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: Accepted)

import java.util.ArrayList;
import java.util.Scanner;


public class Main {

    public static String Y = "Yes";
    public static String N = "No";
    public static String I = "IMPOSSIBLE";
    public static String B = "Bad";
    public static String G = "Good";
    public static long MOD = (long) (Math.pow(10, 9) + 7);
    public static Scanner sc = new Scanner(System.in);

    static int n;
    static int m;
    static int x;
    static int loopCount = 0;
    static int[][] a;
    static int[] c;
    static int sum_c = 0;
    static int[] sum_c_save;
    static int[] understand;

    public static void main(String[] args) {

        // 参考書数
        n = ni();

        // アルゴリズム数
        m = ni();

        // 目標理解度
        x = ni();

        // 参考書値段
        c = new int[n + 1];

        // 参考書アルゴリズム上昇理解度
        a = new int[n + 1][m];

        // 値段が付いた（買う可能性のあるものリスト）
        ArrayList<Integer> c_list = new ArrayList<>();

        sum_c_save = new int[5000];

        for (int i = 0; i < 5000; i++) {
            sum_c_save[i] = Integer.MAX_VALUE;
        }

        for (int i = 0; i < n; i++) {
            c[i] = ni();
            for (int j = 0; j < m; j++) {
                a[i][j] = ni();
            }
        }

        understand = new int[m];

        dfs(0, true);

        sum_c -= c[0];
        for (int h = 0; h < m; h++) {
            understand[h] -= a[0][h];
        }

        dfs(0, false);

        int min_c = Integer.MAX_VALUE;

        for (int i = 0; i < loopCount; i++) {
            if (min_c >= sum_c_save[i]) {
                min_c = sum_c_save[i];

            }
            //out("min_c:" + min_c + " loopCount:" + i);
        }

        if (!(min_c == Integer.MAX_VALUE)) {
            out(min_c);
        } else {
            out(-1);
        }

    }

    static void dfs(int i, boolean takeIt) {

        //out("---------------dfs" + i + "回目---------------------");

        if (takeIt) {
            // 参考書の理解度を足し算
            for (int h = 0; h < m; h++) {
                understand[h] += a[i][h];
            }

            // 値段を足し算
            sum_c += c[i];

        }

        if (i >= n - 1) {

            int sum_c_tmp = sum_c;

            for (int g = 0; g < m; g++) {
                // out(g + ":" + understand[g]);
                if (understand[g] < x) {
                    sum_c_tmp = Integer.MAX_VALUE;
                    break;
                }
            }
            sum_c_save[loopCount++] = sum_c_tmp;

            //out("sum_c:" + sum_c);

            return;
        }

        dfs(i + 1, true);

        sum_c -= c[i + 1];
        for (int h = 0; h < m; h++) {
            understand[h] -= a[i + 1][h];
        }

        dfs(i + 1, false);

    }

    /*
     * 以下メソッド集
     */
    static int ni() {

        return sc.nextInt();
    }

    static long nl() {

        return sc.nextLong();
    }

    static String n() {

        return sc.next();
    }

    static char[] nc() {

        return sc.next().toCharArray();
    }

    static int kaijo(int n) {

        if (n == 0 || n == 1) {
            return 1;
        } else {
            return n * kaijo(n - 1);
        }
    }

    static int fib(int n) {

        return (n == 1 || n == 0) ? n : fib(n - 2) + fib(n - 1);
    }

    static long lcm(long m, long n) {

        return m * n / gcd(m, n);
    }

    static int lcm(int m, int n) {

        return m * n / gcd(m, n);
    }

    static long gcd(long a, long b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcd(int a, int b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static void out(String info) {

        System.out.println(info);
    }

    static void out(int info) {

        System.out.println(info);
    }

    static void out(double info) {

        System.out.println(info);
    }

    static void out(long info) {

        System.out.println(info);
    }

    static void out(char info) {

        System.out.println(info);
    }

    static void outn(String info) {

        System.out.print(info);
    }

    static void outn(int info) {

        System.out.print(info);
    }

    static void outn(double info) {

        System.out.print(info);
    }

    static void outn(long info) {

        System.out.print(info);
    }

    static void outn(char info) {

        System.out.print(info);
    }

    static int max(int a, int b) {

        return Math.max(a, b);
    }

    static long max(long a, long b) {

        return Math.max(a, b);
    }

    static int min(int a, int b) {

        return Math.min(a, b);
    }

    static long min(long a, long b) {

        return Math.min(a, b);
    }
}