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 Scala (2.13.1) (judge verdict: Accepted)

import java.util.Scanner

import scala.annotation.tailrec

object Main {
  def main(args: Array[String]): Unit = {
    //nextLineとnextを同時に使ったら死ぬ
    val sc = new Scanner(System.in)

    val n, m, x = sc.nextInt()

    val bits = bitSearch(n, Vector(true, false))

    val cs = Vector.fill(n)(Vector.fill(m + 1)(sc.nextInt()))

    val ans =
      bits
        .map { bit =>
          val ar = new Array[Int](m + 1)
          cs.zip(bit).foreach {
            case (vec, b) =>
              if (b) {
                (0 to m).foreach { i =>
                  ar(i) += vec(i)
                }
              }
          }

          if (ar.tail.forall(_ >= x)) ar.headOption
          else None
        }
        .filter(_.isDefined)

    val ansStr = if (ans.isEmpty) -1 else ans.min.get

    println(ansStr)
  }

  def f(n: Int): Int = {
    if (n < 0) n + 360
    else if (n > 360) n % 360
    else n
  }

  //region

  def debug(args: Any*): Unit = {
    Console.err.println(args.mkString(" "))
  }

  def printExecTime(process: => Unit): Unit = {
    val start = System.currentTimeMillis
    process
    debug("処理時間： " + (System.currentTimeMillis - start) + " ミリ秒")
  }

  def bitSearch[T](n: Int, choice: Vector[T]): Vector[Vector[T]] = {
    @tailrec
    def bitSearchLogic(n: Int,
                       choice: Vector[T],
                       acc: Vector[Vector[T]]): Vector[Vector[T]] = {
      if (n == 0) acc
      else {
        val newAcc =
          acc.flatMap(vec => {
            choice.map(c => vec :+ c)
          })
        bitSearchLogic(n - 1, choice, newAcc)
      }
    }

    val firstAcc = choice.map(i => Vector(i))
    bitSearchLogic(n - 1, choice, firstAcc)
  }
  //endregion
}