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The +999 will make the result go up by 1 except when xy is exactly 0 mod 1000. It's easy to calculate xy mod 1000 without overflow, as (x mod 1000)*(y mod 1000). So we have two cases: xy = 0 mod 1000: then your f(x,y) is the same as xy div 1000. xy != 0 mod 1000: then your f(x,y) is the same as (xy div 1000) + 1 So we can focus on just calculating xy div ...


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