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.*;
import java.io.*;
import java.math.*;
public class Main{
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		Scanner sc = new Scanner(System.in);
		//FastReader sc = new FastReader();
		int n = sc.nextInt();
		int m = sc.nextInt();
		long x = sc.nextLong();
		long cost[] = new long[n+1];
		int y[] = new int[n];
		for(int i=0;i<n;i++)
			y[i]=i+1;
		ArrayList<ArrayList<Integer>> al = printSubsequences(n, y);
		
		long dp[][] = new long[n+1][m+1];
		for(int i=1;i<=n;i++){
			cost[i] = sc.nextLong();
			for(int j=1;j<=m;j++){
				dp[i][j] = sc.nextLong();
			}
		}
		int siz = al.size();
		long min = Long.MAX_VALUE;
		long p[] = new long[m+1];
		for(int i=0;i<siz;i++){
			p = new long[m+1];
			long co =0 ;
			ArrayList<Integer> temp = al.get(i);
			int l = temp.size();
			for(int j=0;j<l;j++){
				int val = temp.get(j);
				co += cost[val];
				for(int k=1;k<=m;k++){
					p[k] += dp[val][k];
				}
			}
			boolean g = true;
			for(int j=1;j<=m;j++){
				if(p[j]<x){
					g=false;
				}
			}
			if(g==true){
				min = Math.min(min, co);
			}
		}
		if(min== Long.MAX_VALUE)
			System.out.println("-1");
		else 
			System.out.println(min);
	}
	
	
	
	static ArrayList<ArrayList<Integer>> printSubsequences(int n, int arr[]) 
    { 
        /* Number of subsequences is (2**n -1)*/
		ArrayList<ArrayList<Integer>> temp = new ArrayList<>();
        int opsize = (int)Math.pow(2, n); 
       
        /* Run from counter 000..1 to 111..1*/
        for (int counter = 1; counter < opsize; counter++) 
        { 
			ArrayList<Integer> al = new ArrayList<>();
            for (int j = 0; j < n; j++) 
            { 
                /* Check if jth bit in the counter is set 
                    If set then print jth element from arr[] */
                if (BigInteger.valueOf(counter).testBit(j)) 
                    al.add(arr[j]); 
            }  
			if(al.size()!=0)
				temp.add(al);
        } 
		return temp;
    } 
	
	public static class pair{
		int x;
		int y;
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			if(o1.x==o2.x){
				return o1.y-o2.y;
			}
			return o1.x-o2.x;
		}
	}
	
	
	
	static HashMap<Integer,Integer> visited = new HashMap<>();
	
	static class Node{
		int node;
		int d;
		ArrayList<Integer> al = new ArrayList<>();	
	}
	

	static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }
	
		
	static class FastReader 
		{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 
  
		public FastReader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public FastReader(String file_name) throws IOException 
		{ 
			din = new DataInputStream(new FileInputStream(file_name)); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public String readLine() throws IOException 
		{ 
			byte[] buf = new byte[64]; // line length 
			int cnt = 0, c; 
			while ((c = read()) != -1) 
			{ 
				if (c == '\n') 
					break; 
				buf[cnt++] = (byte) c; 
			} 
			return new String(buf, 0, cnt); 
		} 
  
		public int nextInt() throws IOException 
		{ 
			int ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do
			{ 
				ret = ret * 10 + c - '0'; 
			}  while ((c = read()) >= '0' && c <= '9'); 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public long nextLong() throws IOException 
		{ 
			long ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public double nextDouble() throws IOException 
		{ 
			double ret = 0, div = 1; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
  
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
  
			if (c == '.') 
			{ 
				while ((c = read()) >= '0' && c <= '9') 
				{ 
					ret += (c - '0') / (div *= 10); 
				} 
			} 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		private void fillBuffer() throws IOException 
		{ 
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
			if (bytesRead == -1) 
				buffer[0] = -1; 
		} 
  
		private byte read() throws IOException 
		{ 
			if (bufferPointer == bytesRead) 
				fillBuffer(); 
			return buffer[bufferPointer++]; 
		} 
  
		public void close() throws IOException 
		{ 
			if (din == null) 
				return; 
			din.close(); 
		} 
	} 
}