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 Ruby (2.7.1) (judge verdict: Accepted)

#!/usr/bin/env ruby

def calc_costs(buy_lists, costs)
  res = 0
  buy_lists.each_with_index do |buyed, idx|
    # puts "#{idx}: cost #{costs[idx]}" if buyed
    res += costs[idx + 1] if buyed
  end
  return res
end

n, m, x = gets.split.map(&:to_i)
costs = [-1000000000]
exps = [1000000000]
n.times do
  nums = gets.split.map(&:to_i)
  c = nums[0]
  as = nums[1..-1]
  costs << c
  exps << as
end

# dp[cost][idx] = [exps]
# dp = Array.new(100001).map { Array.new(100).map {Array.new(100, -1)} }

# [books_idx][true/false] = [exps]
# dfs = Array.new(100).map { Array.new(2).map {Array.new(100, 0)} }

status = Struct.new('Status', :books, :exps, :idx)


buyed = status.new([true], exps[1], 1)
not_buyed = status.new([false], Array.new(m, 0), 1)

queue = [buyed, not_buyed]
cands = []


while !queue.empty?
  top = queue.pop
  if top.books.size >= n
    # p top
    # p top
    next if top.exps.any? { |exp| exp < x }

    cost = calc_costs(top.books, costs)
    # puts cost
    cands << cost if cost >= 0
    next
  end
  next_idx = top.idx + 1
  current_books = top.books
  current_exps = top.exps
  added_exps = current_exps.dup

  unless exps[next_idx].nil?
    exps[next_idx].each_with_index do |exp, idx|
      added_exps[idx] += exp
    end
  end



  buyed = status.new(current_books + [true], added_exps, next_idx)
  # p buyed
  not_buyed = status.new(current_books + [false], current_exps, next_idx)
  queue << buyed
  queue << not_buyed
end

cands.sort!
puts cands.empty? ? -1 : cands[0]