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.HashMap;
import java.util.Scanner;

/*
問題文

*/

public class Main {
    public static void main(String[] args){

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        long x = sc.nextInt();

        long[][] input = new long[n][m+1];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m + 1; j++) {
                input[i][j] = sc.nextInt();
            }
        }

        int ans = 1200000;

        // 2^Nの買う、買わないの全通りを探索する
        for (int i = 0; i < Math.pow(2,n); i++) {
            boolean flg = true;
            int[] arr = new int[m];
            int sum = 0;

            for (int j = 0; j < n; j++) {

                // 買う場合、金額の計算と、この組み合わせの中で
                // アルゴリズムの習熟度がx以上になるかを計算する
                if ((1 & i >> j) == 1) {
                    sum+=input[j][0];   // 金額の計算
                    
					for(int k = 1; k <= m; k++)   // Aj,1 Aj,2  ⋯ Aj,M の縦の足し算
					{
						arr[k-1]+=input[j][k];
					}
                };
            }
            // 合計結果について、一つずつ、x以上となっているか確認
            for (int j = 0; j < m; j++) {
                if (arr[j] < x) {
                    flg = false;
                }    
            }
            // 習熟度がx以上の場合
            if (flg) {
                ans = Math.min(ans, sum);
            }
        }

        if (ans == 1200000) {
            System.out.println("-1");
        } else {
            System.out.println(ans);

        }
    }
}