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;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

namespace ABC167
{
    public class Solve
    {
        public static void Main(string[] args)
        {
            new ABC_C();
        }
    }
    public class ABC_A
    {
        public ABC_A()
        {
            var s = Ex.Read;
            var t = Ex.Read;

            bool b = s.Length + 1 == t.Length;
            int i = 0;
            while (b && i < s.Length)
            {
                b &= s[i] == t[i];
                i++;
            }

            (b ? "Yes" : "No").Cw();
        }
    }
    public class ABC_B
    {
        public ABC_B()
        {
            var l = Ex.ReadLongArray();
            var a = l[0];
            var b = l[1];
            var c = l[2];
            var k = l[3];
            long ans = 0;

            if (k > 0)
            {
                ans += 1 * Math.Min(k, a);
                k -= a;
            }
            if (k > 0)
            {
                k -= b;
            }
            if (k > 0)
            {
                ans -= 1 * Math.Min(k, c);
                k -= c;
            }

            ans.Cw();
        }
    }
    public class ABC_C
    {
        long[][] arr;
        long n;
        long m;
        long x;
        long min = long.MaxValue;

        public ABC_C()
        {
            var l = Ex.ReadLongArray();
            n = l[0];
            m = l[1];
            x = l[2];

            arr = new long[n][];

            for (int i = 0; i < n; i++)
            {
                arr[i] = Ex.ReadLongArray();
            }


            long[] now = new long[m];
            dfs(0, 0, now);

            if (min == long.MaxValue)
            {
                min = -1;
            }

            min.Cw();
        }

        bool dfs(long t, int i, long[] now)
        {
            if (now.All(v => v >= x))
            {
                min = Math.Min(min, t);
                return true;
            }

            if (i >= n)
            {
                return false;
            }

            dfs(t, i + 1, now);


            for (int j = 0; j < m; j++)
            {
                now[j] += arr[i][j + 1];
            }
            t += arr[i][0];
            dfs(t, i + 1, now);

            for (int j = 0; j < m; j++)
            {
                now[j] -= arr[i][j + 1];
            }

            return false;
        }

        //long dfs(long tmp, int i, Tuple<long, long>[] now)
        //{
        //    if (!now.Any())
        //    {
        //        return tmp;
        //    }

        //    if (i >= n)
        //    {
        //        return long.MaxValue;
        //    }

        //    long b = dfs(tmp, i + 1, now);
        //    if (b) return b;


        //    foreach(var kvp in now)
        //    {
        //        now[kvp.Item1].Item2 += arr[i][kvp.Item1 + 1];
        //    }
        //    now = now.Where(v => v.Value < x);

        //    return dfs(tmp + arr[i][0], i + 1, now);
        //}
    }
    public class ABC_D
    {
        public ABC_D()
        {
        }
    }
    public class ABC_E
    {
        public ABC_E()
        {
        }
    }
    public class ABC_F
    {
        public ABC_F()
        {
        }
    }
    public static class Ex
    {
        public static void Cw(this object s) { Console.WriteLine(s); }

        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }

        public static string Read { get { return Console.ReadLine().Trim(); } }
        public static int ReadInt { get { return int.Parse(Read); } }
        public static long ReadLong { get { return long.Parse(Read); } }
        public static double ReadDouble { get { return double.Parse(Read); } }
        public static string[] ReadArray() { return Read.Split(' '); }
        public static int[] ReadIntArray() { return Read.Split(' ').Select(int.Parse).ToArray(); }
        public static long[] ReadLongArray() { return Read.Split(' ').Select(long.Parse).ToArray(); }
        public static string[] ReadArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public static int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public static long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}