Program Candy;
Const
  MaxN  = 1000;
  Inf   = 'candy.in';
  Ouf   = 'candy.out';

Var
  p,l,i,j,n,k:Longint;
  Value:Array[1..MaxN,1..10] of Longint;
  Data:Array[1..10,1..10] of record
      num:Longint;
      t:Array[1..30] of Longint;
  End;
  Ans:Array[1..MaxN] of Longint;

Procedure Main;
  Begin
      For   i:=1   to   n   do
      Begin
      if   Data[1,i].t[1]<>0
      then   Value[1,i]:=Data[1,i].t[1];
      End;
      For i:=2 to k do
      Begin
        For j:=1 to n do
          Begin
            For l:=1 to n do
              Begin
                if (j<>l) and (Data[l,j].t[(i-1) mod Data[l,j].num+1]<>0)
                          and ((Value[i,j]=0) or (Value[i-1,l]+Data[l,j].t[(i-1) mod Data[l,j].num+1]<Value[i,j]))
                          then   Value[i,j]:=Value[i-1,l]+Data[l,j].t[(i-1)   mod   Data[l,j].num+1];
              End;
          End;
      End;
      Ans[p]:=Value[k,n];
  End;

Procedure Init;
  Begin
    assign(input,Inf); reset(input);
    assign(output,Ouf); rewrite(output);
    readln(n,k);   p:=0;
    while (n<>0) and (k<>0) do
      Begin
        p:=p+1;
        FillChar(Data,sizeof(Data),0);
        FillChar(Value,sizeof(Value),0);
        For   i:=1 to n do
          Begin
            For j:=1 to i-1 do
              Begin
                read(Data[i,j].num);
                For l:=1 to Data[i,j].num do
                read(Data[i,j].t[l]);
              End;
          For j:=i+1 to n do
            Begin
              read(Data[i,j].num);
              For l:=1 to Data[i,j].num do
              read(Data[i,j].t[l]);
            End;
          End;
          Main;
          readln(n,k);
      End;
  End;


Procedure Print;
  Begin
    For i:=1 to p-1 do
      writeln(Ans[i]);
      write(Ans[p]);
    close(input);
    close(output);
  End;

BEGIN
  Init;
  Print;
END.