Language: C++

// Header {{{
// includes {{{
#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 <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <sys/time.h>
#include <unistd.h>
#include <vector>
// }}}
using namespace std;
// consts {{{
static const int INF = 1e9;
static const double PI = acos(-1.0);
static const double EPS = 1e-10;
// }}}
// typedefs {{{
typedef long long int LL;
typedef unsigned long long int ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<ULL> VULL;
typedef vector<VULL> VVULL;
typedef vector<double> VD;
typedef vector<VD> VVD;
typedef vector<bool> VB;
typedef vector<VB> VVB;
typedef vector<char> VC;
typedef vector<VC> VVC;
typedef vector<VVC> VVVC;
typedef vector<string> VS;
typedef vector<VS> VVS;
typedef pair<int, int> PII;
typedef complex<int> P;
#define PQ(type) priority_queue<type>
// priority queue reverse
#define PQR(type) priority_queue< type, vector<type>, greater<type> >
// }}}
// macros & inline functions {{{
// syntax sugars {{{
#define FOR(i, b, e) for (typeof(e) i = (b); i < (e); ++i)
#define FORI(i, b, e) for (typeof(e) i = (b); i <= (e); ++i)
#define REP(i, n) FOR(i, 0, n)
#define REPI(i, n) FORI(i, 0, n)
#define OPOVER(_op, _type) inline bool operator _op (const _type &t) const
#define ASSIGN_MAX(var, val) ((var) = max((var), (val)))
#define ASSIGN_MIN(var, val) ((var) = min((var), (val)))
// }}}
// conversion {{{
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(); }
// }}}
// array and STL {{{
#define ARRSIZE(a) ( sizeof(a) / sizeof(a[0]) )
#define ZERO(a, v) ( assert(v == 0 || v == -1), memset(a, v, sizeof(a)) )
#define F first
#define S second
#define MP(a, b) make_pair(a, b)
#define SIZE(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 REACH(c, it) for(typeof((c).rbegin()) it=(c).rbegin(); it!=(c).rend(); ++it)
#define EXIST(s, e) ((s).find(e) != (s).end())
// }}}
// bit manipulation {{{
// singed integers are not for bitwise operations, specifically arithmetic shifts ('>>', and maybe not good for '<<' too)
#define IS_UNSIGNED(n) (!numeric_limits<typeof(n)>::is_signed)
#define BIT(n) (assert(IS_UNSIGNED(n)), assert(n < 64), (1ULL << (n)))
#define BITOF(n, m) (assert(IS_UNSIGNED(n)), assert(m < 64), ((ULL)(n) >> (m) & 1))
inline int BITS_COUNT(ULL b) { int c = 0; while(b != 0) { c += (b & 1); b >>= 1; } return c; }
inline int MSB(ULL b) { int c = 0; while(b != 0) { ++c; b >>= 1; } return c-1; }
inline int MAKE_MASK(ULL upper, ULL lower) { assert(lower < 64 && upper < 64 && lower <= upper); return (BIT(upper) - 1) ^ (BIT(lower) - 1); }
// }}}
// for readable code {{{
#define EVEN(n) (n % 2 == 0)
#define ODD(n) (!EVEN(n))
// }}}
// debug {{{
#define arrsz(a) ( sizeof(a) / sizeof(a[0]) )
#define dprt(fmt, ...) if (opt_debug) { fprintf(stderr, fmt, ##__VA_ARGS__); }
#define darr(a) if (opt_debug) { copy( (a), (a) + arrsz(a), ostream_iterator<int>(cerr, " ") ); cerr << endl; }
#define darr_range(a, f, t) if (opt_debug) { copy( (a) + (f), (a) + (t), ostream_iterator<int>(cerr, " ") ); cerr << endl; }
#define dvec(v) if (opt_debug) { copy( ALL(v), ostream_iterator<int>(cerr, " ") ); cerr << endl; }
#define darr2(a) if (opt_debug) { FOR(__i, 0, (arrsz(a))){ darr( (a)[__i] ); } }
#define WAIT() if (opt_debug) { string _wait_; cerr << "(hit return to continue)" << endl; getline(cin, _wait_); }
#define dump(x) if (opt_debug) { cerr << " [L" << __LINE__ << "] " << #x << " = " << (x) << endl; }
// dump vector elements in [s, e)
#define dumpv(v, s, e) if (opt_debug) { cerr << " [L" << __LINE__ << "] " << #v << " = "; FOR(__i, s, e) { cerr << v[__i] << "\t"; } cerr << endl; }
#define dumpl(x) if (opt_debug) { cerr << " [L" << __LINE__ << "] " << #x << endl << (x) << endl; }
#define dumpf() if (opt_debug) { cerr << __PRETTY_FUNCTION__ << endl; }
#define where() if (opt_debug) { cerr << __FILE__ << ": " << __PRETTY_FUNCTION__ << " [L: " << __LINE__ << "]" << endl; }
#define dumpb(bit, digits) if (opt_debug) { cerr << " [L" << __LINE__ << "] " << #bit << " = "; for(int __i = digits - 1; __i >= 0; __i--) { cerr << static_cast<bool>(bit & (1 << __i)); if (__i % 4 == 0) { cerr << " "; } } cerr << endl; }

// ostreams {{{
// complex
template<typename T> ostream& operator<<(ostream& s, const complex<T>& d) {return s << "(" << d.real() << ", " << d.imag() << ")";}

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

// vector
template<typename T> ostream& operator<<(ostream& s, const vector<T>& d) {
	int len = d.size();
	REP (i, len) {
		s << d[i]; if (i < len - 1) s << "\t";
	}
	return s;
}

// 2 dimentional vector
template<typename T> ostream& operator<<(ostream& s, const vector< vector<T> >& d) {
	int len = d.size();
	REP (i, len) {
		s << d[i] << endl;
	}
	return s;
}

// set
template<typename T> ostream& operator<<(ostream& s, const set<T>& v) {
	s << "{ ";
	for (typeof(v.begin()) itr = v.begin(); itr != v.end(); ++itr) {
		if (itr != v.begin()) { s << ", "; }
		s << (*itr);
	}
	s << " }";
	return s;
}

// map
template<typename T1, typename T2> ostream& operator<<(ostream& s, const map<T1, T2>& m) {
	s << "{" << endl;
	for (typeof(m.begin()) itr = m.begin(); itr != m.end(); ++itr) {
		s << "\t" << (*itr).first << " : " << (*itr).second << endl;
	}
	s << "}" << endl;
	return s;
}
// }}}
// }}}
// }}}
// time {{{
inline double now(){ struct timeval tv; gettimeofday(&tv, NULL); return (static_cast<double>(tv.tv_sec) + static_cast<double>(tv.tv_usec) * 1e-6); }
// }}}
// string manipulation {{{
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; }
inline string join(VS s, string j) { string t; REP(i, s.size()) { t += s[i] + j; } return t; }
// }}}
// geometry {{{
#define Y real()
#define X imag()
// }}}
// 2 dimentional array {{{
enum { UP, RIGHT, DOWN, LEFT, UP_RIGHT, DOWN_RIGHT, DOWN_LEFT, UP_LEFT };
int dy4[] = { -1, 0, 1, 0 };
int dx4[] = { 0, 1, 0, -1 };
P dydx4[4] = { P(-1, 0), P(0, 1), P(1, 0), P(0, -1) };
P dydx8[8] = { P(-1, 0), P(0, 1), P(1, 0), P(0, -1), P(-1, 1), P(1, 1), P(1, -1), P(-1, -1) };
bool in_field(int H, int W, P p) {
	return (0 <= p.Y && p.Y < H) && (0 <= p.X && p.X < W);
}
// }}}
// input and output {{{
inline void input(string filename) {
	freopen(filename.c_str(), "r", stdin);
}
inline void output(string filename) {
	freopen(filename.c_str(), "w", stdout);
}
// }}}
// }}}

// Header under development {{{

template<typename T>
T GCD(T a, T b) {
	return b == 0 ? a : GCD(b, a % b);
}

template<typename T>
T LCM(T a, T b) {
	return a * b / GCD(a, b);
}

// Fraction class {{{
// ref: http://martin-thoma.com/fractions-in-cpp/
class Fraction {
	public:
		LL numerator;
		LL denominator;
		Fraction(LL _numerator, LL _denominator) {
			assert(_denominator > 0);
			numerator = _numerator;
			denominator = _denominator;
			if (denominator < 0) {
				denominator *= -1;
				numerator *= -1;
			}
			if (numerator == 0) {
				denominator = 1;
			}
		};

		void reduce() {
			LL gcd = GCD(numerator, denominator);
			numerator /= gcd;
			denominator /= gcd;
		}
};

typedef pair<Fraction, Fraction> PFF;

PFF commonize_denominators(const Fraction& lhs, const Fraction& rhs) {
	LL lcm = LCM(lhs.denominator, rhs.denominator);
	Fraction a(lhs.numerator * lcm / lhs.denominator, lcm);
	Fraction b(rhs.numerator * lcm / rhs.denominator, lcm);
	return MP(a, b);
}

Fraction operator+(const Fraction& lhs, const Fraction& rhs) {
	PFF p = commonize_denominators(lhs, rhs);
	Fraction a = p.F, b = p.S;
	return Fraction(a.numerator + b.numerator, a.denominator);
}

Fraction operator-(const Fraction& lhs, const Fraction& rhs) {
	PFF p = commonize_denominators(lhs, rhs);
	Fraction a = p.F, b = p.S;
	return Fraction(a.numerator - b.numerator, a.denominator);
}

Fraction operator*(const Fraction& lhs, const Fraction& rhs) {
	return Fraction(lhs.numerator * rhs.numerator, lhs.denominator * rhs.denominator);
}

Fraction operator/(const Fraction& lhs, const Fraction& rhs) {
	return Fraction(lhs.numerator * rhs.denominator, lhs.denominator * rhs.numerator);
}

bool operator<(const Fraction& lhs, const Fraction& rhs) {
	PFF p = commonize_denominators(lhs, rhs);
	Fraction a = p.F, b = p.S;
	return a.numerator < b.numerator;
}

template<typename T>
bool operator<(const Fraction& lhs, const T rhs) {
	return lhs < Fraction(rhs, 1);
}

bool operator>(const Fraction& lhs, const Fraction& rhs) {
	PFF p = commonize_denominators(lhs, rhs);
	Fraction a = p.F, b = p.S;
	return a.numerator > b.numerator;
}

template<typename T>
bool operator>(const Fraction& lhs, const T rhs) {
	return lhs > Fraction(rhs, 1);
}

bool operator==(const Fraction& lhs, const Fraction& rhs) {
	return !(lhs < rhs) && !(lhs > rhs);
}

template<typename T>
bool operator==(const Fraction& lhs, const T rhs) {
	return lhs == Fraction(rhs, 1);
}


std::ostream& operator<<(std::ostream &s, const Fraction &a) {
	if (a.denominator == 1) {
		s << a.numerator;
	} else {
		s << a.numerator << "/" << a.denominator;
	}
	return s;
}

// }}}

// }}}

bool opt_debug = false;

int p, q, a, n;

int solve(Fraction frac, int start, int ca, int cn, vector<Fraction> fracs) {
	dump(frac);
	if (frac == 0) {
		dump(fracs);
		return 1;
	}
	if (ca >= a) { return 0; }
	if (cn <= 0) { return 0; }
	if (start > ca) { return 0; }
	if (frac > Fraction(1 / start) * cn) { return 0; }

	int ret = 0;
	for (int denom = start; denom <= a / ca; ++denom) {
		Fraction unit(1, denom);
		Fraction remain = frac - unit;
		if (remain < 0) { continue; }
		vector<Fraction> nfracs = fracs;
		nfracs.PB(unit);
		ret += solve(remain, denom, ca * denom, cn - 1, nfracs);
	}
	return ret;
}

int main(int argc, char** argv) {
	std::ios_base::sync_with_stdio(false);
	// set options {{{
	int __c;
	while ( (__c = getopt(argc, argv, "d")) != -1 ) {
		switch (__c) {
			case 'd':
				opt_debug = true;
				break;
			default:
				abort();
		}
	}
	// }}}

	// opt_debug = true;
	// input("./inputs/1");
	// output("./outputs/0");

	while(cin >> p >> q >> a >> n, p) {
		cout << solve(Fraction(p, q), 1, 1, n, vector<Fraction>()) << endl;
	}

	return 0;
}

// vim: foldmethod=marker

Compiler output:
a.cc: In function 'int solve(Fraction, int, int, int, std::vector<Fraction>)':
a.cc:322:38: error: no matching function for call to 'Fraction::Fraction(int)'
  322 |         if (frac > Fraction(1 / start) * cn) { return 0; }
      |                                      ^
a.cc:215:17: note: candidate: 'Fraction::Fraction(LL, LL)'
  215 |                 Fraction(LL _numerator, LL _denominator) {
      |                 ^~~~~~~~
a.cc:215:17: note:   candidate expects 2 arguments, 1 provided
a.cc:211:7: note: candidate: 'constexpr Fraction::Fraction(const Fraction&)'
  211 | class Fraction {
      |       ^~~~~~~~
a.cc:211:7: note:   no known conversion for argument 1 from 'int' to 'const Fraction&'
a.cc:211:7: note: candidate: 'constexpr Fraction::Fraction(Fraction&&)'
a.cc:211:7: note:   no known conversion for argument 1 from 'int' to 'Fraction&&'