MathDB

Iris does not know what to do with her 1-kilogram pie, so she decides to share it with her friend Rosabel. Starting with Iris, they take turns to give exactly half of total amount of pie (by mass) they possess to the other person. Since both of them prefer to have as few number of pieces of pie as possible, they use the following strategy: During each person's turn, she orders the pieces of pie that she has in a line from left to right in increasing order by mass, and starts giving the pieces of pie to the other person beginning from the left. If she encounters a piece that exceeds the remaining mass to give, she cuts it up into two pieces with her sword and gives the appropriately sized piece to the other person.
When the pie has been cut into a total of 2017 pieces, the largest piece that Iris has is

\frac{m}{n}

kilograms, and the largest piece that Rosabel has is

\frac{p}{q}

kilograms, where

m,n,p,q

are positive integers satisfying

\gcd(m,n)=\gcd(p,q)=1

. Compute the remainder when

m+n+p+q

is divided by 2017.
Proposed by Yannick Yao

Problem Statement