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: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

class Main {

  static class Solver {
    final FastScanner sc;
    final PrintWriter writer;

    Solver(final FastScanner sc, final PrintWriter writer) {
      this.sc = sc;
      this.writer = writer;
    }

    int n, m, x;
    int[][] books;
    int price = Integer.MAX_VALUE;

    void run() {
      n = sc.nextInt();
      m = sc.nextInt();
      x = sc.nextInt();
      books = new int[n][1 + m];
      for (int i = 0; i < n; i++) {
        books[i] = sc.nextIntArray(1 + m);
      }
      dfs(new boolean[n], new int[m], 0, 0);
      writer.println(price != Integer.MAX_VALUE ? price : -1);
    }

    private void dfs(boolean[] read, int[] skill, int totalPrice, int totalScore) {
      if (totalScore >= x * m) {
        boolean allPass = true;
        for (int s : skill) {
          if (s < x) {
            allPass = false;
            break;
          }
        }
        if (allPass) {
          price = Math.min(price, totalPrice);
          return;
        }
      }
      for (int i = 0; i < read.length; i++) {
        if (!read[i]) {
          boolean[] newRead = new boolean[read.length];
          System.arraycopy(read, 0, newRead, 0, read.length);
          int[] newSkill = new int[skill.length];
          System.arraycopy(skill, 0, newSkill, 0, skill.length);
          for (int j = 0; j < skill.length; j++) {
            newSkill[j] += books[i][j + 1];
            totalScore += books[i][j + 1];
          }
          newRead[i] = true;
          dfs(newRead, newSkill, totalPrice + books[i][0], totalScore);
        }
      }
    }
  }

  public static void main(final String[] args) {
    final FastScanner sc = new FastScanner();
    try (final PrintWriter w = new PrintWriter(System.out)) {
      new Solver(sc, w).run();
      w.flush();
    }
  }

  // FastScanner
  static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner() {
    }

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (final IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte())
        return buffer[ptr++];
      else
        return -1;
    }

    private boolean isPrintableChar(final int c) {
      return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr]))
        ptr++;
      return hasNextByte();
    }

    public String next() {
      if (!hasNext())
        throw new NoSuchElementException();
      final StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext())
        throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      final long nl = nextLong();
      if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
        throw new NumberFormatException();
      return (int) nl;
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

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

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