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.io.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    int m = Integer.parseInt(sc.next());
    int x = Integer.parseInt(sc.next());
    List<Book> books = new ArrayList<>();
    for (int i = 0; i < n; i++) {
      Book book = new Book(
        i,
        Integer.parseInt(sc.next())
      );
      int a[] = new int[m];
      for (int j = 0; j < m; j++) {
        a[j] = Integer.parseInt(sc.next());
      }
      book.a = a;
      books.add(book);
    }
    int ans = dfs(books, 0, 0, new Understand(x, m));
    pw.println(ans);
  }

  static int dfs(List<Book> books, int index, int price, Understand understand) {
    if (understand.isOk()) {
      return price;
    }
    boolean found = false;
    int ans = Integer.MAX_VALUE;
    for (int i = index; i < books.size(); i++) {
      Understand copy = new Understand(understand);
      copy.read(books.get(i));
      int childAns = dfs(books, i + 1, price + books.get(i).c, copy);
      if (childAns < 0) {
        continue;
      }
      found = true;
      ans = Math.min(ans, childAns);
    }
    if (found) {
      return ans;
    } else {
      return -1;
    }
  }

  static class Understand {

    int x;
    int current[];
    List<Book> read = new ArrayList<>();

    public Understand(int x, int m) {
      this.x = x;
      current = new int[m];
    }

    public Understand(Understand u) {
      this.x = u.x;
      this.current = Arrays.copyOf(u.current, u.current.length);
      this.read = new ArrayList<>(u.read);
    }

    void read(Book b) {
      read.add(b);
      for (int i = 0; i < b.a.length; i++) {
        current[i] += b.a[i];
      }
    }

    boolean isOk() {
      return Arrays.stream(current).allMatch(i -> i >= x);
    }

    @Override
    public String toString() {
      return
        read.stream().map(b -> String.valueOf(b.index)).collect(Collectors.joining(", ")) + ":"
          + Arrays.toString(current);
    }
  }

  static class Book {

    int index;
    int c;
    int a[];

    public Book(int index, int c) {
      this.index = index;
      this.c = c;
    }
  }
}