Arithmetic Progression in CS

In input (through file), there is a positive integer \( N \). In the following \( N \) rows, there will be two integers. In \( i ^\text{th}\) row those will be \( S_i \) and \( D_i \).

Each \( S_i \) belongs to an arithmetic progression \( AP_i \).

Similarly, each \( D_i \) represents the common difference of \( AP_i \).

Answer to the \( i ^\text{th}\) row is a number \( T_i \). That number belongs to \( AP_i \) and is the smallest positive integer of that progression.

Give your answer as \( \displaystyle \sum _{ i = 1 }^{ N }{ T_i } \).

Details and Assumptions:

  • \( N = 5242880 \).

  • If \( D_i = 0 \) then \( S_i > 0 \).

  • All the numbers (including the final answer) are smaller than \( 2^{60} \).

  • The file is "AP1.txt", textual file "Example.txt" is just an example provided.

  • For C/C++ solvers, my personal advice is to use fscanf() because it is significantly faster than the ifstream option.

  • Run time should be about 20 seconds


If something else is left unclear, feel free to ask it here.
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