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.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
	
	static int inf = 1_000_000_007;
	Book[] bookArr;
	int x;
	int m;
	int n;

	public static void main(String[] args) throws IOException {
		Main mainObj = new Main();
		mainObj.solve();
	}

	public void solve() throws IOException {
		FastScanner fs = new FastScanner();
		
		n = fs.nextInt();
		m = fs.nextInt();
		x = fs.nextInt();
		
		bookArr = new Book[n];
		
		for(int i = 0; i < n; i++) {
			bookArr[i] = new Book(fs.nextInt(), m);
			Book ith = bookArr[i];
			for(int j = 0; j < m; j++) {
				ith.a[j] = fs.nextInt();
			}
		}
		
		int minPrice = inf;
		for(int i = 1; i <= n; i++) {
			for(int j = 0; j < n; j++) {
				int[] indexArr = new int[i];
				minPrice = Math.min(dfs(0, indexArr, i, j-1), minPrice);
			}
		}
		
		if(minPrice == inf) {
			System.out.println(-1);
		}else {
			System.out.println(minPrice);
		}
		
	}
	
	class Book{
		int price;
		int[] a;
		
		Book(int price, int m){
			this.price = price;
			this.a = new int[m];
		}
	}

	boolean checkUnderstand(List<Book> bookArr) {
		int[] a = new int[m];
		for(Book book : bookArr) {
			for(int i = 0; i < m; i++) {
				a[i] += book.a[i];
			}
		}
		
		for(int i = 0; i < m; i++) {
			if(a[i] < x) {
				return false;
			}
		}
		return true;
	}
	
	
	int dfs(int depth, int[] indexArr, int stop, int nowIndex) {
		if(depth == stop) {
			List<Book> bookList = new ArrayList<>();
			
			int sumPrice = 0;
			
			for(int i = 0; i < stop; i++) {
				Book book = bookArr[indexArr[i]];
				bookList.add(book);
				sumPrice += book.price;
			}
			
			if(checkUnderstand(bookList)) {
				return sumPrice;
			}else {
				return inf;
			}
		}
		
		if(nowIndex >= n-1) {
			return inf;
		}
		
		int minPrice = inf;
		
		for(int i = nowIndex+1; i < n; i++) {
			indexArr[depth] = i;
			minPrice = Math.min(minPrice, dfs(depth+1, indexArr, stop, i));
		}
		
		return minPrice;
	}

	public class FastScanner {

		BufferedReader reader;
		private StringTokenizer st;

		public FastScanner() {
			st = null;
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements()) {
				st = new StringTokenizer(reader.readLine());
			}
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			st = null;
			String readLine = null;
			readLine = reader.readLine();
			return readLine;
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		public int[] nextIntArr(int n) throws NumberFormatException, IOException {
			int[] retArr = new int[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextInt();
			}
			return retArr;
		}

		public long[] nextLongArr(int n) throws NumberFormatException, IOException {
			long[] retArr = new long[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextLong();
			}
			return retArr;
		}

		public void close() throws IOException {
			reader.close();
		}
	}

}