Problem:
Score : 300 points

Problem

Takahashi, who is a novice in competitive programming, wants to learn M algorithms.
Initially, his understanding level of each of the M algorithms is 0.

Takahashi is visiting a bookstore, where he finds N books on algorithms.
The i-th book (1\leq i\leq N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i,j} for each j (1\leq j\leq M).
There is no other way to increase the understanding levels of the algorithms.

Takahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.

Constraints

All values in input are integers.

1\leq N, M\leq 12

1\leq X\leq 10^5

1\leq C_i \leq 10^5

0\leq A_{i, j} \leq 10^5

Input

Input is given from Standard Input in the following format:

N M X
C_1 A_{1,1} A_{1,2} \cdots A_{1,M}
C_2 A_{2,1} A_{2,2} \cdots A_{2,M}
\vdots
C_N A_{N,1} A_{N,2} \cdots A_{N,M}

Output

If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.

Sample Input 1

3 3 10
60 2 2 4
70 8 7 9
50 2 3 9

Sample Output 1

120

Buying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.

Sample Input 2

3 3 10
100 3 1 4
100 1 5 9
100 2 6 5

Sample Output 2

-1

Buying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.

Sample Input 3

8 5 22
100 3 7 5 3 1
164 4 5 2 7 8
334 7 2 7 2 9
234 4 7 2 8 2
541 5 4 3 3 6
235 4 8 6 9 7
394 3 6 1 6 2
872 8 4 3 7 2

Sample Output 3

1067

Solution in Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.Set;


public class Main {


    static void solve() {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int m = scan.nextInt();
        int x = scan.nextInt();

        Book[] books = new Book[n];

        for(int i=0;i<n;i++) {
            int c = scan.nextInt();
            int[] gain = new int[m];
            for(int t=0;t<m;t++) {
                gain[t] = scan.nextInt();
            }
            Book b = new Book(c, gain);
            books[i] = b;
        }
        //sort
        Arrays.sort(books);

        int mincost = Integer.MAX_VALUE;
        boolean works = false;
        for(int i=0;i<books.length;i++) {
            int[] initalg = new int[m];
           int initCost = books[i].c;
            for (int j=0;j<m;j++) {
                initalg[j]+=books[i].gain[j];
            }
            boolean isOk = enough(initalg, x);
            if(isOk) {
                works = true;
                mincost = Math.min(mincost, initCost);
            }else{
                int u = 1;
                while(i+u<n) {
                    int cost = initCost;
                    int[] alg = new int[m];
                    for (int j=0;j<m;j++) {
                        alg[j]=initalg[j];
                    }
                    for(int j=i+u; j<books.length;j++) {
                        cost+=books[j].c;
                        for (int t=0;t<m;t++) {
                            alg[t]+=books[j].gain[t];
                        }
                        isOk = enough(alg, x);
                        if(isOk) {
                            mincost = Math.min(mincost, cost);
                            works = true;
                        }
                    }
                    u++;
                }
            }
        }
        if(works) {
            System.out.println(mincost);
            return;
        }

//        for(int i=0;i<books.length;i++) {
//            cost+=books[i].c;
//            for (int j=0;j<m;j++) {
//                alg[j]+=books[i].gain[j];
//            }
//            boolean isOk = enough(alg, x);
//            if(isOk) {
//                System.out.println(cost);
//                return;
//            }
//        }

        System.out.println(-1);

//        for (int i = 0; i < t; i++) {
//            int n = scan.nextInt();
//            int k = scan.nextInt();
//            scase(n,k);
////            System.out.println(res);
////            solveCase(i, x,y,s);
//        }
    }

    static boolean enough(int[] alg, int x) {
        for (int i=0;i<alg.length;i++) {
            if(alg[i] < x) {
                return false;
            }
        }
        return true;
    }



    static class Book implements Comparable<Book> {
        int c;
        int[] gain;

        public Book(int c, int[] gain) {
            this.c = c;
            this.gain = gain;
        }

        @Override
        public int compareTo(Book o) {
            if(this.c > o.c) {
                return 1;
            }
            if(this.c < o.c) {
                return -1;
            }
            return 0;
        }
    }




//    static void solveCase(int t, int x, String s) {
//
//    }



    static void scase(int n, int k) {

    }



    public static void main(String[] args) {

        solve();

        //        Main m = new Main();
        //        Scanner scan = new Scanner(System.in);

        //        long n = scan.nextLong();
        //        long r = scan.nextLong();
        //        List<Long> list = new ArrayList<>();
        ////        int[] arr = new int[n];
        //        for (long i=0;i<n;i++){
        //            list.add(scan.nextLong());
        //        }
//            System.out.println(ch);
        //        solve(n, arr);
        //        scan.close();
    }


//
//    class Counter extends HashMap<Integer, Integer> {
//        public int get(int k) {
//            return containsKey(k) ? super.get(k) : 0;
//        }
//
//        public void add(int k, int v) {
//            put(k, get(k) + v);
//        }
//    }


//    static class Node {
//        int val;
//        Node next;
//        Node random;
//
//        public Node(int val) {
//            this.val = val;
//            this.next = null;
//            this.random = null;
//        }
//    }

//    static class Node {
//        int key;
//        int data;
//        Node next;
//        Node prev;
//
//        Node(int key, int data) {
//            this.key = key;
//            this.data = data;
//        }
//    }

    static class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }
}