I tried reading the editorial but cannot understand the solution to this problem
The main point which I cannot understand is why should S % gcd(N,K) be equal to 0?
# | User | Rating |
---|---|---|
1 | tourist | 4009 |
2 | jiangly | 3831 |
3 | Radewoosh | 3646 |
4 | jqdai0815 | 3620 |
4 | Benq | 3620 |
6 | orzdevinwang | 3529 |
7 | ecnerwala | 3446 |
8 | Um_nik | 3396 |
9 | gamegame | 3386 |
10 | ksun48 | 3373 |
# | User | Contrib. |
---|---|---|
1 | cry | 164 |
1 | maomao90 | 164 |
3 | Um_nik | 163 |
4 | atcoder_official | 160 |
5 | -is-this-fft- | 158 |
6 | awoo | 157 |
7 | adamant | 156 |
8 | TheScrasse | 154 |
8 | nor | 154 |
10 | Dominater069 | 153 |
Name |
---|
Assuming that the throne is on position 0, then our current position becomes S. If we're moving in a circle then we are bound to follow a cyclic path. So we need both 0 and S to be on the same path.
In a cycle of length 'n', if you jump by 'k' steps then you can move as follows:
0 => gcd(n, k) => 2*gcd(n, k) => ....... (See this for yourself)
So, iff S % gcd(n, k) = 0, 0 can be reached from S after some moves.