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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

    using System.Collections.Generic;
    using System.Collections;
    using System.IO;
    using System.Linq;
    using System.Text;
    using System;

    namespace cysharp_test
    {
        class Program
        {
            static void Main (string[] args)
            {
                new Program ().solve ();
            }

            void solve ()
            {
                int[] nmx = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();
                //zentansaku?????
                N = nmx[0];
                M = nmx[1];
                X = nmx[2];

                costs = new int[N];
                levels = new int[N][];
                for (int i = 0; i < N; i++) levels[i] = new int[M];

                for (int i = 0; i < N; i++)
                {
                    var input = Console.ReadLine ().Split (' ').Select (int.Parse).ToArray ();
                    costs[i] = input[0];
                    for (int j = 0; j < M; j++) levels[i][j] = input[j + 1];
                }
                search (0, new int[M], 0);
                if (scores.Count > 0) Console.WriteLine (scores.Min ());
                else Console.WriteLine ("-1");
                Console.ReadKey ();
            }

            void search (int nextC, int[] level, int cost)
            {
                if (nextC >= N)
                {
                    if (level.Count (v => v < X) == 0)
                    {
                        scores.Add (cost);
                    }
                }
                else
                {
                    search (nextC + 1, level, cost);
                var newlevel = new int[M];
                for (int i = 0; i < M; i++) newlevel[i] = level[i] + levels[nextC][i];
                    search (nextC + 1, newlevel, cost + costs[nextC]);
                }
            }
            List<int> scores = new List<int> ();
            int N, M, X;
            int[] costs;
            int[][] levels;

        }
        struct Vector2
        {
            public Vector2 (long x, long y)
            {
                this.x = x;
                this.y = y;
            }

            public long x, y;

            public static Vector2 operator + (Vector2 a, Vector2 b)
            {
                return new Vector2 (a.x + b.x, a.y + b.y);
            }

            public static Vector2 operator - (Vector2 a, Vector2 b)
            {
                return new Vector2 (a.x - b.x, a.y - b.y);
            }

            public static Vector2 operator * (Vector2 a, long scala)
            {
                return new Vector2 (a.x * scala, a.y + scala);
            }

            public static bool operator == (Vector2 a, Vector2 b)
            {
                return (a.x == b.x) && (a.y == b.y);
            }

            public static bool operator != (Vector2 a, Vector2 b)
            {
                return !(a.x == b.x) && (a.y == b.y);
            }

            public override int GetHashCode ()
            {
                return (int) (x + y);
            }

            public override bool Equals (object obj)
            {
                if (!(obj == null) && obj is Vector2)
                {
                    return (this == (Vector2) obj);
                }
                else return false;
            }

            public override string ToString ()
            {
                return ("(" + x + "," + y + ")");
            }
        }
    }