program p_e;
const
  maxn=20000+1;
type
  tgroup=record father,members:integer;end;
  ttree=array[1..maxn]of tgroup;
  tstack=array[1..maxn]of integer;
  pnode=^tnode;
  tnode=record node:integer; next:pnode; end;
  plist=array[1..maxn]of pnode;
var
  n,k:longint;
  hands:longint;
  groups:ttree;
  ngroups:integer;
  stack:tstack;
  startstack,endstack:integer;
  list:plist;

procedure Add(x,y:integer);
var
  p:pnode;
begin
  new(p);
  p^.node:=y;
  p^.next:=list[x];
  list[x]:=p;
end;

procedure read_data;
var
  ng:integer;
  index:integer;
  i:integer;
  son,mem:integer;
begin
  readln(n,k);
  ngroups:=1;
  groups[1].father:=0;
  groups[1].members:=n;
  fillchar(list,sizeof(list),0);
  while not eof do
  begin
    read(index);
    read(ng);
    for i:=1 to ng do
    begin
      read(son,mem);
      Add(index,son);
      inc(ng);
      groups[son].father:=index;
      groups[son].members:=mem;
    end;
  end;
end;

procedure EliminateOneCouple(node:integer);
begin
  if node=0 then
    exit;
  dec(groups[node].members);
  EliminateOneCouple(groups[node].father);
end;

procedure eliminate_couples;
var
  p:pnode;
begin
  startstack:=1;
  endstack:=1;
  stack[1]:=1;
  while startstack<=endstack do
  begin
    p:=list[stack[startstack]];
    if (p=nil) and (p^.node=2) then
      EliminateOneCouple(stack[startstack])
    else
      while p<>nil do
      begin
        inc(endstack);
        stack[endstack]:=p^.node;
        p:=p^.next;
      end;
    inc(startstack);
  end;
end;

procedure get_handshackes;
var
  p:pnode;
  current_shackes:longint;
begin
  fillchar(stack,sizeof(stack),0);
  startstack:=1;
  endstack:=1;
  stack[1]:=1;
  while startstack<=endstack do
  begin
    p:=list[stack[startstack]];
    current_shackes:=1;
    if p=nil then current_shackes:=0;
    while p<>nil do
    begin
      inc(endstack);
      stack[endstack]:=p^.node;
      current_shackes:=current_shackes*groups[p^.node].members;
      p:=p^.next;
    end;
  inc(startstack);
  inc(hands,current_shackes);
  end;
end;

procedure write_hands;
begin
  writeln(hands);
end;

begin
  read_data;
  eliminate_couples;
  get_handshackes;
  write_hands;
end.

I don't know why ur program got CRASH but it seems u r fooled by
problem description ;)

The remain datas are not useful at all.

n(n-1)/2-k

If you're solving it that way: There's more groups than what you're allocating for.

Specifically, 20000 hobbits in group #1 split into #2 (with 1) and #3 (with 19999). Then #3 splits into #4 (with 1) and #5 (19998) - eventually that hits the limit before the hobbits finish splitting. Find out the correct amount to allocate to avoid the crash.

Also, there's solutions that don't need to track groups (especially the big shortcut).