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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;    

#define COUNTOF(array) (sizeof(array) / sizeof(array[0]))    
#define OUT(P) cout << (P) << endl    
#define OUT2(P1, P2) cout << (P1) << " " << (P2) << endl    
#define PRINT_ARRAY(P) for(int i=0; i<P.size(); i++) cout << P[i] << endl;    
#define PRINT_ARRAY_INLINE(P) do { for(int i=0; i<P.size(); i++) cout << P[i] << " "; cout << endl; } while(0)    
#define PRINT_ARRAY_WITH_LABEL(L, P) do { cout << L << ": "; PRINT_ARRAY_INLINE(P); cout << endl; } while(0)    
typedef long long ll;    
const long DIVIDE = 1e9+7;

int sum_digits(int num);    
template <class T>    
vector<T> copy_vector(vector<T> vec);    
long gcd(long a, long b);    
long lcm(long a, long b);
vector<vector<long>> comb(long n, long r);
// ****** print functions ****** //
template <class T, class U>
void print_pairs(const vector<pair<T, U>> pairs);
template <class K, class V>
void print_map(const map<K, V> m);

int main() {    
	int n,m,x;
	cin >> n >> m >> x;
	vector<int> costs(n);
	int MAX = 3000000;
	vector<vector<int>> books(n, vector<int>(m, 0));
	for(int i=0; i<n; i++) {
		cin >> costs[i];
		for(int j=0; j<m; j++) {
			cin >> books[i][j];
		}
	}

	vector<vector<vector<int>>> dp(n+1, vector<vector<int>>(m, vector<int>(x+1, MAX)));
	for(int i=0; i<m; i++) {
		dp[0][i][0] = 0;
	}

	for(int i=0; i<n; i++) {
		int cost = costs[i];
		vector<int> book = books[i];
		for(int j=0; j<m; j++) {
			int up = book[j];
			for(int k=0; k<=x; k++) {
				// 選ばない場合
				dp[i+1][j][k] = min(dp[i+1][j][k], dp[i][j][k]);
				// 選ぶ場合
				dp[i+1][j][min(x, k+up)] = min(dp[i+1][j][min(x, k+up)], dp[i][j][k] + cost);
			}
		}
	}
	int ans = dp[n][0][x];
	for(int i=0; i<m; i++) {
		ans = max(ans, dp[n][i][x]);
	}
	if(ans == MAX) ans = -1;
	cout << ans << endl;

	return 0;    
}    

/******************************/    
/***** DECRARED FUNCTIONS *****/    
/******************************/    

int sum_digits(int num) {    
	int rtn = 0;    
	while(num != 0) {    
		int tmp = num % 10;    
		rtn += tmp;    
		num /= 10;    
	}    
	return rtn;    
}    

// vectorのコピー    
template <class T>    
vector<T> copy_vector(vector<T> vec) {    
	vector<T> rtn;    
	rtn.reserve(vec.size());    
	copy(vec.begin(), vec.end(), back_inserter(rtn));    
	return rtn;    
}    

long gcd(long a, long b) {    
	if(b==0) return a;    
	else return gcd(b, a % b);    
}

long lcm(long a, long b) {
	long gcd_ = gcd(a, b);
	return (a * b) / gcd_;
}

vector<vector<long>> comb(long n, long r) {                                                                             
	vector<vector<long>> v(n+1, vector<long>(n+1, 0));    
	for(int i=0; i<v.size(); i++) {    
		v[i][0] = 1;    
		v[i][i] = 1;    
	}    
	for(int i=1; i<v.size(); i++) {    
		for(int j=1; j < i; j++) {    
			v[i][j] = (v[i-1][j-1] + v[i-1][j]) % DIVIDE;    
		}    
	}    
	return v;    
} 

template <class T, class U>
void print_pairs(const vector<pair<T, U>> &pairs) {
	for(int i=0; i<pairs.size(); i++) { 
		cout << "(" << pairs[i].first << ", " << pairs[i].second << ")" << " "; 
	} 
	cout << endl;
}

template <class K, class V>
void print_map(const map<K, V> &m) {
	for(auto it=m.cbegin(); it!=m.cend(); it++) {
		cout << it->first << ": " << it->second << endl;
	}
}