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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int h = cin.Int();
			int w = cin.Int();
			var a = new int[h, w];
			var b = new int[h, w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					a[i, j] = cin.Int();
				}
			}

			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					b[i, j] = cin.Int();
				}
			}

			int max = (h + w) * 80 + 1;
			int offset = (h + w) * 40;
			var enable = new Bitset[h, w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					enable[i, j] = new Bitset(max);
				}
			}

			enable[0, 0][a[0, 0] - b[0, 0] + offset] = true;
			enable[0, 0][b[0, 0] - a[0, 0] + offset] = true;
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					int dif = Math.Abs(a[i, j] - b[i, j]);
					if (i != 0) {
						enable[i, j] |= enable[i - 1, j] << dif;
						enable[i, j] |= enable[i - 1, j] >> dif;
					}

					if (j != 0) {
						enable[i, j] |= enable[i, j - 1] << dif;
						enable[i, j] |= enable[i, j - 1] >> dif;
					}
				}
			}

			long ans = long.MaxValue;
			for (int k = 0; k < max; k++) {
				if (enable[h - 1, w - 1][k]) {
					int val = Math.Abs(k - offset);
					ans = Math.Min(ans, val);
				}
			}

			Console.WriteLine(ans);
		}
	}

	public class Bitset
	{
		private readonly int length_;
		private readonly ulong[] bits_;

		public int Size { get; }
		public Bitset(int size, bool fillTrue = false)
		{
			Size = size;
			length_ = ((size - 1) >> 6) + 1;
			bits_ = new ulong[length_];
			if (fillTrue) {
				int y = size % 64;
				if (y == 0) {
					for (int i = 0; i < length_; i++) {
						bits_[i] = ulong.MaxValue;
					}
				} else {
					for (int i = 0; i < length_ - 1; i++) {
						bits_[i] = ulong.MaxValue;
					}

					bits_[length_ - 1] = (1UL << y) - 1;
				}
			}
		}
		public Bitset(int size, long initialValue)
		{
			Size = size;
			length_ = ((size - 1) >> 6) + 1;
			bits_ = new ulong[length_];
			bits_[0] = (ulong)initialValue;
		}

		public bool this[int i]
		{
			get { return ((bits_[i >> 6] >> i) & 1) != 0; }
			set { bits_[i >> 6] = (bits_[i >> 6] & (ulong.MaxValue ^ (1ul << i))) | ((ulong)(value ? 1 : 0) << i); }
		}

		public static Bitset operator &(Bitset lhs, Bitset rhs)
		{
			int min = Math.Min(lhs.length_, rhs.length_);

			var ret = new Bitset(Math.Max(lhs.Size, rhs.Size));
			for (int i = 0; i < min; i++) {
				ret.bits_[i] = lhs.bits_[i] & rhs.bits_[i];
			}

			return ret;
		}
		public static Bitset operator |(Bitset lhs, Bitset rhs)
		{
			int max = Math.Max(lhs.length_, rhs.length_);
			int min = Math.Min(lhs.length_, rhs.length_);
			var ret = new Bitset(Math.Max(lhs.Size, rhs.Size));

			for (int i = 0; i < min; i++) {
				ret.bits_[i] = lhs.bits_[i] | rhs.bits_[i];
			}

			if (lhs.length_ > rhs.length_) {
				for (int i = min; i < max; i++) {
					ret.bits_[i] = lhs.bits_[i];
				}
			} else {
				for (int i = min; i < max; i++) {
					ret.bits_[i] = rhs.bits_[i];
				}
			}

			return ret;
		}
		public static Bitset operator ^(Bitset lhs, Bitset rhs)
		{
			int max = Math.Max(lhs.length_, rhs.length_);
			int min = Math.Min(lhs.length_, rhs.length_);
			var ret = new Bitset(Math.Max(lhs.Size, rhs.Size));

			for (int i = 0; i < min; i++) {
				ret.bits_[i] = lhs.bits_[i] ^ rhs.bits_[i];
			}

			if (lhs.length_ > rhs.length_) {
				for (int i = min; i < max; i++) {
					ret.bits_[i] = lhs.bits_[i];
				}
			} else {
				for (int i = min; i < max; i++) {
					ret.bits_[i] = rhs.bits_[i];
				}
			}

			return ret;
		}
		public static Bitset operator <<(Bitset target, int shift)
		{
			var ret = new Bitset(target.Size);
			if (shift > target.length_ << 6) {
				return ret;
			}

			int minIndex = (shift + 63) >> 6;
			if (shift % 64 == 0) {
				for (int i = target.length_ - 1; i >= minIndex; i--) {
					ret.bits_[i] = target.bits_[i - minIndex];
				}
			} else {
				for (int i = target.length_ - 1; i >= minIndex; i--) {
					ret.bits_[i] = (target.bits_[i - minIndex + 1] << shift)
						| (target.bits_[i - minIndex] >> (64 - shift));
				}

				ret.bits_[minIndex - 1] = target.bits_[0] << shift;
			}

			return ret;
		}
		public static Bitset operator >>(Bitset target, int shift)
		{
			var ret = new Bitset(target.Size);
			if (shift > target.length_ << 6) {
				return ret;
			}

			int minIndex = (shift + 63) >> 6;
			if (shift % 64 == 0) {
				for (int i = 0; i + minIndex < ret.length_; i++) {
					ret.bits_[i] = target.bits_[i + minIndex];
				}
			} else {
				for (int i = 0; i + minIndex < ret.length_; i++) {
					ret.bits_[i] = (target.bits_[i + minIndex - 1] >> shift)
						| (target.bits_[i + minIndex] << (64 - shift));
				}

				ret.bits_[ret.length_ - minIndex] = target.bits_[ret.length_ - 1] >> shift;
			}

			return ret;
		}
		public static bool operator ==(Bitset lhs, Bitset rhs)
		{
			int max = Math.Max(lhs.length_, rhs.length_);
			int min = Math.Min(lhs.length_, rhs.length_);
			for (int i = 0; i < min; i++) {
				if (lhs.bits_[i] != rhs.bits_[i]) {
					return false;
				}
			}

			if (lhs.length_ > rhs.length_) {
				for (int i = min; i < max; i++) {
					if (lhs.bits_[i] != 0) {
						return false;
					}
				}
			} else {
				for (int i = min; i < max; i++) {
					if (rhs.bits_[i] != 0) {
						return false;
					}
				}
			}

			return true;
		}
		public static bool operator !=(Bitset lhs, Bitset rhs)
		{
			return !(lhs == rhs);
		}
		public override bool Equals(object obj)
		{
			return false;
		}

		public override int GetHashCode()
		{
			var hashCode = -723801931;
			hashCode = hashCode * -1521134295 + length_.GetHashCode();
			hashCode = hashCode * -1521134295 + EqualityComparer<ulong[]>.Default.GetHashCode(bits_);
			hashCode = hashCode * -1521134295 + Size.GetHashCode();
			return hashCode;
		}

		public override string ToString()
		{
			string ret = "";
			for (int i = 0; i < length_ - 1; i++) {
				string temp = Convert.ToString((long)bits_[i], 2);
				temp = (64 > temp.Length ? new string('0', 64 - temp.Length) : "")
					+ temp;
				ret = temp + ret;
			}

			{
				string temp = Convert.ToString((long)bits_[length_ - 1], 2);
				temp = ((Size % 64) > temp.Length ? new string('0', (Size % 64) - temp.Length) : "")
					+ temp;
				ret = temp + ret;
			}

			return ret;
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}