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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var M = cin.ReadInt;
            var X = cin.ReadInt;

            var books = new List<int[]>();
            for (int i = 0; i < N; i++)
            {
                var book = new int[M + 1];
                book[0] = cin.ReadInt;
                for (int j = 0; j < M; j++)
                {
                    book[j + 1] = cin.ReadInt;
                }
                books.Add(book);
            }

            Func<List<int[]>, int, List<int[]>> GetResults = null;
            GetResults = (List<int[]> results, int count) =>
            {
                if (count >= N) return results;

                var resultZoro = this.GetDeepCopy(results);

                var book = books[count];

                var resultOne = new List<int[]>(results);
                foreach (var res in resultOne)
                {
                    for (int i = 0; i < M + 1; i++)
                    {
                        res[i] += book[i];
                    }
                }

                var newResults = new List<int[]>();
                newResults.AddRange(resultZoro);
                newResults.AddRange(resultOne);

                return GetResults(newResults, count + 1);
            };

            var results = GetResults(new List<int[]>() { new int[M + 1] }, 0);

            var min = -1;
            foreach (var result in results)
            {
                var check = true;
                for (int i = 1; i < result.Length; i++)
                {
                    if (result[i] < X) check = false;
                }
                if (check) {
                    if(min == -1) min = result[0];
                    if (min > result[0]) min = result[0]; 
                }
            }
            WriteLine(min);
        }

        public List<int[]>GetDeepCopy(List<int[]> target)
        {
            var result = new List<int[]>();
            foreach (var array in target)
            {
                var newArray = new int[array.Length];
                Array.Copy(array,newArray,array.Length);
                result.Add(newArray);
            }
            return result;
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; i++)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }

        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }

    public static class TestCheck
    {
        public static void Display(int[] array)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item.ToString();
            }
            WriteLine("{0}", txt);
        }

        public static void Display(int index, int[] array)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item.ToString();
            }
            WriteLine("{0} : {1}", index, txt);
        }

        public static void Display(List<int>[] list)
        {
            for (int i = 0; i < list.Length; i++)
            {
                Display(i, list[i].ToArray());
            }
        }

        public static void Display(List<int[]> list)
        {
            for (int i = 0; i < list.Count; i++)
            {
                Display(i, list[i].ToArray());
            }
        }

        public static void Display(int index,List<int[]> list)
        {
            for (int i = 0; i < list.Count; i++)
            {
                Display(index, list[i].ToArray());
            }
        }

        public static void DisplayLine(string text)
        {
            WriteLine("----------" + text + "----------");
        }

        public static void DisplayLine()
        {
            DisplayLine("");
        }
    }
}