using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static string InputPattern = "InputX";
static List<string> GetInputList()
{
var WillReturn = new List<string>();
if (InputPattern == "Input1") {
WillReturn.Add("2 2 1 2");
//4
}
else if (InputPattern == "Input2") {
WillReturn.Add("3 3 4 1");
//18
}
else if (InputPattern == "Input3") {
WillReturn.Add("4 4 8 0");
//36
}
else if (InputPattern == "Input4") {
WillReturn.Add("4 4 0 16");
}
else if (InputPattern == "Input5") {
WillReturn.Add("4 4 8 0");
}
else {
string wkStr;
while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
}
return WillReturn;
}
static int UB_X;
static int UB_Y;
static int mA;
static int mB;
static void Main()
{
List<string> InputList = GetInputList();
int[] wkArr = InputList[0].Split(' ').Select(pX => int.Parse(pX)).ToArray();
UB_Y = wkArr[0] - 1;
UB_X = wkArr[1] - 1;
mA = wkArr[2];
mB = wkArr[3];
Solve();
}
//ピースごとの配置候補
static Dictionary<char, List<bool[,]>> HaitiKouhoListDict =
new Dictionary<char, List<bool[,]>>();
static char[] PieceNameArr = { 'A', 'B' };
struct JyoutaiDef
{
internal char[,] BanArr;
internal int CurrX;
internal int CurrY;
internal Dictionary<char, int> UsePieceDict;
}
static void Solve()
{
int[,] QuestionArr = new int[UB_X + 1, UB_Y + 1];
Dictionary<char, int> CanUsePieceDict = new Dictionary<char, int>() { { 'A', mA }, { 'B', mB } };
for (int X = 0; X <= UB_X; X++) {
for (int Y = 0; Y <= UB_Y; Y++) {
QuestionArr[X, Y] = 1;
}
}
foreach (char AnyPiece in PieceNameArr) {
if (mA == 0 && AnyPiece == 'A') continue;
if (mB == 0 && AnyPiece == 'B') continue;
HaitiKouhoListDict[AnyPiece] = DeriveHaitiKouhoList(AnyPiece);
}
if (mA == 0) HaitiKouhoListDict.Remove('A');
if (mB == 0) HaitiKouhoListDict.Remove('B');
var stk = new Stack<JyoutaiDef>();
JyoutaiDef WillPush;
WillPush.BanArr = new char[UB_X + 1, UB_Y + 1];
for (int X = 0; X <= UB_X; X++)
for (int Y = 0; Y <= UB_Y; Y++)
WillPush.BanArr[X, Y] = (QuestionArr[X, Y] == 1 ? ' ' : '*');
WillPush.CurrX = WillPush.CurrY = 0;
WillPush.UsePieceDict = new Dictionary<char, int>();
stk.Push(WillPush);
long Answer = 0;
while (stk.Count > 0) {
JyoutaiDef Popped = stk.Pop();
//クリア判定
if (Popped.BanArr.Cast<char>().All(X => X != ' ')) {
//Console.WriteLine("解を発見。");
//PrintAnswer(Popped.BanArr);
Answer++;
continue;
}
//Y座標の繰上げ処理
if (Popped.CurrY > UB_Y) {
Popped.CurrY = 0;
Popped.CurrX++;
}
//最終列を超えた場合
if (Popped.CurrX > UB_X) continue;
foreach (char AnyPiece in PieceNameArr) {
if (mA == 0 && AnyPiece == 'A') continue;
if (mB == 0 && AnyPiece == 'B') continue;
if (CanUsePieceDict.ContainsKey(AnyPiece) == false) continue;
if (Popped.UsePieceDict.ContainsKey(AnyPiece)) {
//使用上限に到達している場合は、不可
if (Popped.UsePieceDict[AnyPiece] >= CanUsePieceDict[AnyPiece])
continue;
}
//ピースの配置候補リスト
List<bool[,]> HaitiKouhoList = new List<bool[,]>();
HaitiKouhoList.AddRange(HaitiKouhoListDict[AnyPiece]);
//現在のマス目が空白の場合は、マス目を埋める必要あり
if (Popped.BanArr[Popped.CurrX, Popped.CurrY] == ' ') {
HaitiKouhoList.RemoveAll(X => X[0, 0] == false);
}
//マス目にピースを埋めれない候補をRemove
HaitiKouhoList.RemoveAll(X =>
CanFillPiece(X, Popped.CurrX, Popped.CurrY, Popped.BanArr) == false);
WillPush.UsePieceDict = new Dictionary<char, int>(Popped.UsePieceDict);
if (WillPush.UsePieceDict.ContainsKey(AnyPiece))
WillPush.UsePieceDict[AnyPiece]++;
else WillPush.UsePieceDict[AnyPiece] = 1;
//ピースを配置する経路のPush処理
foreach (bool[,] AnyPieceMap in HaitiKouhoList) {
WillPush.BanArr = (char[,])Popped.BanArr.Clone();
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY + 1;
for (int X = 0; X <= AnyPieceMap.GetUpperBound(0); X++) {
for (int Y = 0; Y <= AnyPieceMap.GetUpperBound(1); Y++) {
if (AnyPieceMap[X, Y] == false) continue;
WillPush.BanArr[Popped.CurrX + X, Popped.CurrY + Y] = AnyPiece;
}
}
stk.Push(WillPush);
}
}
//現在のマス目が空白でない場合は、ピースを配置しない経路のPush
if (Popped.BanArr[Popped.CurrX, Popped.CurrY] != ' ') {
WillPush.BanArr = Popped.BanArr;
WillPush.CurrX = Popped.CurrX;
WillPush.CurrY = Popped.CurrY + 1;
WillPush.UsePieceDict = Popped.UsePieceDict;
stk.Push(WillPush);
}
}
Console.WriteLine(Answer);
}
//ピース名を引数として、回転させた配置のListを返す
static List<bool[,]> DeriveHaitiKouhoList(char pPieceName)
{
bool[,] wkArr = null;
//■
//■
if (pPieceName == 'A') {
wkArr = new bool[1, 2];
wkArr[0, 0] = true;
wkArr[0, 1] = true;
}
//■
if (pPieceName == 'B') {
wkArr = new bool[1, 1];
wkArr[0, 0] = true;
}
return DeriveKaitenArrList(wkArr);
}
//配列を引数として、回転させた配列のリストをDistinctして返す
static List<bool[,]> DeriveKaitenArrList(bool[,] pBaseArr)
{
var KaitenArrList = new List<bool[,]>();
//1個目はそのまま
//■
//■■■
//2個目は1個目を時計回りに90度回転
//■■
//■
//■
//3個目は2個目を時計回りに90度回転
//■■■
// ■
//4個目は3個目を時計回りに90度回転
// ■
// ■
//■■
//5個目は1個目とX軸で線対称
//■■■
//■
//6個目は5個目を時計回りに90度回転
//■■
// ■
// ■
//7個目は6個目を時計回りに90度回転
// ■
//■■■
//8個目は7個目を時計回りに90度回転
//■
//■
//■■
int BaseArrUB_X = pBaseArr.GetUpperBound(0);
int BaseArrUB_Y = pBaseArr.GetUpperBound(1);
for (int I = 1; I <= 8; I++) KaitenArrList.Add(null);
for (int P = 0; P <= 6; P += 2) KaitenArrList[P] = new bool[BaseArrUB_X + 1, BaseArrUB_Y + 1];
for (int P = 1; P <= 7; P += 2) KaitenArrList[P] = new bool[BaseArrUB_Y + 1, BaseArrUB_X + 1];
for (int X = 0; X <= BaseArrUB_X; X++) {
for (int Y = 0; Y <= BaseArrUB_Y; Y++) {
bool SetVal = pBaseArr[X, Y];
KaitenArrList[0][X, Y] = SetVal;
KaitenArrList[1][Y, BaseArrUB_X - X] = SetVal;
KaitenArrList[2][BaseArrUB_X - X, BaseArrUB_Y - Y] = SetVal;
KaitenArrList[3][BaseArrUB_Y - Y, X] = SetVal;
KaitenArrList[4][X, BaseArrUB_Y - Y] = SetVal;
KaitenArrList[5][BaseArrUB_Y - Y, BaseArrUB_X - X] = SetVal;
KaitenArrList[6][BaseArrUB_X - X, Y] = SetVal;
KaitenArrList[7][Y, X] = SetVal;
}
}
//Distinctする
for (int I = KaitenArrList.Count - 1; 0 <= I; I--) {
for (int J = 0; J <= I - 1; J++) {
if (KaitenArrList[I].GetUpperBound(0) !=
KaitenArrList[J].GetUpperBound(0)) continue;
if (KaitenArrList[I].GetUpperBound(1) !=
KaitenArrList[J].GetUpperBound(1)) continue;
IEnumerable<bool> wkEnum1 = KaitenArrList[I].Cast<bool>();
IEnumerable<bool> wkEnum2 = KaitenArrList[J].Cast<bool>();
if (wkEnum1.SequenceEqual(wkEnum2) == false) continue;
KaitenArrList.RemoveAt(I);
break;
}
}
return KaitenArrList;
}
//マス目にピースを埋めれるか
static bool CanFillPiece(bool[,] pPieceMap, int pTargetX, int pTargetY, char[,] pBanArr)
{
for (int X = 0; X <= pPieceMap.GetUpperBound(0); X++) {
if (pTargetX + X > UB_X) return false;
for (int Y = 0; Y <= pPieceMap.GetUpperBound(1); Y++) {
if (pTargetY + Y > UB_Y) return false;
if (pPieceMap[X, Y] && pBanArr[pTargetX + X, pTargetY + Y] != ' ')
return false;
}
}
return true;
}
//解を出力
static void PrintAnswer(char[,] pBanArr)
{
var sb = new System.Text.StringBuilder();
for (int Y = 0; Y <= UB_Y; Y++) {
for (int X = 0; X <= UB_X; X++) {
sb.Append(pBanArr[X, Y]);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
}