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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Queue;

class Main implements Runnable {
	private final FastScanner sc;
	private final PrintWriter out;
	//private final long MOD = 1000000007;
	//private final int[] d8x = {-1,0,1,1,1,0,-1,-1};
	//private final int[] d8y = {-1,-1,-1,0,1,1,1,0};
	//private final int[] d4x = {0,1,0,-1};
	//private final int[] d4y = {-1,0,1,0};
	int n,m,x;
	int[] c;
	int[][] a;
	
	public static void main(String[] args) {
		new Thread(null, new Main(), "", 16L * 1024 * 1024).start();
	}

	Main() {
		sc = new FastScanner();
		out = new PrintWriter(System.out);
	}

	private void init() throws Exception {
		n = sc.nextInt();
		m = sc.nextInt();
		x = sc.nextInt();
		c = new int[n];
		a = new int[n][m];
		for(int i=0;i<n;i++){
			c[i] = sc.nextInt();
			for(int j=0;j<m;j++){
				a[i][j] = sc.nextInt();
			}
		}
	}

	private void solve() throws Exception{
		int min = Integer.MAX_VALUE;
		Queue<Data> q = new ArrayDeque<Data>();
		q.offer(new Data(0,0,m));
		while(q.size()>0){
			Data d = q.poll();
			if(d.isMastered(x)) min = Math.min(min, d.getSum());
			if(d.getIndex()<n){
				q.add(d.make(d.getIndex()+1, d.getSum()+c[d.getIndex()],a[d.getIndex()]));
				q.add(d.make(d.getIndex()+1, d.getSum()));
			}
		}
		out.println(min==Integer.MAX_VALUE?-1:min);
	}

	public void run() {
		try {
			init();
			sc.close();
			solve();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
		out.flush();
		out.close();
	}
}

class Data {
	private int index;
	private int sum;
	private int[] skills;
	
	public Data(int index,int sum,int x){
		this.index = index;
		this.sum = sum;
		this.skills = new int[x];
	}
	public Data make(int index,int sum,int[] c){
		return new Data(index,sum,skills.length,skills,c);
	}
	public Data make(int index,int sum){
		return new Data(index,sum,skills.length,skills);
	}
	private Data(int index,int sum,int m,int[] skills){
		this(index, sum, m);
		for(int i=0;i<m;i++){
			this.skills[i] = skills[i];
		}
	}
	private Data(int index,int sum,int m,int[] skills,int[] a){
		this(index,sum,m);
		for(int i=0;i<m;i++){
			this.skills[i] = skills[i] + a[i];
		}
	}
	public int getIndex() {
		return index;
	}
	public int getSum() {
		return sum;
	}
	public boolean isMastered(int x){
		for(int i=0;i<skills.length;i++){
			if(skills[i]<x){
				return false;
			}
		}
		return true;
	}
}

class MyMath{
	public static int floor(double a){
		BigDecimal ans = new BigDecimal(String.format("%.6f", a));
		return ans.setScale(0, RoundingMode.FLOOR).intValue();
	}
	public static int ceil(double a){
		BigDecimal ans = new BigDecimal(String.format("%.6f", a));
		return ans.setScale(0, RoundingMode.CEILING).intValue();
	}
	public static double NthRoot(double num,double n){
		return Math.pow(Math.E, Math.log(num)/n);
	}
	public static long gcd(long a,long b){
		if(a<b) return gcd(b,a);
		if(b==0) return a;
		return gcd(b,a%b);
	}
	public static long gcd(long... num){
		if(num.length<2) throw new IllegalArgumentException();
		if(num.length == 2) return gcd(num[0],num[1]);
		num[num.length-2] = gcd(num[num.length-2]);
		return gcd(Arrays.copyOfRange(num,0,num.length-1));
	}
}

class ExIntVector {
	private int[] a;
	private int cnt;
	public ExIntVector(int max){
		a = new int[max];
		cnt = 0;
	}
	public int size(){
		return cnt;
	}
	public void add(int x){
		a[cnt++] = x;
	}
	public int get(int i){
		return a[i];
	}
	public int getLast(){
		return a[cnt-1];
	}
	public int[] toArray(){
		return a;
	}
}

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

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

	private boolean hasNext() {
		while (read() && !isVisibleChar(buffer[ptr]))
			ptr++;
		return read();
	}

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

	private static boolean isVisibleChar(int code) {
		return code >= 33 && code <= 126;
	}

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

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

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

	public double nextDouble() {
		return Double.parseDouble(next());
	}
	
	public char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		int b = getNextChar();
		while (!isVisibleChar(b)) {
			b = getNextChar();
		}
		return (char) b;
	}

	public void close() {
		try {
			in.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
}

class IntQueue {
	protected int[] a;
	protected int head, tail;

	public IntQueue(int max) {
		a = new int[max];
	}

	public void offer(int x) {
		a[tail++] = x;
	}

	public int poll() {
		return a[head++];
	}

	public int peek() {
		return a[head];
	}
	
	public int size() {
		return tail - head;
	}
}