Doub gammln(const Doub xx) {
	Int j;
	Doub x,tmp,y,ser;
	static const Doub cof[14]={57.1562356658629235,-59.5979603554754912,
	14.1360979747417471,-0.491913816097620199,.339946499848118887e-4,
	.465236289270485756e-4,-.983744753048795646e-4,.158088703224912494e-3,
	-.210264441724104883e-3,.217439618115212643e-3,-.164318106536763890e-3,
	.844182239838527433e-4,-.261908384015814087e-4,.368991826595316234e-5};
	if (xx <= 0) throw("bad arg in gammln");
	y=x=xx;
	tmp = x+5.24218750000000000;
	tmp = (x+0.5)*log(tmp)-tmp;
	ser = 0.999999999999997092;
	for (j=0;j<14;j++) ser += cof[j]/++y;
	return tmp+log(2.5066282746310005*ser/x);
}
Doub factrl(const Int n) {
	static VecDoub a(171);
	static Bool init=true;
	if (init) {
		init = false;
		a[0] = 1.;
		for (Int i=1;i<171;i++) a[i] = i*a[i-1];
	}
	if (n < 0 || n > 170) throw("factrl out of range");
	return a[n];
}
Doub factln(const Int n) {
	static const Int NTOP=2000;
	static VecDoub a(NTOP);
	static Bool init=true;
	if (init) {
		init = false;
		for (Int i=0;i<NTOP;i++) a[i] = gammln(i+1.);
	}
	if (n < 0) throw("negative arg in factln");
	if (n < NTOP) return a[n];
	return gammln(n+1.);
}
Doub bico(const Int n, const Int k) {
	if (n<0 || k<0 || k>n) throw("bad args in bico");
	if (n<171) return floor(0.5+factrl(n)/(factrl(k)*factrl(n-k)));
	return floor(0.5+exp(factln(n)-factln(k)-factln(n-k)));
}
Doub beta(const Doub z, const Doub w) {
	return exp(gammln(z)+gammln(w)-gammln(z+w));
}