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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

/**
 * https://kenkoooo.com/atcoder/#/contest/show/79ed76d9-ba5f-44c8-901c-8a7d357a0e7c
 */
public class Main {

    public Main() throws IOException {
    }

    public static void main(String[] args) throws IOException {
        new Main().solve();
    }

    //    private final InputStream in = Files.newInputStream(Paths.get("C:\\Users\\ryo.suzuki\\Downloads\\02.txt"));
    private final InputStream in = System.in;
    private final PrintWriter out = new PrintWriter(System.out);
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private void solve() throws IOException {
        try {
//            solveA();
//            solveB();
//            solveC();
//            solveD();
//            solveE();
            solveF();
        } finally {
            if (in != null) {
                in.close();
            }
            if (out != null) {
                out.flush();
                out.close();
            }
        }

    }

    // mods
    long MOD = (long) Math.pow(10, 9) + 7;

    /**
     * https://atcoder.jp/contests/abc068/tasks/abc068_b
     * B - Break Number
     */
    private void solveA() {
        int n = nextInt();
        {
            int res = 1;
            while (res * 2 <= n)
                res *= 2;
            out.println(res);
        }
        {
//            int res = 0;
//            int maxCnt = -1;
//            for (int i = 1; i <= n; i++) {
//                int cnt = 0;
//                int tmp = i;
//                while (tmp % 2 == 0) {
//                    tmp /= 2;
//                    cnt++;
//                }
//                if (maxCnt < cnt) {
//                    maxCnt = cnt;
//                    res = i;
//                }
//            }
//            out.println(res);
        }

    }

    /**
     * https://atcoder.jp/contests/abc115/tasks/abc115_c
     * C - Christmas Eve
     */
    private void solveB() {
        int n = nextInt();
        int k = nextInt();
        int[] h = IntStream.range(0, n).map(i -> nextInt()).sorted().toArray();
        long res = Integer.MAX_VALUE;
        for (int i = 0; i < n - k + 1; i++) {
            res = Math.min(res, h[i + k - 1] - h[i]);
        }
        out.println(res);
    }

    /**
     * https://atcoder.jp/contests/code-festival-2015-qualb/tasks/codefestival_2015_qualB_c
     * C - 旅館
     */
    private void solveC() {
        int n = nextInt();
        int m = nextInt();
        int[] a = IntStream.range(0, n).map(i -> nextInt()).sorted().toArray();
        int[] b = IntStream.range(0, m).map(i -> nextInt()).sorted().toArray();
        int idx = -1;
        for (int item : b) {
            idx = lowerBound(a, item, idx);
            if (idx >= n) {
                out.println("NO");
                return;
            }
        }
        out.println("YES");
    }

    private int lowerBound(int[] a, int val, int idx) {
        int left = idx;
        int right = a.length;
        while (right - left > 1) {
            int mid = left + (right - left) / 2;
            if (a[mid] >= val)
                right = mid;
            else
                left = mid;
        }
        return right;
    }


    /**
     * https://atcoder.jp/contests/agc017/tasks/agc017_a
     * A - Biscuits
     * <p>
     * https://drken1215.hatenablog.com/entry/2020/04/09/150100
     * https://www.hamayanhamayan.com/entry/2017/07/10/015836
     */
    private void solveD() {
        int n = nextInt();
        int p = nextInt();
        int[] a = IntStream.range(0, n).map(i -> nextInt()).toArray();
        {
            int eve = 0;
            int odd = 0;
            for (int item : a) {
                if (item % 2 == 0)
                    eve++;
                else
                    odd++;
            }
            long resOdd = 0;
            int c = p == 1 ? 1 : 0;
            while (c <= odd) {
                resOdd += aCb(odd, c);
                c += 2;
            }
            long resEve = 1;
            for (int i = 0; i < eve; i++) {
                resEve *= 2L;
            }
            out.println(resOdd * resEve);
        }
        {
            /**
             * DP[i][p]はi番目まで使った時に何通り
             * pは余り
             */
//            long[][] dp = new long[55][2];
//            dp[0][0] = 1;
//            for (int i = 0; i < n; i++) {
//                long item = a[i];
//
//                /** i番目が偶数
//                 * 今までの偶数に今回の使う使わないで×2
//                 * 今までの奇数に今回の使う使わないで×2
//                 * i番目が奇数
//                 * 奇数だった通り数がi番目を使うことで偶数にできるので、
//                 * 今までの偶数+今までの奇数=新しい偶数
//                 * 今までの奇数に今回の使う使わないで×2
//                 */
//                if (item % 2 == 0) {
//                    dp[i + 1][0] = dp[i][0] * 2L;
//                    dp[i + 1][1] = dp[i][1] * 2L;
//                } else {
//                    dp[i + 1][0] = dp[i][0] + dp[i][1];
//                    dp[i + 1][1] = dp[i][0] + dp[i][1];
//                }
//            }
//            out.println(dp[n][p]);
        }

        {
//            long eve = 0;
//            long odd = 0;
//            for (int item : a) {
//                if (item % 2 == 0)
//                    eve++;
//                else
//                    odd++;
//            }
//            if (eve > 0 && odd == 0) {
//                if (p == 0)
//                    out.println(pow(2, eve));
//                else if (p == 1)
//                    out.println(0);
//            } else if (eve == 0 && odd > 0) {
//                if (p == 0)
//                    out.println(pow(2, odd - 1));
//                else if (p == 1)
//                    out.println(pow(2, odd - 1));
//            } else if (eve > 0 && odd > 0) {
//                if (p == 0)
//                    out.println(pow(2, n - 1));
//                else if (p == 1)
//                    out.println(pow(2, n - 1));
//            } else {
//                out.println(0);
//            }
        }
    }

    private boolean isInit = false;
    long[][] memo = new long[1010][1010];

    private long aCb(int a, int b) {
        if (!isInit) {
            for (long[] item : memo) {
                Arrays.fill(item, -1);
            }
            isInit = !isInit;
        }
        if (b == 0 || a == b)
            return 1;
        if (0 <= memo[a][b])
            return memo[a][b];
        return memo[a][b] = aCb(a - 1, b - 1) + aCb(a - 1, b);
    }

    /**
     * https://atcoder.jp/contests/abc087/tasks/arc090_b
     * D - People on a Line
     */
    private void solveE() {
        int n = nextInt();
        int m = nextInt();
        int[][] lrd = IntStream.range(0, m).mapToObj(i -> new int[]{nextInt(), nextInt(), nextInt()}).toArray(int[][]::new);
        Map<Long, GraphNode> graph = new HashMap<Long, GraphNode>();
        Arrays.stream(lrd).forEach(l -> {
            long a = l[0] - 1;
            long b = l[1] - 1;
            long d = l[2];
            graph.put(a, graph.getOrDefault(a, new GraphNode(a)));
            if (graph.get(a).getChild(b).v != CONST_INF) {
                out.println("No");
                return;
            }
            graph.get(a).addChild(b, d);
            graph.put(b, graph.getOrDefault(b, new GraphNode(b)));
            graph.get(b).addChild(a, -d);
        });
        boolean[] visited = new boolean[n];
        int[] dist = new int[n];
//        Arrays.fill(dist, -1);
        for (int i = 1; i <= n; i++) {
            long wkI = i - 1;
            if (visited[i - 1])
                continue;
            Queue<Long> queue = new ArrayDeque<Long>();
            queue.add(wkI);
            while (!queue.isEmpty()) {
                int cnt = queue.size();
                for (int j = 0; j < cnt; j++) {
                    long from = queue.poll();
                    Map<Long, SimplePair> entry = graph.getOrDefault(from, new GraphNode(-1)).childs;
                    for (SimplePair item : entry.values()) {
                        if (visited[(int) item.k]) {
                            if (dist[(int) from] + item.v == dist[(int) item.k])
                                continue;
                            out.println("No");
                            return;
                        }
                        visited[(int) item.k] = true;
                        dist[(int) item.k] = (int) (dist[(int) from] + item.v);
                        queue.add(item.k);
                    }
                }
//                        if (dist[(int) item.k] != -1) {
//                            if (dist[(int) item.k] == dist[(int) from] + item.v)
//                                continue;
//                            out.println("No");
//                            return;
//                        }
//                        dist[(int) item.k] = dist[(int) from] + item.v;
//                        queue.add(item.k);
            }
        }
        out.println("Yes");
    }

    /**
     * https://atcoder.jp/contests/abc147/tasks/abc147_e
     * E - Balanced Path
     */
    private void solveF() {
        int h = nextInt();
        int w = nextInt();
        int[][] a = new int[h][w];
        int[][] b = new int[h][w];
        for (int i = 0; i < 2; i++) {
            int[][] wk = i == 0 ? a : b;
            for (int j = 0; j < h; j++) {
                for (int k = 0; k < w; k++) {
                    wk[j][k] = nextInt();
                }
            }
        }
        final int CONST_K = 80 * 80 * 80;
        final int CONST_INF = Integer.MIN_VALUE / 10;
        int[][][] dp = new int[h][w][CONST_K + 1];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                Arrays.fill(dp[i][j], CONST_INF);
            }
        }
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                int diff = Math.abs(a[i][j] - b[i][j]);
                if (i == 0 && j == 0) {
                    dp[i][j][diff] = 1;
                    continue;
                }
                if (i == 0) {
                    for (int k = 0; k <= CONST_K; k++) {
                        if (dp[i][j - 1][k] != 1)
                            continue;
                        dp[i][j][Math.abs(k + diff)] = 1;
                        dp[i][j][Math.abs(k - diff)] = 1;
                    }
                } else if (j == 0) {
                    for (int k = 0; k <= CONST_K; k++) {
                        if (dp[i - 1][j][k] != 1)
                            continue;
                        dp[i][j][Math.abs(k + diff)] = 1;
                        dp[i][j][Math.abs(k - diff)] = 1;
                    }
                } else {
                    for (int k = 0; k <= CONST_K; k++) {
                        if (dp[i][j - 1][k] == 1) {
                            dp[i][j][Math.abs(k + diff)] = 1;
                            dp[i][j][Math.abs(k - diff)] = 1;
                        }
                        if (dp[i - 1][j][k] == 1) {
                            dp[i][j][Math.abs(k + diff)] = 1;
                            dp[i][j][Math.abs(k - diff)] = 1;
                        }
                    }
                }
            }
        }
        for (int i = 0; i <= CONST_K; i++) {
            if (dp[h - 1][w - 1][i] == CONST_INF)
                continue;
            out.println(i);
            return;
        }
    }

    static final long CONST_INF = Long.MAX_VALUE / 4;


    private static class VectorCalculation {
        /**
         * 点Pと線(AB)の距離
         *
         * @param p
         * @param a
         * @param b
         * @return
         */
        private double distanceDotAndLine(DoublePair p, DoublePair a, DoublePair b) {
            DoublePair ab = new DoublePair(b.x - a.x, b.y - a.y);
            DoublePair ap = new DoublePair(p.x - a.x, p.y - a.y);

            // ベクトルAB、APの外積の絶対値が平行四辺形Dの面積になる
            double d = Math.abs(crossVector(ab, ap));

            double l = distanceVertex(a, b); // AB間の距離

            double h = d / l;
            return h;
        }

        /**
         * 2点間距離
         *
         * @param p1
         * @param p2
         * @return
         */
        private double distanceVertex(DoublePair p1, DoublePair p2) {
            double dx = p1.x - p2.x;
            double dy = p1.y - p2.y;
            return Math.sqrt(dx * dx + dy * dy);
        }

        /**
         * ベクトル外積
         *
         * @param vl
         * @param vr
         * @return
         */
        private double crossVector(DoublePair vl, DoublePair vr) {
            return vl.x * vr.y - vl.y * vr.x;
        }
    }

    private static class DoublePair implements Comparable<DoublePair> {
        double x;
        double y;

        public DoublePair(double k, double v) {
            this.x = k;
            this.y = v;
        }

        public int compareTo(DoublePair pair) {
            return Double.compare(this.y, pair.y);
        }
    }

    private static class SimplePair implements Comparable<SimplePair> {
        long k;
        long v;

        public SimplePair(int k, int v) {
            this.k = k;
            this.v = v;
        }

        public SimplePair(long k, long v) {
            this.k = k;
            this.v = v;
        }

        public int compareTo(SimplePair pair) {
            return Long.compare(this.v, pair.v);
        }
    }


    private static class SimpleGraphNode {
        private int n;
        private Map<Integer, Integer> childs;

        public SimpleGraphNode(int n) {
            this.n = n;
            childs = new HashMap<Integer, Integer>();
        }

        public void addChild(int child, int d) {
            this.childs.put(child, d);
        }
    }

    private static class SimpleGraph {

        private Map<Integer, SimpleGraphNode> graph;

        public SimpleGraph(int[][] list) {
            graph = new HashMap<Integer, SimpleGraphNode>();
            Arrays.stream(list).forEach(l -> {
                int a = l[0];
                int b = l[1];
                int d = l[2];
                graph.put(a, graph.getOrDefault(a, new SimpleGraphNode(a)));
                graph.get(a).addChild(b, d);
                graph.put(b, graph.getOrDefault(b, new SimpleGraphNode(b)));
                graph.get(b).addChild(a, d);
            });
        }

        public SimpleGraphNode getNode(int i) {
            return graph.getOrDefault(i, new SimpleGraphNode(-1));
        }

    }

    private static class GraphNode {
        private long n;
        private Map<Long, SimplePair> childs;

        public GraphNode(long n) {
            this.n = n;
            childs = new HashMap<Long, SimplePair>();
        }

        /**
         * not update
         *
         * @param child
         * @param d
         */
        public void addChild(long child, long d) {
            this.childs.put(child, this.childs.getOrDefault(child, new SimplePair(child, d)));
        }

        public SimplePair getChild(long child) {
            return this.childs.getOrDefault(child, new SimplePair(child, CONST_INF));
        }
    }

    private static class Graph {

        private Map<Long, GraphNode> graph;
        int n;

        /**
         * @param n    頂点数
         * @param list
         */
        public Graph(int n, int[][] list) {
            this.n = n;
            graph = new HashMap<Long, GraphNode>();
            /*
            隣接行列作成
            0-indexed
             */
            Arrays.stream(list).forEach(l -> {
                long a = l[0] - 1;
                long b = l[1] - 1;
                long d = l[2];
                graph.put(a, graph.getOrDefault(a, new GraphNode(a)));
                graph.get(a).addChild(b, d);
                graph.put(b, graph.getOrDefault(b, new GraphNode(b)));
                graph.get(b).addChild(a, d);
            });
            /*
            たどり着けない場所はCONST_INFで埋める
            自分へはCOST=0でたどり着ける
             */
            for (long i = 0; i < n; i++) {
                graph.put(i, graph.getOrDefault(i, new GraphNode(i)));
                GraphNode node = graph.get(i);
                for (int j = 0; j < n; j++) {
                    if (i == j)
                        node.addChild(j, 0L);
                    else
                        node.addChild(j, CONST_INF);
                }
            }
        }

        /**
         * ワーシャルフロイド
         */
        public void warshallFloyd() {
            for (long k = 0; k < n; k++) {
                for (long i = 0; i < n; i++) {
                    for (long j = 0; j < n; j++) {
                        long min = Math.min(graph.get(i).getChild(j).v, graph.get(i).getChild(k).v + graph.get(k).getChild(j).v);
                        graph.get(i).getChild(j).v = min;
                    }
                }
            }
        }

        public void partialUpdateAndWarshallFloyd(long x, long y, long w) {
            if (graph.get(x).getChild(y).v > w)
                graph.get(x).getChild(y).v = graph.get(y).getChild(x).v = w;
            long[] l = {x, y};
            for (long k : l) {
                for (long i = 0; i < n; i++) {
                    for (long j = 0; j < n; j++) {
                        if (graph.get(i).getChild(j).v > graph.get(i).getChild(k).v + graph.get(k).getChild(j).v) {
                            graph.get(i).getChild(j).v = graph.get(i).getChild(k).v + graph.get(k).getChild(j).v;
                        }
                    }
                }
            }
        }

        /**
         * 2点間の距離
         *
         * @param from
         * @param to
         * @return
         */
        public long getDistance(long from, long to) {
            return graph.get(from).getChild(to).v;
        }

    }

    public long calcSimpleCombination(long n, long m, long CONST_MOD) {
        long mole = 1;
        for (long i = 1; i <= n + m; i++) {
            mole *= i;
            mole %= CONST_MOD;
        }
        long deno = 1;
        for (long i = 1; i <= n; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        for (int i = 1; i <= m; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        deno = modInverse(deno, CONST_MOD);
        return (mole * deno) % CONST_MOD;
    }

    long abs(double x) {
        return (long) Math.abs(x);
    }

    long round(double x) {
        return Math.round(x);
    }

    long floor(double x) {
        return (long) Math.floor(x);
    }

    long ceil(double x) {
        return (long) Math.ceil(x);
    }

    double sqrt(double x) {
        return Math.sqrt(x);
    }

    double pow(double x, double y) {
        return Math.pow(x, y);
    }

    long pow(long x, long y) {
        return (long) Math.pow(x, y);
    }

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

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

    public long lcmMod(long... ab) {

        Map<Long, Long> ps = new HashMap<Long, Long>();

        for (int abl = 0; abl < ab.length; abl++) {
            long target = ab[abl];
            long l = target;
            for (long p = 2; p * p <= l; p++) {
                long cnt = 0;
                while (target > 1 && target % p == 0) {
                    cnt++;
                    target /= p;
                }
                if (cnt == 0)
                    continue;
                ps.put(p, Long.max(cnt, ps.getOrDefault(p, 0L)));
            }
            if (target > 1)
                ps.put(target, Long.max(1, ps.getOrDefault(target, 0L)));
        }
        long res = 1L;
        for (Map.Entry<Long, Long> e : ps.entrySet()) {
            res *= powMod(e.getKey(), e.getValue());
            res %= MOD;
        }
        return res;
    }

    int upperToInt(char a) {
        return a - 'A';
    }

    int lowerToInt(char a) {
        return a - 'a';
    }

    int numToInt(char a) {
        return a - '0';
    }

    int charToInt(char a) {
        return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a);
    }

    char intToUpper(int a) {
        return (char) (a + 'A');
    }

    char intToLower(int a) {
        return (char) (a + 'a');
    }

    char intToNum(int a) {
        return (char) (a + '0');
    }

    void reverse(String array[]) {
        String reversed[] = new String[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(int array[]) {
        int reversed[] = new int[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(long array[]) {
        long reversed[] = new long[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(double array[]) {
        double reversed[] = new double[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(boolean array[]) {
        boolean reversed[] = new boolean[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void fill(int array[][], int x) {
        for (int a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(long array[][], long x) {
        for (long a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(double array[][], double x) {
        for (double a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(boolean array[][], boolean x) {
        for (boolean a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(int array[][][], int x) {
        for (int a[][] : array) {
            fill(a, x);
        }
    }

    void fill(long array[][][], long x) {
        for (long a[][] : array) {
            fill(a, x);
        }
    }

    void fill(double array[][][], double x) {
        for (double a[][] : array) {
            fill(a, x);
        }
    }

    void fill(boolean array[][][], boolean x) {
        for (boolean a[][] : array) {
            fill(a, x);
        }
    }

    long L_INF = (long) 1e18 + 7;

    boolean isINF(long a) {
        return abs(a) > L_INF / 1000;
    }

    boolean isPlusINF(long a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(long a) {
        return isPlusINF(-a);
    }

    int I_INF = (int) 1e9 + 7;

    boolean isINF(int a) {
        return abs(a) > I_INF / 1000;
    }

    boolean isPlusINF(int a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(int a) {
        return isPlusINF(-a);
    }

    /**
     * 指定したx以下の素数をリストアップする
     */
    public long[] getPrimesUnderX(long x) {
        return LongStream.rangeClosed(2, x)
                .filter(i -> LongStream.rangeClosed(2, (long) Math.sqrt(i)).allMatch(j -> i % j != 0)).toArray();
    }


    public long mod(long i) {
        return i % MOD + ((i % MOD) < 0 ? MOD : 0);
    }

    long powMod(long x, long y) {
        if (y == 0) {
            return 1;
        } else {
            long tmp = powMod(x, y / 2);
            return mod(mod(tmp * tmp) * (y % 2 == 0 ? 1 : x));
        }
    }

    long inv(long x) {
        return powMod(x, MOD - 2);
    }

    int MAX_FACT = 5_000_100;
    long fact[];
    long invFact[];

    /**
     * Combination簡易版
     * 5 C 2
     * 異なる n個のものから r個を選ぶ組み合わせの総数 nCr を求めます。
     * 5!(5*4*3*2*1)
     * /
     * 2!(2*1) *  (5-2)!(3*2*1)
     *
     * @param n
     * @param r
     * @return
     */
    private long getComb(int n, int r) {
        long tmp = 1;
        for (int i = 1; i <= r; i++) {
            tmp *= n - i + 1;
            tmp = mod(tmp);
            tmp *= inv(i);
            tmp = mod(tmp);
        }
        return tmp;
    }

    /**
     * 階乗計算の事前累積和
     * [1, 1, 2, 3, 4, 5, … FACTORIAL_NUM]
     * mod済
     */
    void prepareFact() {
        fact = new long[MAX_FACT];
        Arrays.fill(fact, 0);
        invFact = new long[MAX_FACT];
        Arrays.fill(invFact, 0);
        fact[0] = 1;
        int maxIndex = (int) min(MAX_FACT, (int) MOD);
        for (int i = 1; i < maxIndex; i++) {
            fact[i] = mod(fact[i - 1] * i);
        }
        invFact[maxIndex - 1] = inv(fact[maxIndex - 1]);
        for (int i = maxIndex - 1; i > 0; i--) {
            invFact[i - 1] = mod(invFact[i] * i);
        }
    }

    /**
     * 順列
     * nPk -> n! / (n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long permutation(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(fact[n] * invFact[n - r]);
    }

    /**
     * 組み合わせ
     * nCk -> n! / k!・(n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long combination(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(permutation(n, r) * invFact[r]);
    }

    /**
     * 重複組合せ nHr （同次積）
     * nHr = (n+r-1)Cr
     * 異なるn個のものから重複を許してr個取る組合せの総数
     * 例：
     * リンゴ，ミカン，牛肉の3種類の果物があります．これらの中から6個の食材を買って帰ります．
     * このとき，何通りの買い方がありますか？ただし，含まれない食材があってもよいものとします
     *
     * @param n
     * @param r
     * @return
     */
    long homogeneousProduct(int n, int r) {
        return combination((n - 1) + r, r);
    }

    /**
     * 多項係数
     * 文字aをp個,bをq個,cをr個, dをs個 あわせてn個を1列に並べるときの並べ方
     * n! / p!・q!・r!・s!
     *
     * @param n
     * @param strNum
     * @param mod
     * @return
     */

    /**
     * フェルマーの小定理を用いて逆元を求める。
     * ある数xのmod p（pは素数）の逆数x'はx' = x^(p-2)
     * 繰り返し二乗法を用いて計算する。
     * http://satanic0258.hatenablog.com/entry/2016/04/29/004730
     * {@link BigInteger#modInverse(BigInteger)}とどちらが速いか？
     *
     * @param x
     * @return
     */
    private long modInverse(long x, long mod) {
        long res = 1L;
        long k = mod - 2L;
        long y = x;
        while (k != 0) {
            if (k % 2 != 0) {
                res = (res * y) % mod;
            }
            y = (y * y) % mod;
            k /= 2;
        }
        return res;
    }

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
    }

    public boolean hasNext() {
        skipUnprintable();
        return hasNextByte();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public long min(long... v) {
        long min = Long.MAX_VALUE;
        for (long i : v) min = Math.min(min, i);
        return min;
    }

    public long max(long... v) {
        long max = Long.MIN_VALUE;
        for (long i : v) max = Math.max(max, i);
        return max;
    }
}