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: Wrong Answer)

n, m, k = gets.chomp.split(" ").map {|c| c.to_i}
calist = []
n.times do |i|
  calist.push(gets.chomp.split(" ").map {|c| c.to_i})
end

val = Array.new(calist[0].length, 0)

sorted = calist.sort_by{|x| x[0]}.reverse

sorted.each do |l|
  val = val.zip(l).map {|v, l| v+l}
end

if not val[1...val.length].all? {|v| v >= k}
  puts -1
  exit
end

temp_l = Array.new(calist[0].length, 0)

while true do
  sorted = sorted.sort_by{|x| x[0]}.reverse
  all_flag = true
  # 高いやつから引いてく
  sorted.each do |l|
    temp = val
    val = val.zip(l).map {|v, x| v-x}

    # 引いて10以下になったらもとに戻して次に高いやつにTRY
    if not val[1...val.length].all? {|v| v >= k}
	  #val = val.zip(l).map {|v, l| v+l}
      val = temp
      next 
    else
      all_flag = false
      temp = sorted - [l]
      sorted = temp
      break
    end
  end

  if all_flag
    break
  end
end
puts val[0]