The following two situations: 1. Select (a-1) (b-1)+1and c, numbered as (a-1) (b-1) (c-1.

2. Choose C and D to get (c-1) (d-1)+1.

And (a- 1)(b-1)+1and (c-1) (d-1)+1,respectively.

Judging from the above law, the final number is

( 1/2? - 1)*( 1/3? - 1)*…( 1/20 13? - 1)+ 1=( 1- 1/2? )( 1- 1/3? )*…( 1- 1/20 13? )+ 1

Because 1- 1/i? =((I- 1)/I)*((I+ 1)/I)

So the above formula =1/2 * 2/3 * 3/4 * ... * 2012/2013+1= (1/2) * (20/kloc.

So the last thing left is 6037/4024.