h,i+1,j) not in s):
        heappush(q,(-(a[h]+b[i+1]+c[j]),h,i+1,j))
        s.add((h,i+1,j))
        
    if  (j+1<z) and ((h,i,j+1) not in s):
        heappush(q,(-(a[h]+b[i]+c[j+1]),h,i,j+1))        
        s.add((h,i,j+1))
        
    print(-p)
         
for j in range(1,k):
  q_value=q[-1][0]
  q_x=q[-1][1]
  q_y=q[-1][2]
  q_z=q[-1][3]
  new=max(

Submission status: Runtime Error

Solution code:
def d_cake_123_priority_queue(X, Y, Z, K, A, B, C):
    # editionalの解法3
    import heapq
    # 数列A, B, Cを降順ソート
    a, b, c = sorted(A, reverse=True), sorted(B, reverse=True), sorted(C, reverse=True)

    def evaluation(x, y, z):
        # heapqは最小値を取り出す方式なので、符号を反転させないといけない
        return (-(a[x] + b[y] + c[z]), x, y, z)

    # priority queue を定義し、(A_1 + B_1 + C_1, 1, 1, 1) を追加
    q = []
    heapq.heappush(q, evaluation(0, 0, 0))
    ans = []

    # priority queueに対するK回の操作の部分
    for _ in range(K):
        (e, x, y, z) = heapq.heappop(q)
        ans.append(-e)
        if x + 1 < X and evaluation(x + 1, y, z) not in q:
            heapq.heappush(q, evaluation(x + 1, y, z))
        if y + 1 < Y and evaluation(x, y + 1, z) not in q:
            heapq.heappush(q, evaluation(x, y + 1, z))
        if z + 1 < Z and evaluation(x, y, z + 1) not in q:
            heapq.heappush(q, evaluation(x, y, z + 1))
    return '\n'.join(map(str, ans[:K]))

X, Y, Z, K = [int(i) for i in input().split()]
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]
C = [int(i) for i in input().split()]
print(d_cake_123_sort_modified(X, Y, Z, K, A, B, C))

Submission status: Runtime Error

Solution code:
x, y, z, k = map(int, input().split())
c_s = list(map(int, input().split()))
b_s = list(map(int, input().split()))
a_s = list(map(int, input().split()))
a_s.sort(reverse=True)
b_s.sort(reverse=True)
c_s.sort(reverse=True)

d = {}
abcs = [0]
j = -1

for a in a_s:
    for b in b_s:
        for c in c_s:
            abc = a + b + c
            if j >= k and abcs[k-1] >= abc:
                break
            if abcs[0] == 0:
                abcs[0] = abc
            else:
                for i in reversed(range(len(abcs))):
                    if abcs[i] >= abc:
                        abcs.insert(i+1, abc)
                        break
                abcs = abcs[:k-1]
            j += 1
for i in range(k):
    print(abcs[i])

Submission status: Runtime Error

Solution code:
def d_cake_123_sort_modified(X, Y, Z, K, A, B, C):
    # editionalの解法1
    ab = sorted([a + b for b in B for a in A], reverse=True)[:K]
    ans = sorted([e + c for e in ab for c in C], reverse=True)[:K]
    return ' '.join(map(str, ans))

X, Y, Z, K = [int(i) for i in input().split()]
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]
C = [int(i) for i in input().split()]
print(d_cake_123_sort_all(X, Y, Z, K, A, B, C))