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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {
	public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
    	int money_min = 1200000;//金額の最小値をここに求める
    	int ans = -1;//
    	int all_XormorethanX = 1;

    	//N,M,Xの読み込み処理を行う
		int N = sc.nextInt();
		int M = sc.nextInt();
		int X = sc.nextInt();
		int C[] = new int[N+1];
		int A[][] = new int[N+1][M+1];
		int skill_sum[] = new int[M+1];
		int money_sum = 0;

		//CとAの読み込み処理
		for(int i=1;i<=N;i++){
			C[i]=sc.nextInt();
			for(int j=1;j<=M;j++){
				A[i][j]=sc.nextInt();
			}
		}

		//bit全探索処理、探索すると同時に条件を満たすものについては最小値を更新する
		for (int i=0; i<(1<<N); i++) {//ex. 1<<3=1000		
			//条件を満たすかどうかの判定処理
			//1.判断材料を整える処理
			//初期化処理
		    for(int k=1;k<=M;k++){
		        skill_sum[k] = 0;		
		    }

		    for (int j = 0; j < N; j++) {
		        if ((1 & (i >> j)) == 1){//bitからj(0~)桁目を抽出する
		        	for(int k=1;k<=M;k++){
		        		skill_sum[k] = skill_sum[k] + A[j+1][k];

		        	}
		    	}
			}

		    //2.整えた判断材料に対する判断処理
		    all_XormorethanX = 1;//初期化    	
		    for(int l=1;l<=M;l++){
		    	if (skill_sum[l]<X) {
		    		all_XormorethanX = -1;
		    	}
		    	break;
		    }
		    //条件を満たす場合は金額の最小値を更新しておく
		    //金額の合計を求める
		    if (all_XormorethanX==1) {
		    	money_sum = 0;
		    	for (int j = 0; j < N; j++) {
		        	if ((1 & (i >> j)) == 1) {//bitからj(0~)桁目を抽出する
		        		money_sum = money_sum + C[j+1];
		        	}
		    	}
		    //金額の合計を最小値に更新する
		    money_min = Math.min(money_sum,money_min);
		    }
		}
		if (money_min==1200000) {
			System.out.println(ans);
		}
		else{
			ans=money_min;
			System.out.println(ans);
		}

	}
}