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.Collections.Generic;
using System.Collections;
using System.Linq;
namespace Atcoder_0404
{
    class Program
    {
        static void Main(string[] args)
        {
            var NMX = GetInput_int();
            var _count_sankousyo = NMX[0];
            var _count_targetCount = NMX[1];
            var _targetRikaid = NMX[2];
            int[] _prices = new int[_count_sankousyo];
            int[][] _rikaids = new int[_count_sankousyo][];

            for(int i = 0; i < _count_sankousyo; i++)
            {
                var input = GetInput_int();
                _prices[i] = input[0];
                _rikaids[i] = new int[_count_targetCount];
                Array.Copy(input,1,_rikaids[i],0,_count_targetCount);
            }

            int _priceMin = -1;
            int[] lookList = new int[_count_sankousyo];
            Stack<int> _lookStack=new Stack<int>();
            while(_lookStack.Count< _count_sankousyo)
            {
                _lookStack.Push(0);
            }
            while (true)
            {
                var templist = _lookStack.ToArray();
                var tempsum = 0;
                var tempRikaid = new int[_count_targetCount];
                for(int i = 0; i < templist.Length; i++)
                {
                    if (templist[i] == 1)
                    {
                        tempsum += _prices[i];
                        for(int j = 0; j < _rikaids[i].Length; j++)
                        {
                            tempRikaid[j]+= _rikaids[i][j];
                        }
                    }
                }
                bool clear = true;
                for(int i = 0; i < _count_targetCount; i++)
                {
                    if (tempRikaid[i] < _targetRikaid)
                    {
                        clear = false;
                        break;
                    }
                }
                if (clear)
                {
                    if (_priceMin < 0&&tempsum>0)
                    {
                        _priceMin = tempsum;
                    }
                    else if (tempsum < _priceMin && tempsum > 0)
                    {
                        _priceMin = tempsum;
                    }
                }

                if (!templist.Contains(0)) break;

                var head = _lookStack.Pop();
                while (head == 1)
                {
                    head = _lookStack.Pop();
                }
                _lookStack.Push(1);
                while (_lookStack.Count< _count_sankousyo)
                {
                    _lookStack.Push(0);
                }
            }
            Console.WriteLine(_priceMin);
        }

        
        #region input
        

        static string[] GetInput_string()
        {
            var input = Console.ReadLine().Split(' ');
            return input;
        }

        static int[] GetInput_int()
        {
            var input = GetInput_string();
            var result = new int[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = int.Parse(input[i]);
            }
            return result;
        }
        static long[] GetInput_long()
        {
            var input = GetInput_string();
            var result = new long[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = long.Parse(input[i]);
            }
            return result;
        }
        #endregion
        #region sonota
        static void Swap_array<T>(T[] target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        static void Swap_list<T>(List<T> target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        /// <summary>
        /// 最大公約数
        /// </summary>
        public static int GCD(int a, int b)
        {

            /* 自然数 a > b を確認・入替 */
            if (a < b)
            {
                int tmp = a;
                a = b;
                b = tmp;
            }

            /* ユークリッドの互除法 */
            int r = a % b;
            while (r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }
            return b;
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        public static int LCM(int a, int b)
        {
            int x = a * b;
            b = GCD(a, b);
            return x / b;

        }
        #endregion

        static long mod = 1000000000 + 7;
    }

}