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codeforces 414B help

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codeforces 414B << link
solution i was looking at >> 31509108

There's a note at bottom that says:[1, 2], [1, 3] will be lists included.
if i divide 1 by 2 (successor) as 1/2=0.5 or leaves remainder as 1.
and also b1 <= b2 therefore the list can't be [2,1]. Why is [1,2] included in the good sequence?
Can we consider fractions?
So i tried looking at the above mentioned solution but couldn't get it. I am able to solve dp problems with usually 1D array memorization much easily but fail implementing such where we need 2D. Am i missing some concepts of DP or is it only a matter of practice. How to i get to form logics for such problems. Shall I take some tutorials or learn practicing?
* i am a newbie started a month ago, and don't have any idea about combinatorics, so need guidance.


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