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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import sys; sys.setrecursionlimit(2147483647); input = sys.stdin.readline
from math import floor, ceil, sqrt, factorial, log
from collections import Counter, defaultdict, deque
from operator import itemgetter
INF = float('inf'); MOD = 10**9+7
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(MI())
def LIR(n): return [LI() for i in range(n)]
def IS(): return input().rstrip()
from itertools import permutations
import numpy as np
def create_gen(string):
    for char in string: yield char
def main(): 
    N, M, X = MI()
    C = []; A = []; P = ''
    for i in range(N):
        tmp = LI()
        C.append(tmp[0]); A.append(tmp[1:]); P += str(i)
    origin_list = list(create_gen(P)); l = set()
    for i, _ in enumerate(origin_list, 1):
        for j in permutations(origin_list, r=i):
            l.add(j)
    c = {}
    for i in l: c[sum([C[int(j)] for j in i])] = i
    c = sorted(c.items(), key=itemgetter(0))
    for cost, i in c:
        r = np.zeros(M)
        for j in i: r += np.array(A[int(j)])
        if sum(r<X): continue
        else: print(cost); sys.exit()
    print(-1)

if __name__ == '__main__':
    main()