/* bc program tangent */
/* This constructs the tangent number  t[n]. In fact it constructs t[1],...,t[n].
   See slides by Richard Brent at https://maths-people.anu.edu.au/~brent/pd/tangent.pdf
 */
define tangent(n){
auto k,j
   t[1]=1
   for(k=2;k<=n;k++){
      t[k]=(k-1)*t[k-1]
   }
   for(k=2;k<=n;k++){
      for(j=k;j<=n;j++){
         t[j]=(j-k)*t[j-1]+(j-k+2)*t[j]
      }
   }
  /* for(k=1;k<=n;k++){
      print "t[",k,"]=",t[k]," "
   }*/
   return(t[n]) 
}

define tangentp(n,p){
auto k,j,temp1,temp2
   t[1]=1
   for(k=2;k<=n;k++){
      t[k]=((k-1)*t[k-1])%p
   }
   for(k=2;k<=n;k++){
      for(j=k;j<=n;j++){
         temp1=((j-k)*t[j-1])%p
         temp2=((j-k+2)*t[j])%p
         t[j]=(temp1+temp2)%p
      }
   }
   for(k=1;k<n;k++){
      print "t[",k,"]=",t[k]," "
   }
   print "t[",n,"]="
   return(t[n]) 
}