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: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {
        private static void Main(string[] args)
        {
            var s = Scanner.ArrayInt(3);
            var max = s[2];
            var columnCount = s[1] + 1;
            var books = new List<int[]>();
            for (int i = 0; i < s[0]; i++)
            {
                books.Add(Scanner.ArrayInt(columnCount).ToArray());
            }

            for (int i = 1; i < columnCount; i++)
            {
                if (books.Select(xs => xs[i]).Sum() < max)
                {
                    Console.WriteLine("-1");
                    return;
                }
            }

            var patternAll = (int)Math.Pow(2, s[0]);
            var array = new BitArray();
            var indexArray = Enumerable.Range(0,patternAll).Select(x => array.Integer(x,s[0])).ToList();
            for (int i = 1; i < s[1]; i++)
            {
                var removeArray = new List<List<int>>();
                foreach (var indArray in indexArray)
                {
                    if (indArray.Sum(x => books[x][i]) < max)
                    {
                        removeArray.Add(indArray);
                    }
                }

                indexArray = indexArray.Except(removeArray).ToList();
            }

            Console.WriteLine(indexArray.Select(xs => xs.Sum(x => books[x][0])).Min());
        }

        #region Utility
        static readonly StreamScanner Scanner = new StreamScanner(Console.OpenStandardInput());

        /// <summary> 一括出力 </summary>
        private static void OutAllLine(IEnumerable<dynamic> items)
        {
            var sb = new StringBuilder();
            foreach (var result in items)
            {
                sb.Append(result + "\n");
            }
            sb = sb.Remove(sb.Length - 1, 1);
            Console.WriteLine(sb);
        }

        /// <summary> 素数判定 </summary>
        public static bool IsPrime(int num)
        {
            if (num < 2) {return false;}
            if (num == 2) {return true;}
            if (num % 2 == 0) {return false;}

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0) { return false; }
            }
            return true;
        }
        
        public static IEnumerable<int> PrimeFactors(int n)
        {
            int i = 2;
            int tmp = n;

            while (i * i <= n) //※1
            {
                if(tmp % i == 0){
                    tmp /= i;
                    yield return i;
                }else{
                    i++;
                }
            }
            if(tmp != 1) yield return tmp;
        }
        #endregion
    }

    #region Utility Class
    
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        private readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len) {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        public char Char() 
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b; 
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (int)Long(); }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
        
        /// <summary> 数値読み込み </summary>
        public List<long> ArrayLong(int count = 0)
        {
            var scan = new List<long>();
            for (int i = 0; i < count; i++)
            {
                scan.Add(Long());
            }
            return scan;
        }
        /// <summary> 数値読み込み </summary>
        public List<int> ArrayInt(int count = 0)
        {
            var scan = new List<int>();
            for (int i = 0; i < count; i++)
            {
                scan.Add(Integer());
            }
            return scan;
        }
    }
    public class Mod109
    {
        public const int _7 = 1000000007;
        public const int _9 = 1000000009;
        public const int _3 = 998244353;
        
        private readonly int ModValue;

        public Mod109(int modValue = Mod109._7)
        {
            ModValue = modValue;
        }
        
        /// <summary> 和 </summary>
        public long Addition(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(0, (current, num) => ModifyPositive((current + num) % ModValue));
        }
        
        /// <summary> 差 </summary>
        public long Subtraction(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(0, (current, num) => ModifyPositive((current - num) % ModValue));
        }
        
        /// <summary> 積 </summary>
        public long Multiplication(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(1, (current, num) => ModifyPositive((current * num) % ModValue));
        }

        private long ModifyPositive(long value)
        {
            return value < 0 ? (value + ModValue) : value;
        }
    }

    public class BitArray
    {
        public List<int> Integer(int bitValue, int length)
        {
            var list = new List<int>();
            for (int i = 0; i < length; i++)
            {
                if (bitValue % 2 == 1)
                {
                    list.Add(i);
                }
                bitValue /= 2;
            }
            return list;
        }
    }
    
    #endregion
    
}