#define DEBUG_ON
#define CONDITION true
using namespace std;/*{{{*/

#include <algorithm>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <sys/time.h>
#include <vector>

#define INF (1e9)
static const double PI = acos(-1.0);
static const double EPS = 1e-10;

typedef long long int LL;
typedef unsigned long long int ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<double> VD;
typedef vector<VD> VVD;
typedef vector<char> VC;
typedef vector<VC> VVC;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef complex<double> P;

#define FOR(i, b, e) for (typeof(e) i = (b); i != (e); i < (e)? ++i : --i)
#define REP(i, n) FOR(i, 0, n)

#define IFC(c) if(c) continue;
#define IFB(c) if(c) break;
#define IFR(c, r) if(c) return r;

#define OPOVER(_op, _type) inline bool operator _op (const _type &t) const

#define arrsz(a) ( sizeof(a) / sizeof(a[0]) )

#define F first
#define S second
#define MP(a, b) make_pair(a, b)

#define SZ(a) ((LL)a.size())
#define PB(e) push_back(e)
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())

#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EACH(c,it) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define EXIST(s,e) ((s).find(e)!=(s).end())

#define BIT(n) (assert(n < 64), (1ULL << (n)))
#define BITOF(n, m) (assert(m < 64), ((ULL)(n) >> (m) & 1))

#define RANGE(a, b, c) ((a) <= (b) && (b) <= (c))

#define PQ priority_queue
#define SC static_cast

#ifdef DEBUG_ON
	#define dprt(fmt, ...) if (CONDITION) fprintf(stderr, fmt, ##__VA_ARGS__)
	#define darr(a) if (CONDITION) copy( (a), (a) + arrsz(a), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define darr_range(a, f, t) if (CONDITION) copy( (a) + (f), (a) + (t), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define dvec(v) if (CONDITION) copy( ALL(v), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define darr2(a, n, m) if (CONDITION) FOR(i, 0, (n)){ darr_range( (a)[i], 0, (m) ); }
	#define dvec2(v) if (CONDITION) FOR(i, 0, SZ(v)){ dvec( (v)[i] ); }
	#define WAIT() if (CONDITION) { string _wait_; cerr << "(hit return to continue)" << endl; getline(cin, _wait_); }
	#define dump(x) if (CONDITION) cerr << " [L" << __LINE__ << "] " << #x << " = " << (x) << endl;
	#define dumpf() if (CONDITION) cerr << __PRETTY_FUNCTION__ << endl;
	#define dumpv(x) if (CONDITION) cerr << " [L:" << __LINE__ << "] " << #x << " = "; REP(q, (x).size()) cerr << (x)[q] << " "; cerr << endl;
	#define where() if (CONDITION) cerr << __FILE__ << ": " << __PRETTY_FUNCTION__ << " [L: " << __LINE__ << "]" << endl;
	#define show_bits(b, s) if(CONDITION) { REP(i, s) { cerr << BITOF(b, s-1-i); if(i%4 == 3) cerr << ' '; } cerr << endl; }
#else
	#define cerr if(0) cerr
	#define dprt(fmt, ...)
	#define darr(a)
	#define darr_range(a, f, t)
	#define dvec(v)
	#define darr2(a, n, m)
	#define dvec2(v)
	#define WAIT()
	#define dump(x)
	#define dumpf()
	#define dumpv(x)
	#define where()
	#define show_bits(b, s)
#endif

/* Inline functions */
inline int onbits_count(ULL b) { int c = 0; while(b != 0) { c += (b & 1); b >>= 1; } return c; }
inline int bits_count(ULL b) { int c = 0; while(b != 0) { ++c; b >>= 1; } return c; }
inline int toInt(string s) { int v; istringstream sin(s);sin>>v;return v; }
template<class T> inline string toString(T x) { ostringstream sout;sout<<x;return sout.str(); }
inline double now(){ struct timeval tv; gettimeofday(&tv, NULL); return (static_cast<double>(tv.tv_sec) + static_cast<double>(tv.tv_usec) * 1e-6); }
inline VS split(string s, char delimiter) { VS v; string t; REP(i, s.length()) { if(s[i] == delimiter) v.PB(t), t = ""; else t += s[i]; } v.PB(t); return v; }

/* Tweaks */
template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& d) {return s << "(" << d.first << ", " << d.second << ")";}

/* Frequent stuffs */
int n_dir = 4;
int dx[] = {0, 1, 0, -1}, dy[] = {-1, 0, 1, 0}; /* CSS order */
enum direction {
	UP, RIGHT, DOWN, LEFT
};
// int n_dir = 8;
// int dx[] = {0, 1, 1, 1, 0, -1, -1, -1}, dy[] = {-1, -1, 0, 1, 1, 1, 0, -1};
// enum direction {
	// UP, UPRIGHT, RIGHT, DOWNRIGHT, DOWN, DOWNLEFT, LEFT, UPLEFT
// }
#define FORDIR(d) REP (d, n_dir)

/*}}}*/

enum state {
	EMPTY,
	HL, HR,
	VT, VB
};
vector< vector<state> > field;
int H, W;

int rec(int i, int j)
{
	if (i == H) {
		return 1;
	}
	if (j >= W) {
		return rec(i + 1, 0);
	}
	if (field[i][j] != EMPTY) {
		return rec(i, j + 1);
	}

	// REP (y, H) {
		// REP (x, W) {
			// cerr << field[y][x] << " ";
		// }
		// cerr << endl;
	// }

	int ret = 0;
	// horizontal
	if (i - 1 < 0 || j - 1 < 0 || field[i-1][j-1] == HL || field[i-1][j-1] == VT) {
		if (i - 1 < 0 || j + 2 == W || field[i-1][j+2] == HR || field[i-1][j+2] == VT) {
			if (j + 1 < W && field[i][j+1] == EMPTY) {
				field[i][j] = HL, field[i][j+1] = HR;
				ret += rec(i, j+1);
				field[i][j] = EMPTY, field[i][j+1] = EMPTY;
			}
		}
	}
	// vertical
	if (i - 1 < 0 || j - 1 < 0 || field[i-1][j-1] == HL || field[i-1][j-1] == VT) {
		if (i - 1 < 0 || j + 1 == W || field[i-1][j+1] == HR || field[i-1][j+1] == VT) {
			if (i + 1 < H) {
				field[i][j] = VT, field[i+1][j] = VB;
				ret += rec(i, j+1);
				field[i][j] = EMPTY, field[i+1][j] = EMPTY;
			}
		}
	}
	return ret;
}

int main()
{
	std::ios_base::sync_with_stdio(false);
	while (cin >> H >> W, H | W) {
		field = vector< vector<state> >(H, vector<state>(W, EMPTY));
		cout << rec(0, 0) << endl;
	}
}

// vim: foldmethod=marker
### Prompt

In Cpp, your task is to solve the following problem:

A tatami mat, a Japanese traditional floor cover, has a rectangular form with aspect ratio 1:2. When spreading tatami mats on a floor, it is prohibited to make a cross with the border of the tatami mats, because it is believed to bring bad luck.

Your task is to write a program that reports how many possible ways to spread tatami mats of the same size on a floor of given height and width.



Input

The input consists of multiple datasets. Each dataset cosists of a line which contains two integers H and W in this order, separated with a single space. H and W are the height and the width of the floor respectively. The length of the shorter edge of a tatami mat is regarded as a unit length.

You may assume 0 < H, W ≤ 20.

The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.

Output

For each dataset, print the number of possible ways to spread tatami mats in one line.

Example

Input

3 4
4 4
0 0


Output

4
2

### Response

```cpp
#define DEBUG_ON
#define CONDITION true
using namespace std;/*{{{*/

#include <algorithm>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <sys/time.h>
#include <vector>

#define INF (1e9)
static const double PI = acos(-1.0);
static const double EPS = 1e-10;

typedef long long int LL;
typedef unsigned long long int ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<double> VD;
typedef vector<VD> VVD;
typedef vector<char> VC;
typedef vector<VC> VVC;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef complex<double> P;

#define FOR(i, b, e) for (typeof(e) i = (b); i != (e); i < (e)? ++i : --i)
#define REP(i, n) FOR(i, 0, n)

#define IFC(c) if(c) continue;
#define IFB(c) if(c) break;
#define IFR(c, r) if(c) return r;

#define OPOVER(_op, _type) inline bool operator _op (const _type &t) const

#define arrsz(a) ( sizeof(a) / sizeof(a[0]) )

#define F first
#define S second
#define MP(a, b) make_pair(a, b)

#define SZ(a) ((LL)a.size())
#define PB(e) push_back(e)
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())

#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EACH(c,it) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define EXIST(s,e) ((s).find(e)!=(s).end())

#define BIT(n) (assert(n < 64), (1ULL << (n)))
#define BITOF(n, m) (assert(m < 64), ((ULL)(n) >> (m) & 1))

#define RANGE(a, b, c) ((a) <= (b) && (b) <= (c))

#define PQ priority_queue
#define SC static_cast

#ifdef DEBUG_ON
	#define dprt(fmt, ...) if (CONDITION) fprintf(stderr, fmt, ##__VA_ARGS__)
	#define darr(a) if (CONDITION) copy( (a), (a) + arrsz(a), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define darr_range(a, f, t) if (CONDITION) copy( (a) + (f), (a) + (t), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define dvec(v) if (CONDITION) copy( ALL(v), ostream_iterator<int>(cerr, " ") ); cerr << endl
	#define darr2(a, n, m) if (CONDITION) FOR(i, 0, (n)){ darr_range( (a)[i], 0, (m) ); }
	#define dvec2(v) if (CONDITION) FOR(i, 0, SZ(v)){ dvec( (v)[i] ); }
	#define WAIT() if (CONDITION) { string _wait_; cerr << "(hit return to continue)" << endl; getline(cin, _wait_); }
	#define dump(x) if (CONDITION) cerr << " [L" << __LINE__ << "] " << #x << " = " << (x) << endl;
	#define dumpf() if (CONDITION) cerr << __PRETTY_FUNCTION__ << endl;
	#define dumpv(x) if (CONDITION) cerr << " [L:" << __LINE__ << "] " << #x << " = "; REP(q, (x).size()) cerr << (x)[q] << " "; cerr << endl;
	#define where() if (CONDITION) cerr << __FILE__ << ": " << __PRETTY_FUNCTION__ << " [L: " << __LINE__ << "]" << endl;
	#define show_bits(b, s) if(CONDITION) { REP(i, s) { cerr << BITOF(b, s-1-i); if(i%4 == 3) cerr << ' '; } cerr << endl; }
#else
	#define cerr if(0) cerr
	#define dprt(fmt, ...)
	#define darr(a)
	#define darr_range(a, f, t)
	#define dvec(v)
	#define darr2(a, n, m)
	#define dvec2(v)
	#define WAIT()
	#define dump(x)
	#define dumpf()
	#define dumpv(x)
	#define where()
	#define show_bits(b, s)
#endif

/* Inline functions */
inline int onbits_count(ULL b) { int c = 0; while(b != 0) { c += (b & 1); b >>= 1; } return c; }
inline int bits_count(ULL b) { int c = 0; while(b != 0) { ++c; b >>= 1; } return c; }
inline int toInt(string s) { int v; istringstream sin(s);sin>>v;return v; }
template<class T> inline string toString(T x) { ostringstream sout;sout<<x;return sout.str(); }
inline double now(){ struct timeval tv; gettimeofday(&tv, NULL); return (static_cast<double>(tv.tv_sec) + static_cast<double>(tv.tv_usec) * 1e-6); }
inline VS split(string s, char delimiter) { VS v; string t; REP(i, s.length()) { if(s[i] == delimiter) v.PB(t), t = ""; else t += s[i]; } v.PB(t); return v; }

/* Tweaks */
template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& d) {return s << "(" << d.first << ", " << d.second << ")";}

/* Frequent stuffs */
int n_dir = 4;
int dx[] = {0, 1, 0, -1}, dy[] = {-1, 0, 1, 0}; /* CSS order */
enum direction {
	UP, RIGHT, DOWN, LEFT
};
// int n_dir = 8;
// int dx[] = {0, 1, 1, 1, 0, -1, -1, -1}, dy[] = {-1, -1, 0, 1, 1, 1, 0, -1};
// enum direction {
	// UP, UPRIGHT, RIGHT, DOWNRIGHT, DOWN, DOWNLEFT, LEFT, UPLEFT
// }
#define FORDIR(d) REP (d, n_dir)

/*}}}*/

enum state {
	EMPTY,
	HL, HR,
	VT, VB
};
vector< vector<state> > field;
int H, W;

int rec(int i, int j)
{
	if (i == H) {
		return 1;
	}
	if (j >= W) {
		return rec(i + 1, 0);
	}
	if (field[i][j] != EMPTY) {
		return rec(i, j + 1);
	}

	// REP (y, H) {
		// REP (x, W) {
			// cerr << field[y][x] << " ";
		// }
		// cerr << endl;
	// }

	int ret = 0;
	// horizontal
	if (i - 1 < 0 || j - 1 < 0 || field[i-1][j-1] == HL || field[i-1][j-1] == VT) {
		if (i - 1 < 0 || j + 2 == W || field[i-1][j+2] == HR || field[i-1][j+2] == VT) {
			if (j + 1 < W && field[i][j+1] == EMPTY) {
				field[i][j] = HL, field[i][j+1] = HR;
				ret += rec(i, j+1);
				field[i][j] = EMPTY, field[i][j+1] = EMPTY;
			}
		}
	}
	// vertical
	if (i - 1 < 0 || j - 1 < 0 || field[i-1][j-1] == HL || field[i-1][j-1] == VT) {
		if (i - 1 < 0 || j + 1 == W || field[i-1][j+1] == HR || field[i-1][j+1] == VT) {
			if (i + 1 < H) {
				field[i][j] = VT, field[i+1][j] = VB;
				ret += rec(i, j+1);
				field[i][j] = EMPTY, field[i+1][j] = EMPTY;
			}
		}
	}
	return ret;
}

int main()
{
	std::ios_base::sync_with_stdio(false);
	while (cin >> H >> W, H | W) {
		field = vector< vector<state> >(H, vector<state>(W, EMPTY));
		cout << rec(0, 0) << endl;
	}
}

// vim: foldmethod=marker
```