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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			var inputArray = retreiveLongArray();
			var inputCount = 3;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long N = inputArray[0];
			long M = inputArray[1];
			long X = inputArray[2];
			_docCount = N;
			_alogoCount = M;
			_kijun = X;
			 _sankoushoInfo = new List<long[]>();

			for (int i = 0; i < N; i++) {
				var sankousho = retreiveLongArray();
				_sankoushoInfo.Add(sankousho);
			}
			_minMoney = int.MaxValue;

			var buyCheck = new Dictionary<long, bool>();
			var gakuryoku = new Dictionary<long, long>();

			for (int i = 0; i < N; i++) {
				buyCheck.Add(i, false);
			}

			for (int i = 1; i <= M; i++) {
				gakuryoku.Add(i, 0);
			}

			for (int i = 0; i < N; i++) {
				DFS(i, buyCheck, gakuryoku, 0);
			}

			//答えの出力
			var ans = _minMoney == int.MaxValue? -1:_minMoney;
			Console.WriteLine(ans);

		}

		private static long _minMoney;
		private static long _alogoCount;
		private static long _docCount;
		private static long _kijun;

		private static List<long[]> _sankoushoInfo;

		private static void DFS(int buyBook,Dictionary<long, bool> buyCheck, Dictionary<long, long> gakuryoku,long currentMoney) {
			buyCheck[buyBook] = true;

			//学力を向上させる
			var sankousho = _sankoushoInfo[buyBook];
			for (int i = 1; i <= _alogoCount; i++) {
				gakuryoku[i] += sankousho[i];
			}
			//金額を加算する
			currentMoney += sankousho[0];


			//学力が基準を満たしているか判定
			var hantei = true;
			for (int i = 1; i <= _alogoCount; i++) {
				if(gakuryoku[i] < _kijun) {
					hantei = false;
				}
			}

			//すでに学力を満たしている場合、これ以上本を買わない
			if (hantei) {
				_minMoney = Math.Min(_minMoney, currentMoney);
				//呼び出し前の状態に戻す
				buyCheck[buyBook] = false;
				currentMoney -= sankousho[0];

				for (int i = 1; i <= _alogoCount; i++) {
					gakuryoku[i] -= sankousho[i];
				}
				return;
			}


			for (int i = 0; i < _docCount; i++) {
				if (buyCheck[i]) {//購入済みの本の場合は処理しない
					continue;
				}
				DFS(i, buyCheck, gakuryoku, currentMoney);

			}

			//呼び出し前の状態に戻す
			buyCheck[buyBook] = false;
			currentMoney -= sankousho[0];

			for (int i = 1; i <= _alogoCount; i++) {
				gakuryoku[i] -= sankousho[i];
			}

			return;
		}

		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}