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.

Examples

Input

2 2 2 8
4 6
1 5
3 8


Output

19
17
15
14
13
12
10
8


Input

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


Output

400
310
310
301
301


Input

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


Output

23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547
/*
* @Author Silviase(@silviasetitech)
* For ProCon
*/

import java.util.*;
import java.lang.*;
import java.math.*;

public class Main{

        static int MOD = (int)1e9+7;

        // for dfs
        static int n;
        static int ansi;
        static int[] w;
        static int[] ww;
        static boolean[] isvisited;
        //
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int x = sc.nextInt();
        int y = sc.nextInt();
        int z = sc.nextInt();
        int banme = sc.nextInt();
        long[] a = new long[x];
        long[] b = new long[y];
        long[] c = new long[z];
        long[] hoge = new long[1000000];
        for (int i = 0; i < x; i++) {
            a[i] = sc.nextLong();
        }
        for (int i = 0; i < y; i++) {
            b[i] = sc.nextLong();
        }
        for (int i = 0; i < z; i++) {
            c[i] = sc.nextLong();
        }
        Arrays.sort(a);
        Arrays.sort(b);
        Arrays.sort(c);

        int tmp = 0;
        
        for (int i = x-1; i >= 0; i--) {
            for (int j = y-1; j >= 0; j--) {
                for (int k = z-1; k >= 0; k--) {
                    if ( (x-i)*(y-j)*(z-k) > banme) {
                        break;
                    }else{
                        hoge[tmp] = a[i]+b[j]+c[k];
                        tmp++;
                    }
                }
            }
        }
        Arrays.sort(hoge);
        for (int i = 0; i < banme; i++) {
            System.out.println(hoge[hoge.length-1-i]);
        }

    
        sc.close();
    }

    /*
    For Numeric Analysis
    */
    public static int ManhattanDist(int x, int y, int xx, int yy) {
        return(Math.abs(xx-x) + Math.abs(yy-y));
    }

    public static double FuncOfx(double x, int funcnum) {
        switch (funcnum) {
            case 1:
                return x*x;

            case 2:
                return Math.exp(-1*x)-x*x;
        
            default:
                throw new IllegalArgumentException("Such Func doesn't Exist.");
        }
            
    }

    public static void Nibutan(double target, int funcnum) {
        int callcounter = 0;
        double lowbound = Integer.MIN_VALUE;
        double highbound = Integer.MAX_VALUE;
        double pivot = (lowbound + highbound)/2;
        double tmp;
        double tmp4swap;
        if (funcnum == 1) {
            lowbound = 0;
            pivot = (lowbound+highbound)/2;
        }
        while (true) {
            callcounter++;
            if (FuncOfx(highbound, funcnum) < FuncOfx(lowbound, funcnum)) {
                tmp4swap = highbound;
                highbound = lowbound;
                lowbound = tmp4swap;
            }

            if (FuncOfx(pivot,funcnum) > target) {
                System.out.println(String.format("%2d", callcounter) + ": " 
                            + String.format("%.6f", pivot) + " f(" + String.format("%.6f", pivot) +") is " 
                            + String.format("%.6f",FuncOfx(pivot,funcnum))  + ", so too high :(");
                tmp = (lowbound + pivot)/2;
                if ( Math.abs(tmp-pivot) < 0.00005 ) {
                    System.out.println("Found!" +String.format("%.3f", tmp)+" is the answer.");
                    return;
                }
                highbound = pivot;
                pivot = tmp;
            }else if(FuncOfx(pivot,funcnum) < target){
                System.out.println(String.format("%2d", callcounter) + ": " 
                            + String.format("%.6f", pivot) + " f(" + String.format("%.6f", pivot) +") is " 
                            + String.format("%.6f",FuncOfx(pivot,funcnum))  + ", so too high :(");
                tmp = (highbound + pivot)/2;
                if ( Math.abs(tmp-pivot) < 0.00005 ) {
                    System.out.println("Found!" +String.format("%.3f", tmp)+" is the answer.");
                    return;
                }
                lowbound = pivot;
                pivot = tmp;
            }
        }
        
    }

    /*
    Numeric Analysis End
    */

    private static long[][] CombinationLong_nCk(long n, long k) {
        n++; k++;
        long[][] ans = new long[(int)n][(int)k];
        for (int i = 0; i < n; i++) {
            ans[i][0] = 1;
        }
        for (int i = 0; i < n-1; i++) {
            for (int j = 0; j < k-1; j++) {
                if (i < j) {
                    ans[i][j] = 0;
                }else{
                    ans[i+1][j+1] = ans[i][j] + ans[i][j+1];
                }
            }
        }
        return ans;
    }

        public static int gcd_int(int a, int b) {
        
            if (a < b) {
                int tmpp = a;
                a = b;
                b = tmpp;
            }
            if (b == 0) {
                return a;
            }else{
                return gcd_int(b, a%b);
            }
        } 

        public static long gcd_long(long a, long b) {
        
            if (a < b) {
                long tmpp = a;
                a = b;
                b = tmpp;
            }
            if (b == 0) {
                return a;
            }else{
                return gcd_long(b, a%b);
            }
        }

        public static int lcm_int(int a, int b) {
            int gcd = gcd_int(a,b);
            return a/gcd*b;
        }

        public static long lcm_long(long a, long b) {
            long gcd = gcd_long(a,b);
            return a/gcd*b;
        }

        public static void dfs(int placenow) {
            // if went all -> success! 
            // if not went all -> fail...
            
            /*
            dfs    
            Go All Place that there is wayto to and not having been yet. 

             if island 1 is start point, dfs(1);
            if there is wayto to island 2 and island 3,
            - island 2 changes non-visited -> visited, and dfs(2).
            - island 3 changes non-visited -> visited, and dfs(3).
    
            */

            isvisited[placenow] = true;
            boolean success = true;
            for (int i = 0; i < n; i++) {
                if (isvisited[i] == false) { // not go all place
                    success = false;
                    break;
                }
            }
            if (success) {
                ansi++;
                isvisited[placenow] = false;
                return;
            }

            for (int i = 0; i < n; i++) {
                if (w[i] == placenow && isvisited[ww[i]] == false ) {
                    dfs(ww[i]);
                }else if(ww[i] == placenow && isvisited[w[i]] == false){
                    dfs(w[i]);
                }else{
                    continue;
                }
            }
            isvisited[placenow] = false;
            return;
        }

}

