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 11.0.6) (judge verdict: Wrong Answer)

import java.util.Map.Entry;
import java.util.*;
import java.math.*;
import org.w3c.dom.css.Counter;


public class Main {
    public static void main(final String[] args){
        final Scanner s = new Scanner(System.in);
        final int N = Integer.parseInt(s.next());
        final int M = Integer.parseInt(s.next());
        final int X = Integer.parseInt(s.next());
        //final HashSet<Integer> bookInfo= new HashSet<Integer>();
        final HashMap<Integer,ArrayList<Integer>> bookList= new HashMap<Integer,ArrayList<Integer>>();
       for(int i = 0;i<N;i++){
        ArrayList<Integer> bookInfo= new ArrayList<Integer>();
            for( int i2=0; i2<M+1; i2++){
                bookInfo.add(Integer.parseInt(s.next()));
            } 
        bookList.put(i,bookInfo);
       }
       long price =999999999;
       //ビット全検索
       for(int Mnum=0;Mnum<(1<<N);Mnum++){
           int tmpPrice = 0;
           int testFirst =0;
           ArrayList<Integer> targetBookInfo;
            for (int j=0; j<N; j++) {
                //ビットが１かの確認
                if ((1 & Mnum>>j) == 1) {
                        //アルゴリズムA1の習熟度だけ調査
                        targetBookInfo = bookList.get(j);
                        Iterator<Integer> hoge = targetBookInfo.iterator();
                        tmpPrice += hoge.next();
                        testFirst += hoge.next();
                };
            }
            //A1の習熟度が十分な場合,あと安いとき.本格的な計算
            if(testFirst >= X ){
                boolean Hoge = false;
                int argoChecker=0;
                //一つの学習度に着目して
                for(int targetArgo = 2;targetArgo <M;targetArgo++){
                    //bitが１かの確認
                    for (int j=0; j<N; j++) {
                        if ((1 & Mnum>>j) == 1) {
                            argoChecker += bookList.get(j).get(targetArgo);
                        }
                    }
                    //学習度がXを超えてるかの確認
                    if(argoChecker <X){
                        argoChecker=0;
                        Hoge = true;
                        break;
                    }else{
                        argoChecker=0;
                    }
                }
                //無事全条件をクリアしたので更新
                if(tmpPrice<price && Hoge ==false){
                    price = tmpPrice;
                }
            }
        }
        if(price == 999999999){
            price =-1;
        }
    System.out.println(price);
    }
}