Problem:
Score : 500 points

Problem Statement

We have a grid with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.

The square (i, j) has two numbers A_{ij} and B_{ij} written on it.

First, for each square, Takahashi paints one of the written numbers red and the other blue.

Then, he travels from the square (1, 1) to the square (H, W). In one move, he can move from a square (i, j) to the square (i+1, j) or the square (i, j+1). He must not leave the grid.

Let the unbalancedness be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares (1, 1) and (H, W).

Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it.

Find the minimum unbalancedness possible.

Constraints

2 \leq H \leq 80

2 \leq W \leq 80

0 \leq A_{ij} \leq 80

0 \leq B_{ij} \leq 80

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W
A_{11} A_{12} \ldots A_{1W}
:
A_{H1} A_{H2} \ldots A_{HW}
B_{11} B_{12} \ldots B_{1W}
:
B_{H1} B_{H2} \ldots B_{HW}

Output

Print the minimum unbalancedness possible.

Sample Input 1

2 2
1 2
3 4
3 4
2 1

Sample Output 1

0

By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are 3+3+1=7 and 1+2+4=7, respectively, for the unbalancedness of 0.

Sample Input 2

2 3
1 10 80
80 10 1
1 2 3
4 5 6

Sample Output 2

2

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

//! ----------------------------------------------
//! Framework <https://github.com/vain0x/procon>
//!
//! See the bottom of file for solution.
//! ----------------------------------------------

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Display, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

/// Print values to standard error if debug mode.
#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

/// Read from standard input and parse each word.
/// - `read!(T, U, ..)` parses a line as a tuple of words.
/// - `read![[T]]` parses a line as an array of words.
/// - `read![..; N]` parses `N` lines, using `read!(..)` repeatedly.
#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

/// Read a line from standard input.
#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    #[allow(deprecated)]
    buf.trim_right().to_owned()
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

pub fn lower_bound<T: Ord>(xs: &[T], y: &T) -> usize {
    // True-side.
    let mut l = 0;
    let mut r = xs.len() + 1;

    while r - l > 1 {
        let m = l + (r - l) / 2;
        if &xs[m - 1] < y {
            l = m;
        } else {
            r = m;
        }
    }

    l
}

struct Solver {
    H: usize,
    W: usize,
    A: Vec<Vec<i64>>,
    B: Vec<Vec<i64>>,
    forward_balances: Vec<HashSet<i64>>,
    backward_balances: Vec<HashSet<i64>>,
    boundary: i64,
    tick: usize,
}

impl Solver {
    fn forward_dfs(&mut self, y: usize, x: usize, balance: i64) {
        let (H, W) = (self.H, self.W);

        self.tick += 1;

        if balance.abs() >= self.boundary || self.tick >= 100_000_000 {
            return;
        }

        if y == H / 2 {
            if self.forward_balances[x].insert(balance) {
                debug!(("forward", x, balance));
            }
            return;
        }

        let d = self.A[y][x] - self.B[y][x];

        for &t in &[balance + d, balance - d] {
            if y + 1 <= H / 2 {
                self.forward_dfs(y + 1, x, t);
            }

            if x + 1 < W {
                self.forward_dfs(y, x + 1, t);
            }
        }
    }

    fn backward_dfs(&mut self, y: usize, x: usize, balance: i64) {
        let (H, _) = (self.H, self.W);
        let d = self.A[y][x] - self.B[y][x];

        self.tick += 1;

        if balance.abs() >= self.boundary || self.tick >= 10_000_000 {
            return;
        }

        if y == H / 2 {
            if self.backward_balances[x].insert(balance + d) {
                debug!(("backward", balance));
            }
            if self.backward_balances[x].insert(balance - d) {
                debug!(("backward", balance));
            }
        }

        for &t in &[balance + d, balance - d] {
            if y >= H / 2 + 1 {
                self.backward_dfs(y - 1, x, t);
            }

            if x >= 1 {
                self.backward_dfs(y, x - 1, t);
            }
        }
    }

    fn solve(&mut self) -> i64 {
        let (H, W) = (self.H, self.W);

        self.forward_dfs(0, 0, 0);
        self.backward_dfs(H - 1, W - 1, 0);

        let mut m = std::i64::MAX;

        if self.tick >= 10_000_000 {
            return m;
        }

        for x in 0..W {
            let mut backward_balances = self.backward_balances[x]
                .iter()
                .cloned()
                .collect::<Vec<_>>();
            backward_balances.sort();

            for &f in &self.forward_balances[x] {
                self.tick += 1;

                let i = lower_bound(&backward_balances, &f);
                if i < backward_balances.len() {
                    let b = backward_balances[i];
                    let balance = f - b;
                    debug!((f, b, balance));
                    m = min(m, balance.abs());
                }
            }
        }

        m
    }
}

fn main() {
    let (H, W) = read!(usize, usize);
    let A = read![[i64]; H];
    let B = read![[i64]; H];

    let mut tick = 0;
    let mut m = std::i64::MAX;

    for h in 8..40 {
        let boundary = 1 << h;

        if m == 0 || tick >= 10_000_000 {
            break;
        }

        let mut s = Solver {
            H: H,
            W: W,
            A: A.clone(),
            B: B.clone(),
            boundary: boundary,
            tick: tick,
            forward_balances: vec![HashSet::new(); W],
            backward_balances: vec![HashSet::new(); W],
        };

        m = min(m, s.solve());
        tick = s.tick;

        debug!((h, tick));
    }

    println!("{}", m)
}