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.Numerics;
using System.Linq;
using System.Text;
using static System.Math;

class MainClass
{


    public static void Main(string[] args)
    {
        var _ = LnInts();
        var N = _[0];
        var M = _[1];
        var X = _[2];
        var As = new int[N][]; for (int i = 0; i < As.Length; i++) { As[i] = new int[M]; }
        var Cs = new int[N];
        for (int i = 0; i < N; i++)
        {
            var __ = LnInts();
            Cs[i] = __[0];
            for (int n = 1; n <= M; n++)
            {
                As[i][n - 1] = __[n];
            }
        }

        var minCost = int.MaxValue;
        for (int i = 0; i < 1 << N; i++)
        {
            var cost = 0;
            var smart = new int[M];
            for (int n = 0; n < N; n++)
            {
                if ((i >> n) % 2 == 0) continue;
                for (int m = 0; m < M; m++)
                {
                    smart[m] += As[n][m];
                }
                cost += Cs[n];
              //  print(string.Join(" ", smart)+" "+cost);
                bool Ok = true;
                foreach (var m in smart)
                {
                    if (m < X) { Ok = false; break; }
                }
                if (Ok) { minCost = Min(cost, minCost); }
            }
        }
        print(minCost != int.MaxValue ? minCost : -1);
    }


    public static long SumAtoB(long a, long b) { var length = b - a + 1; return (a + b) * (length / 2) + (length % 2 == 1 ? (a + b) / 2 : 0); }
    public static long PowLite(long n, long p, long mod = (long)1e9 + 7) { long ans = 1; long now = n; for (; p > 0; p >>= 1) { if ((p & 1) == 1) { ans *= now; ans %= mod; } now *= now; now %= mod; } return ans; }
    public static void print(object obj) { Console.WriteLine(obj); }
    public static long Gcd(long a, long b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
    public static int Gcd(int a, int b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
    public static int[] LnInts() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new int[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = int.Parse(vs[i]); return ins; }
    public static int LnInt() { var vs = Console.ReadLine().Trim(); return int.Parse(vs); }
    public static long[] LnLngs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new long[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = long.Parse(vs[i]); return ins; }
    public static long LnLng() { var vs = Console.ReadLine().Trim(); return long.Parse(vs); }
    public static string[] LnStrs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); return vs; }
    public static string LnStr() { var vs = Console.ReadLine().Trim(); return vs; }
    public static List<T[]> AllPermutation<T>(params T[] array) where T : IComparable { var a = new List<T>(array).ToArray(); var res = new List<T[]>(); res.Add(new List<T>(a).ToArray()); var n = a.Length; var next = true; while (next) { next = false; int i; for (i = n - 2; i >= 0; i--) { if (a[i].CompareTo(a[i + 1]) < 0) break; } if (i < 0) break; var j = n; do { j--; } while (a[i].CompareTo(a[j]) > 0); if (a[i].CompareTo(a[j]) < 0) { var tmp = a[i]; a[i] = a[j]; a[j] = tmp; Array.Reverse(a, i + 1, n - i - 1); res.Add(new List<T>(a).ToArray()); next = true; } } return res; }
}