Problem:
Score : 300 points

Problem Statement

Snuke has N dogs and M monkeys. He wants them to line up in a row.

As a Japanese saying goes, these dogs and monkeys are on bad terms. ("ken'en no naka", literally "the relationship of dogs and monkeys", means a relationship of mutual hatred.) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.

How many such arrangements there are? Find the count modulo 10^9+7 (since animals cannot understand numbers larger than that).
Here, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.

Constraints

1 ≤ N,M ≤ 10^5

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of possible arrangements, modulo 10^9+7.

Sample Input 1

2 2

Sample Output 1

8

We will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.

Sample Input 2

3 2

Sample Output 2

12

Sample Input 3

1 8

Sample Output 3

0

Sample Input 4

100000 100000

Sample Output 4

530123477

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;
namespace Program {
    class MainClass {
        //C#Lover///////////////////////////////////////////////////
        int N,M;
        void Solve() {
            io.i(out N, out M);

            long ans = 0;

            if (Math.Abs(N - M) > 1) {
                goto EXIT;
            } else {
                Mat mat = new Mat();
                if(Math.Abs(N-M)==0)
                    ans=(2*(mat.newFact(N)*mat.newFact(M))%mat.mod)%mat.mod;
                else
                    ans = (mat.newFact(N) * mat.newFact(M)) % mat.mod;
            }

            EXIT:;
            io.o(ans);

        }

        ////////////////////////////////////////////////////////////
        public static void Main(string[] args) { new MainClass().Stream(); }
        IO io = new IO();
        void Stream() { Solve(); io.writeFlush(); }
        //void Stream() { Test(); io.writeFlush(); }
        void Test() {
            //100000 100000
            Mat mat = new Mat();
            io.o(mat.newFact(1000000));
        }
        #region MockMacro
        //Hack Update
        //cannot use break,continue,goto
        void FOR(int a, int b, Action<int> act) { for (int i = a; i < b; i++) act(i); }
        void REP(int n, Action<int> act) { for (int i = 0; i < n; i++) act(i); }
        #endregion
    }
    #region default
    class IO {
        TYPE tp;
        string[] nextBuffer; int BufferCnt; char[] cs = new char[] { ' ' };
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        public IO() { nextBuffer = new string[0]; BufferCnt = 0; Console.SetOut(sw); tp = new TYPE(); }
        public string Next() {
            if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public string String => Next();
        public char Char => char.Parse(String);
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string[] arr => Console.ReadLine().Split(' ');
        public char[] arrChar => Array.ConvertAll(arr, char.Parse);
        public int[] arrInt => Array.ConvertAll(arr, int.Parse);
        public long[] arrLong => Array.ConvertAll(arr, long.Parse);
        public double[] arrDouble => Array.ConvertAll(arr, double.Parse);
        public T i<T>() { return tp.suitType<T>(String); }
        public void i<T>(out T v) { v = tp.suitType<T>(String); }
        public void i<T, U>(out T v1, out U v2) { i(out v1); i(out v2); }
        public void i<T, U, V>(out T v1, out U v2, out V v3) { i(out v1); i(out v2); i(out v3); }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4) { i(out v1); i(out v2); i(out v3); i(out v4); }
        public void i<T, U, V, W, X>(out T v1, out U v2, out V v3, out W v4, out X v5) { i(out v1); i(out v2); i(out v3); i(out v4); i(out v5); }
        public void ini<T>(out T[] a, int n) { a = new T[n]; for (int i = 0; i < n; i++) a[i] = tp.suitType<T>(String); }
        public void ini<T>(out T[] a, out T[] b, int n) { a = new T[n]; b = new T[n]; for (int i = 0; i < n; i++) { a[i] = i<T>(); b[i] = i<T>(); } }
        public void ini<T>(out T[,] a, int h, int w) { a = new T[h, w]; for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) a[i, j] = i<T>(); }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void o<T>(params T[] a) { Array.ForEach(a, n => o(n)); }
        public void ol<T>(T v) { Console.Write(v + " "); }
        public void ol<T>(params T[] a) { o(connect<T>(a)); }
        public void br() { o(""); }
        public void writeFlush() { Console.Out.Flush(); }
        private string connect<T>(params T[] s) { return string.Join(" ", s); }
    }
    class Operation<T> {
        public Operation() {
            var availableT = new Type[] { typeof(int), typeof(long), typeof(double) };
            if (!availableT.Contains(typeof(T))) throw new NotSupportedException();
            var p1 = Expression.Parameter(typeof(T));
            var p2 = Expression.Parameter(typeof(T));
            Add = Expression.Lambda<Func<T, T, T>>(Expression.Add(p1, p2), p1, p2).Compile();
            Sub = Expression.Lambda<Func<T, T, T>>(Expression.Subtract(p1, p2), p1, p2).Compile();
            Mul = Expression.Lambda<Func<T, T, T>>(Expression.Multiply(p1, p2), p1, p2).Compile();
            Div = Expression.Lambda<Func<T, T, T>>(Expression.Divide(p1, p2), p1, p2).Compile();
            Mod = Expression.Lambda<Func<T, T, T>>(Expression.Modulo(p1, p2), p1, p2).Compile();
            EQ = Expression.Lambda<Func<T, T, bool>>(Expression.Equal(p1, p2), p1, p2).Compile();
            GT = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThan(p1, p2), p1, p2).Compile();
            GE = Expression.Lambda<Func<T, T, bool>>(Expression.GreaterThanOrEqual(p1, p2), p1, p2).Compile();
            LT = Expression.Lambda<Func<T, T, bool>>(Expression.LessThan(p1, p2), p1, p2).Compile();
            LE = Expression.Lambda<Func<T, T, bool>>(Expression.LessThanOrEqual(p1, p2), p1, p2).Compile();
        }
        public Func<T, T, T> Add { get; private set; }
        public Func<T, T, T> Sub { get; private set; }
        public Func<T, T, T> Mul { get; private set; }
        public Func<T, T, T> Div { get; private set; }
        public Func<T, T, T> Mod { get; private set; }
        public Func<T, T, bool> EQ { get; private set; }
        public Func<T, T, bool> GT { get; private set; }
        public Func<T, T, bool> GE { get; private set; }
        public Func<T, T, bool> LT { get; private set; }
        public Func<T, T, bool> LE { get; private set; }
    }
    class OP {
        //Matを簡潔に...
        public T Add<T>(T a, T b) { var op = new Operation<T>(); return op.Add(a, b); }
        public T Sub<T>(T a, T b) { var op = new Operation<T>(); return op.Sub(a, b); }
        public T Mul<T>(T a, T b) { var op = new Operation<T>(); return op.Mul(a, b); }
        public T Div<T>(T a, T b) { var op = new Operation<T>(); return op.Div(a, b); }
        public T Mod<T>(T a, T b) { var op = new Operation<T>(); return op.Mod(a, b); }
        public bool EQ<T>(T a, T b) { var op = new Operation<T>(); return op.EQ(a, b); }
        public bool GT<T>(T a, T b) { var op = new Operation<T>(); return op.GT(a, b); }
        public bool GE<T>(T a, T b) { var op = new Operation<T>(); return op.GE(a, b); }
        public bool LT<T>(T a, T b) { var op = new Operation<T>(); return op.LT(a, b); }
        public bool LE<T>(T a, T b) { var op = new Operation<T>(); return op.LE(a, b); }
    }
    class TYPE {
        public bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        public T convertType<T, U>(U v) { return (T)Convert.ChangeType(v, typeof(T)); }
        public T suitType<T>(string s) {
            if (typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if (typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if (typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if (typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
    }
    class PQueue<T> where T : IComparable {
        public List<T> heap;
        private Comparison<T> comp;
        private IComparer<T> comparer;
        private int size = 0;
        private int type;
        public PQueue(int type = 0) : this(Comparer<T>.Default) { this.type = type; }
        public PQueue(IComparer<T> comparer) : this(16, comparer.Compare) { this.comparer = comparer; }
        public PQueue(Comparison<T> comparison) : this(16, comparison) { }
        public PQueue(int capacity, Comparison<T> comparison) { this.heap = new List<T>(capacity); this.comp = comparison; }
        public void Enqueue(T item) {
            this.heap.Add(item); var i = size++;
            while (i > 0) { var p = (i - 1) >> 1; if (Compare(this.heap[p], item) <= 0) break; this.heap[i] = heap[p]; i = p; }
            this.heap[i] = item;
        }
        public T Dequeue() {
            var ret = this.heap[0]; var x = this.heap[--size]; var i = 0;
            while ((i << 1) + 1 < size) {
                var a = (i << 1) + 1; var b = (i << 1) + 2; if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                if (Compare(heap[a], x) >= 0) break; heap[i] = heap[a]; i = a;
            }
            heap[i] = x; heap.RemoveAt(size);
            return ret;
        }
        public T Peek() { return heap[0]; }
        public int Count { get { return size; } }
        public bool Any() { return size > 0; }
        public bool Empty() { return !Any(); }
        public bool Contains(T v) { return heap.Contains(v); }
        private int Compare(T x, T y) { return type == 0 ? x.CompareTo(y) : y.CompareTo(x); }
    }
    #endregion
    #region other
    class Mat {
        OP op;
        public Mat() { op = new OP(); }
        public int mod = 1000000007;//10^9+7
        public long Pow(long a, long b) {
            if (b == 0) return 1;
            if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n) {//1e4
            return (n != 0) ? (n % mod * (Fact(n - 1) % mod) % mod) : 1;
        }
        public long newFact(long n) {
            long ret = 1;
            for (long i = 1; i <= n; i++)
                ret = (ret * i) % mod;
            return ret;
        }
        public long C(long n, long r) {
            if (r == 0 || n == r) return 1;
            else if (n == 0) return 0;
            else if (n < 0 || n < r) throw new ArgumentException("n,r invalid");
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public bool isPrime(long n) {
            if (n == 2) return true; if (n < 2 || n % 2 == 0) return false;
            for (long v = 3; v <= (long)Math.Sqrt(n); v += 2) if (n % v == 0) return false;
            return true;
        }
        public long LCM(long a, long b) { return a * (b / GCD(a, b)); }
        public long LCM(params long[] a) { return a.Aggregate((v, n) => LCM(v, n)); }
        public long GCD(long a, long b) { if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b); }
        public long GCD(params long[] array) { return array.Aggregate((v, next) => GCD(v, next)); }
        public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
        public T Max<T>(params T[] v) { return v.Max(); }
        public T Min<T>(params T[] v) { return v.Min(); }
        public double Dis(int x1, int y1, int x2, int y2) { return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2)); }
        public int mDis(int x1, int y1, int x2, int y2) { return Math.Abs(x1 - x2) + Math.Abs(y1 - y2); }
        public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        public int DigVal(int n, int dig) { return (n % (int)Pow(10, dig)) / (int)Pow(10, dig - 1); }
        public int[] DigValArr(int n) { int[] ret = new int[Digit(n)]; M.REP(ret.Length, i => ret[i] = DigVal(n, i + 1)); return ret; }
        public int Clamp(int n, int a, int b) { return (n < a) ? a : (b < n) ? b : n; }
        public long Clamp(long n, long a, long b) { return (n < a) ? a : (b < n) ? b : n; }
        public double Clamp(double n, double a, double b) { return (n < a) ? a : (b < n) ? b : n; }
        public long Tousa(long a, long d, int n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, int n) { return n * (2 * a + (n - 1) * d) / 2; }
    }
    class AssociativeArray<T> {//hack:配列時要初期化
        public Dictionary<T, int> dic;
        public AssociativeArray() { dic = new Dictionary<T, int>(); }
        public AssociativeArray(params T[] a) { dic = new Dictionary<T, int>(); Add(a); }
        public void Add(params T[] a) { M.REP(a.Length, i => { if (!conK(a[i])) dic[a[i]] = 0; dic[a[i]]++; }); }
        public void Set(T k, int v) { if (!dic.ContainsKey(k)) dic[k] = 0; dic[k] = v; }
        public void Remove(params T[] a) { M.REP(a.Length, i => { if (conK(a[i])) dic.Remove(a[i]); }); }
        public T[] Keys() { return dic.Keys.ToArray<T>(); }
        public int Val(T k) { return (dic.ContainsKey(k)) ? dic[k] : 0; }
        public int ValSum => dic.Values.Sum();
        public int KeyNum => dic.Keys.Count;
        public int MaxVal => dic.Values.Max();
        public int MinVal => dic.Values.Min();
        public T MaxKey => dic.First(d => d.Value == MaxVal).Key;
        public T MinKey => dic.First(d => d.Value == MinVal).Key;
        public bool conK(T k) { return dic.ContainsKey(k); }
        public bool anyK(params T[] k) { return k.Any(key => conK(key)); }
        public bool allK(params T[] k) { return k.All(key => conK(key)); }
        public void Show() { foreach (var v in dic) { Console.WriteLine(v.Key + " : " + v.Value); } }
        //:sort->array
    }
    class UnionFind {
        public long[] parent; public long[] depth;
        public void Init(long n) { parent = new long[n]; depth = new long[n]; M.REP(n, i => parent[i] = i); }
        public long Find(long x) { return (parent[x] == x) ? x : parent[x] = Find(parent[x]); }
        public void Unite(long x, long y) {
            x = Find(x); y = Find(y); if (x == y) return;
            if (depth[x] < depth[y]) parent[x] = y; else { parent[y] = x; if (depth[x] == depth[y]) depth[x]++; }
        }
        public bool Same(long a, long b) { return Find(a) == Find(b); }
    }
    class Time { public bool isLeapYear(int y) { return (y % 400 == 0 || (y % 4 == 0 && y % 100 != 0)); } }
    #endregion
    #region Graph
    class Index {
        public int[] Comp(int[] bef) {
            int[] aft = new int[bef.Length];
            var tmp = bef.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
            aft = bef.Select(v => tmp[v]).ToArray();
            return aft;
        }
    }
    class BasicGraph {//まとめよう      
        public List<Tuple<int, long>>[] G;
        public void Init(int n) { G = new List<Tuple<int, long>>[n + 1]; G.Length.REP(i => G[i] = new List<Tuple<int, long>>()); }
        public void Dir(int[] f, int[] t) { f.Length.REP(i => G[f[i]].Add(Tuple.Create(t[i], 1L))); }
        public void Dir(int[] f, int[] t, long[] c) { f.Length.REP(i => G[f[i]].Add(Tuple.Create(t[i], c[i]))); }
        public void NonDir(int[] f, int[] t) { f.Length.REP(i => { G[f[i]].Add(Tuple.Create(t[i], 1L)); G[t[i]].Add(Tuple.Create(f[i], 1L)); }); }
        public void NonDir(int[] f, int[] t, long[] c) { f.Length.REP(i => { G[f[i]].Add(Tuple.Create(t[i], c[i])); G[t[i]].Add(Tuple.Create(f[i], c[i])); }); }
    }
    class TreeDis {//test
        public List<Tuple<long, long>>[] g; public long[] a2other; private int type;
        public TreeDis(int type = 0) { this.type = type; }//0->bfs,other->dfs
        public void Init(long n) { g = new List<Tuple<long, long>>[n + 1]; M.REP(g.Length, i => g[i] = new List<Tuple<long, long>>()); }
        public void Run(long[] a, long[] b) { M.REP(a.Length, i => { g[a[i]].Add(Tuple.Create(b[i], 1L)); g[b[i]].Add(Tuple.Create(a[i], 1L)); }); }
        public void Run(long[] a, long[] b, long[] w) { M.REP(a.Length, i => { g[a[i]].Add(Tuple.Create(b[i], w[i])); g[b[i]].Add(Tuple.Create(a[i], w[i])); }); }
        public long[] a2iArr(long a) { a2other = new long[g.Count()]; if (type == 0) BFS(a); else DFS(a); return a2other; }
        private void BFS(long a) {
            var q = new Queue<Tuple<long, long>>(); q.Enqueue(Tuple.Create(a, -1L));
            while (q.Count > 0) {
                var c = q.Dequeue();
                foreach (var v in g[c.Item1]) {
                    if (v.Item1 == c.Item2) continue;
                    a2other[v.Item1] = a2other[c.Item1] + v.Item2; q.Enqueue(Tuple.Create(v.Item1, c.Item1));
                }
            }
        }
        private void DFS(long a) {
            var s = new Stack<Tuple<long, long>>(); s.Push(Tuple.Create(a, -1L));
            while (s.Count > 0) {
                var c = s.Pop();
                foreach (var v in g[c.Item1]) {
                    if (v.Item1 == c.Item2) continue;
                    a2other[v.Item1] = a2other[c.Item1] + v.Item2; s.Push(Tuple.Create(v.Item1, c.Item1));
                }
            }
        }
    }
    class ShortestPath {
        protected int I = -1; protected long INF = (int)1e9; public List<Tuple<int, long>>[] Adj;
        public void Init(int n) { I = n + 1; Adj = new List<Tuple<int, long>>[I]; I.REP(i => Adj[i] = new List<Tuple<int, long>>()); }
        public void AddPath(int f, int t, long c) { Adj[f].Add(Tuple.Create(t, c)); Adj[t].Add(Tuple.Create(f, c)); }
        public void AddPath(int[] f, int[] t, long[] c) { f.Length.REP(i => AddPath(f[i], t[i], c[i])); }
    }
    class Dijkstra : ShortestPath {//隣接対応後未検証
        public long MinCost(int f, int t) {
            long[] cost = new long[I]; cost.Set(INF); cost[f] = 0;
            var pq = new PQueue<Tuple<int, long>>(); pq.Enqueue(Tuple.Create(f, 0L));//(from,cost)
            while (pq.Count > 0) {
                var cur = pq.Dequeue();
                if (cost[cur.Item1] < cur.Item2) continue; Adj[cur.Item1].Count.REP(i => {
                    var tmp = Adj[cur.Item1][i];
                    if (cost[tmp.Item1] > cost[cur.Item1] + tmp.Item2) {
                        cost[tmp.Item1] = cost[cur.Item1] + tmp.Item2; pq.Enqueue(Tuple.Create(tmp.Item1, cost[tmp.Item1]));
                    }
                });
            }
            return cost[t];
        }
    }
    class BellmanFord : ShortestPath {
        public long MinCost(int f, int t) {
            long[] cost = new long[I]; cost.Set(INF); cost[f] = 0; bool isUpdate = true;
            while (isUpdate) {
                isUpdate = false;
                I.REP(i => Adj[i].Count.REP(j => {
                    var cur = Adj[i][j];
                    if (cost[cur.Item1] > cost[i] + cur.Item2) { cost[cur.Item1] = cost[i] + cur.Item2; isUpdate = true; }
                }));
            }
            return cost[t];
        }
    }
    class WarshallFloyd {//TODO:update
        private int E; private int INF = (int)1e9; public long[,] G;
        public void Init(int n) { E = n + 1; G = new long[E, E]; G.Set(INF); E.REP(i => G[i, i] = 0); }
        public void AddPath(int f, int t, long c) { G[f, t] = c; G[t, f] = c; }
        public void AddPath(int[] f, int[] t, long[] c) { f.Length.REP(i => AddPath(f[i], t[i], c[i])); }
        public long[,] MinCostArr() { E.REP(i => E.REP(j => E.REP(k => G[j, k] = Math.Min(G[j, k], G[j, i] + G[i, k])))); return G; }
    }
    #endregion
    #region Ex
    static class StringEX {//文字
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
        public static int toInt(this string s) { int n; return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0; }
        public static int toInt(this char c) { return toInt(c.ToString()); }
        public static int toInt(this char[] c) { return toInt(new string(c)); }
        public static string toString(this char[] c) { return new string(c); }
    }
    static class NumericEx {//数値
        public static string pad0<T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
        public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
        public static bool isOdd(this int v) { return v % 2 != 0; }
    }
    static class ArrayEX {
        public static T[] Sort<T>(this T[] a) { Array.Sort(a); return a; }
        public static void Set<T>(this T[] a, T v) { M.REP(a.Length, i => a[i] = v); }
        public static void Set<T>(this T[,] a, T v) { M.REP(a.GetLength(0), i => M.REP(a.GetLength(1), j => a[i, j] = v)); }
    }
    static class BitEx {
        public static bool Any(this BitArray b) { foreach (bool f in b) if (f) return true; return false; }
        public static bool All(this BitArray b) { foreach (bool f in b) if (!f) return false; return true; }
        public static bool None(this BitArray b) { return !Any(b); }
        public static void Flip(this BitArray b, int index) { b.Set(index, !b.Get(index)); }
    }
    static class M {//otherExへ移行
        public static void REP(int n, Action<int> a) { for (int i = 0; i < n; i++) a(i); }
        public static void REP(long n, Action<long> a) { for (long i = 0; i < n; i++) a(i); }
    }
    static class OtherEx {
        public static void REP(this int v, Action<int> act) { for (int i = 0; i < v; i++) act(i); }

    }
    #endregion
}