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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();
    let x: i64 = sc.cin();
    let mut cs: Vec<i64> = vec![0; n];
    let mut a: Vec<Vec<i64>> = vec![vec![0; m]; n];
    for i in 0..n {
        cs[i] = sc.cin();
        for j in 0..m {
            a[i][j] = sc.cin();
        }
    }

    let mut ans = Inf;

    for p in PowerPermutation::new(2, n) {
        let inds: Vec<_> = (0..n).filter(|&i| p[i] == 1).collect();
        let costs: i64 = inds.iter().map(|&i| cs[i]).sum();
        if Real(costs) > ans {
            continue;
        }
        let mut ks = vec![0; m];
        for &i in inds.iter() {
            for j in 0..m {
                ks[j] += a[i][j];
            }
        }
        let mut ok = true;
        for j in 0..m {
            if ks[j] < x {
                ok = false
            }
        }
        if ok {
            ans = Real(costs);
        }
    }

    if let Real(ans) = ans {
        put!(ans);
    } else {
        put!(-1);
    }
}

trait Group:
    std::ops::Add<Output = Self>
    + std::ops::Sub<Output = Self>
    + std::ops::Neg<Output = Self>
    + std::iter::Sum
    + Clone
    + Copy
{
    fn zero() -> Self;
}
impl Group for i32 {
    fn zero() -> Self {
        0
    }
}
impl Group for i64 {
    fn zero() -> Self {
        0
    }
}
impl Group for f32 {
    fn zero() -> Self {
        0.0
    }
}
impl Group for f64 {
    fn zero() -> Self {
        0.0
    }
}

trait Ring: Group + std::ops::Mul<Output = Self> + std::ops::Div<Output = Self> {
    fn one() -> Self;
}
impl Ring for i32 {
    fn one() -> Self {
        1
    }
}
impl Ring for i64 {
    fn one() -> Self {
        1
    }
}
impl Ring for f32 {
    fn one() -> Self {
        1.0
    }
}
impl Ring for f64 {
    fn one() -> Self {
        1.0
    }
}

#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Debug)]
enum Hyper<X> {
    NegInf,
    Real(X),
    Inf,
}
use Hyper::{Inf, NegInf, Real};
impl<X> Hyper<X> {
    fn unwrap(self) -> X {
        if let Hyper::Real(x) = self {
            x
        } else {
            panic!()
        }
    }
}
impl<X: Ring> std::ops::Add for Hyper<X> {
    type Output = Self;
    fn add(self, rhs: Hyper<X>) -> Hyper<X> {
        match (self, rhs) {
            (Real(x), Real(y)) => Real(x + y),
            (Inf, _) => Inf,
            (_, Inf) => Inf,
            _ => NegInf,
        }
    }
}
impl<X: Ring> std::ops::Sub for Hyper<X> {
    type Output = Self;
    fn sub(self, rhs: Hyper<X>) -> Hyper<X> {
        self + (-rhs)
    }
}
impl<X: Ring> std::ops::Neg for Hyper<X> {
    type Output = Self;
    fn neg(self) -> Hyper<X> {
        match self {
            Inf => NegInf,
            NegInf => Inf,
            Real(x) => Real(-x),
        }
    }
}

struct PowerPermutation {
    n: usize,
    m: usize,
    ar: Vec<usize>,
}
impl PowerPermutation {
    fn new(n: usize, m: usize) -> PowerPermutation {
        let ar = vec![0; m];
        PowerPermutation { n: n, m: m, ar: ar }
    }
}
impl Iterator for PowerPermutation {
    type Item = Vec<usize>;
    fn next(&mut self) -> Option<Vec<usize>> {
        if self.ar[self.m - 1] >= self.n {
            return None;
        }
        let r = self.ar.clone();
        self.ar[0] += 1;
        for i in 0..self.m - 1 {
            if self.ar[i] == self.n {
                self.ar[i] = 0;
                self.ar[i + 1] += 1;
            } else {
                break;
            }
        }
        return Some(r);
    }
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}