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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function calc(index, l, cost, Ai, C, X) {
  const A = Ai[index]
  const c = C[index]
  // console.log('input:', index, A, l, cost)
  cost += c
  let ok = true
  for(let i = 0; i < l.length; i++) {
    l[i] += A[i]
    if (l[i] < X) {
      ok = false
    }
  }
  // それ以下のものを計算

  // console.log('calced', index, A, l, cost, ok)

  if (ok) {
    return cost
  }
  if (index === C.length - 1) {
    return -1
  }

  let min = -1
  for (let i = index + 1; i < C.length; i++) {
    // console.log('recursive', index, i)
    let _min = calc(i, Array.from(l), cost, Ai, C, X)
    if (_min === -1) continue
    if (min === -1) {
      min = _min
    }
    min = min < _min ? min : _min
    // console.log('min:', min)
  }
  return min
}

function main(input) {
  const inputs = input.trim().split('\n')
  let [N, M, X] = inputs[0].split(' ').map(Number)
  let C = []
  let Ai = inputs.slice(1).map(e => {
    const [c, ...ai] = e.split(' ').map(Number)
    C.push(c)
    return ai
  })

  // console.log('log')
  // console.log(N, M, X)
  // console.log(C)
  // console.log(Ai)
  // 総当り 12冊しかないの

  let min = -1

  // すべての本について1冊からM冊まで計算、 最小の値を取得する/
  for(let i = 0; i < N; i++) {
    let _min = calc(i, Array.from(new Array(M)).map(e => 0), 0, Ai, C, X)
    // console.log('root:', _min)
    if (_min === -1) continue
    if (min === -1) {
      min = _min
    }
    min = min < _min ? min : _min
  }
  console.log(min)
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));