Init ialize ] ▁i ▁ ← ▁F k , ▁p ▁ ← ▁F k - 1 , ▁q ▁ ← ▁F k - 2 ▁( through out ▁the ▁algorithm , ▁p ▁and ▁q ▁will ▁be ▁consecutive ▁F ib on acci ▁numbers ) ▁ ▁Step ▁ 2 . ▁[ Comp are ] ▁If ▁K ▁< ▁Ki , ▁go ▁to ▁Step ▁ 3 ; ▁if ▁K ▁> ▁Ki ▁go ▁to ▁Step ▁ 4 ; ▁and ▁if ▁K ▁= ▁Ki , ▁the ▁algorithm ▁termin ates ▁successfully . ▁ ▁Step ▁ 3 . ▁[ Dec re ase ▁i ] ▁If ▁q = 0 , ▁the ▁algorithm ▁termin ates ▁un success fully . ▁Otherwise ▁set ▁( i , ▁p , ▁q ) ▁ ← ▁( i ▁- ▁q , ▁q , ▁p ▁- ▁q ) ▁( which ▁moves ▁p ▁and ▁q ▁one ▁position ▁back ▁in ▁the ▁F ib on acci ▁sequence ); ▁then ▁return ▁to ▁Step ▁ 2 ▁ ▁Step ▁ 4 . ▁[ In cre ase ▁i ] ▁If ▁p = 1 , ▁the ▁algorithm ▁termin ates ▁un success fully . ▁Otherwise ▁set ▁( i , p , q ) ▁ ← ▁( i ▁+ ▁q , ▁p ▁- ▁q , ▁ 2 q ▁- ▁p ) ▁( which ▁moves ▁p ▁and ▁q ▁two ▁positions ▁back ▁in ▁the ▁F ib on acci ▁sequence ); ▁and ▁return ▁to ▁Step ▁ 2 ▁ ▁The ▁two ▁variants ▁of ▁the ▁algorithm ▁presented ▁above ▁always ▁divide ▁the ▁current ▁interval ▁into ▁a ▁larger ▁and ▁a ▁smaller ▁sub interval . ▁The ▁original ▁algorithm ,