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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
    static PrintWriter out;
    static CF_Reader in;
    static int[][] books;
    static int[] algos;
    static int algoLen;
    static int minKnowledge;
    static long result = -1;
    static int bookLen;

    public static void main(String[] args) throws IOException {
        out = new PrintWriter(new OutputStreamWriter(System.out));
        in = new CF_Reader();

        bookLen = in.intNext();
        algoLen = in.intNext();
        minKnowledge = in.intNext();
        books = new int[bookLen][algoLen+1];
        for (int i = 0; i < bookLen; i++) {
            int[] book = in.nextIntArray(algoLen + 1);
            books[i] = book;
        }
        algos = new int[algoLen];
        solve(0, 0);
        out.println(result);

        out.close();
    }

    static void solve(int idx, long cost) {
        if (idx >= bookLen) return;
        cost += books[idx][0];
        add(idx, cost);

        solve(idx + 1, cost);

        cost -= books[idx][0];
        subtract(idx);
        solve(idx + 1, cost);
    }

    static void add(int bookNum, long cost) {
        boolean isValid = true;
        int[] book = books[bookNum];
        for (int i = 0; i < algoLen; i++) {
            algos[i] += book[i + 1];
            if (algos[i] < minKnowledge) isValid = false;
        }
        if (isValid && (result == -1 || cost < result)) result = cost;
    }

    static void subtract(int bookNum) {
        int[] book = books[bookNum];
        for (int i = 0; i < algoLen; i++) {
            algos[i] -= book[i + 1];
        }
    }

    static class CF_Reader {
        BufferedReader br;
        StringTokenizer st;

        public CF_Reader() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine().trim());
            return st.nextToken();
        }

        long longNext() throws IOException {
            return Long.parseLong(next());
        }

        int intNext() throws IOException {
            return Integer.parseInt(next());
        }

        double doubleNext() throws IOException {
            return Double.parseDouble(next());
        }

        char charNext() throws IOException {
            return next().charAt(0);
        }

        public int[] nextIntArray(final int n) throws IOException {
            final int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = intNext();
            return a;
        }

        public long[] nextLongArray(final int n) throws IOException {
            final long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = longNext();
            return a;
        }

        String line() throws IOException {
            return br.readLine().trim();
        }
    }
}