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)

var read = require('readline').createInterface({
  input: process.stdin,
  output: process.stdout
});
var obj;
var inLine = [];
read.on('line', function(input){inLine.push(input);});
read.on('close', function(){
  obj = init(inLine);
  myerr("-----start-----");
  var start = new Date();
  Main();
  var end = new Date() - start;
  myerr("----- end -----");
  myerr("time : " + (end) + "ms");
});
function nextInt(){return myconv(next(),1);} function nextStrArray(){return myconv(next(),2);}
function nextIntArray(){return myconv(next(),4);} function nextCharArray(){return myconv(next(),6);}
function next(){return obj.next();} function hasNext(){return obj.hasNext();}
function init(input){  
  var returnObj = {
    list : input, index : 0, max : input.length,
    hasNext : function(){return (this.index < this.max);},
    next : function(){if(!this.hasNext()){throw "ArrayIndexOutOfBoundsException これ以上ないよ";}else{var returnInput = this.list[this.index];this.index++;return returnInput;}}
  };
  return returnObj;
}
function myout(s){console.log(s);}
function myerr(s){console.error("debug:" + require("util").inspect(s,false,null));}
//[no]要素の扱い。数値型
//不明値、異常時:引数そのまま返す 1:数値へ変換
//2:半角SPで分割 4:半角SPで分割し、数値配列へ
//6:1文字で分割  7:1文字で分割し、数値配列へ
//8:半角SPで結合 9:改行で結合 0:文字なしで結合
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map(Number);case 6:return i.split("");case 7:return i.split("").map(Number);case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}
function Main(){
	var one = nextIntArray();
	var N = one[0];
	var M = one[1];
	var X = one[2];
	var list = new Array(N);
	for(var i = 0; i < N; i++){
		var tmp = nextIntArray();
		var cost = tmp[0];
		tmp.shift();
		list[i] = {
			cost : cost,
			rikai : tmp
		};
	}
	var max = 1000000000;
	var output = 1000000000;
	for(var i = 0; i < (1 << N); i++){
		var allRikai = new Array(M).fill(0);
		var isOK = true;
		var cost = 0;
		for(var j = 0; j < N; j++){
			if((i & (1 << j)) != 0){
				cost += list[j].cost;
				for(var k = 0; k < M; k++){
					allRikai[k] += list[j].rikai[k];
				}
			//ここにbitが一致したときの処理入れる
			}
		}
		for(var j = 0; j < M; j++){
			if(allRikai[j] < X){
				isOK = false;
			}
		}
		if(isOK){
			output = Math.min(output, cost);
		}
	//ある1つのbit探索を終えたらここに処理を入れる
	}
	if(output == max){
		myout(-1);
	}else{
		myout(output);
	}
}