When I was doing 1207F - Задача об остатках, I don't know why my program got TLE. Then this ONE trick cut 1 second off my program. You can see this video for more information: https://www.youtube.com/watch?v=ssDBqQ5f5_0. When the compiler compiles `x/9`

, the code roughly converts to `((long long)954437177*x)>>33`

. Division is a much more expensive operation than multiplies and shifts. But what's the special constant `954437177`

? It's $$$\lceil \frac{2^{33}}{9} \rceil$$$. So we have this identity which is vaild for every $$$0\leq a < 2^{31}, 0 < x < 2^{31}$$$:

You can clearly see how this speeds up 1207F: 244531668, 244540601. Note that gcc also does this trick on 64 bits.

After brute forcing with $$$a = 2^{31}-1$$$ I got this new, fixed identity. This should work for all $$$a$$$ (while the old one does not).

very good

thank you

Really cool trick! Sadly g++ doesn’t optimise divisions with numbers not known at compile-time this way.

You can make GCC use this trick in just one line:

`#pragma GCC unroll B`

where`B`

is your block size!With

`B = 700`

it is`1000ms`

faster: 262433429, 262433450Compile to assembly and you can see fixed point multiplication being used.

just remove #define int long long

https://codeforces.com/contest/1207/submission/262501542