public static FiniteField nCm(FiniteField n, FiniteField m)
{
if (n < m)
{
return(0);
}
if (n < 0 || m < 0)
{
return(0);
}
return(Factorial(n) / (Factorial(m) * Factorial(n - m)));
}
public static FiniteField Derangement(FiniteField n)
{
if (der.Length < n.Value)
{
der = new FiniteField[n];
der[0] = new FiniteField(0);
der[1] = new FiniteField(1);
for (int i = 2; i < n; i++)
{
der[i] = i * (der[i - 1] + der[i - 2]);
}
}
return(der[n - 1]);
}
public static FiniteField Factorial(FiniteField n)
{
if (fac.Length <= n.Value)
{
fac = new FiniteField[n + 1];
fac[0] = new FiniteField(1);
fac[1] = new FiniteField(1);
for (int i = 2; i <= n; i++)
{
fac[i] = i * fac[i - 1];
}
}
return(fac[n]);
}
static FiniteField inversion(FiniteField a)
{
long b = p, u = 1, v = 0;
while (b != 0)
{
long t = a.Value / b;
a.Value -= t * b;
long tmp = a.Value;
a.Value = b;
b = tmp;
u -= t * v;
tmp = u;
u = v;
v = tmp;
}
u %= p;
if (u < 0)
{
u += p;
}
return(u);
}
public FiniteField(FiniteField value)
{
Value = value.Value;
}
public static FiniteField Catalan(FiniteField n)
{
return(nCm(2 * n, n) / (n + 1));
}
