35234번 - Hyper Smawk Bros 다국어
| 시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
|---|---|---|---|---|---|
| 9 초 | 2048 MB | 5 | 1 | 1 | 33.333% |
문제
You and Bob are playing Hyper Smawk Bros against each other, facing a single boss with health $n$.
You and Bob act alternately, and you start. On your turn, you may use an attack that deals an integer amount of damage $x$ in $[1, m]$, replacing $n$ with $n − x$. However, you cannot use the same $x$ that your opponent just used on the previous turn (on the very first move of the game, any $x$ in $[1, m]$ is allowed).
The winner is the first player to reduce the boss’s health to $n ≤ 0$. Determine whether you can force a win if Bob plays optimally.
입력
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 ≤ t ≤ 10^4$). The description of the test cases follows.
The only line of each test case contains two integers $n$, $m$ ($1 ≤ n ≤ 10^6$, $2 ≤ m ≤ 10^6$) — the starting health $n$ and the maximum damage per attack $m$.
Note that there are no constraints on the sum of $n$ over all test cases, and there are no constraints on the sum of $m$ over all test cases.
출력
For each test case, output YES if you can force a win against Bob, and NO otherwise.
예제 입력 1
8 6 9 20 10 69 2 42 9 42 10 44 9 44 10 400000 400000
예제 출력 1
YES YES NO NO YES YES NO YES
In the first test case, you can win immediately by dealing damage $8$, so that $n$ becomes $6 − 8 = −2 ≤ 0$.
In the second test case,
- you choose to deal damage $10$;
- Bob can choose to deal any damage in $[1, 10]$ different from $10$;
- then you can choose to deal damage $10$ and win.
In the third test case,
- either you start by dealing damage $1$, then Bob must deal damage $2$, then you must deal damage $1$, etc.;
- or you start by dealing damage $2$, then Bob must deal damage $1$, then you must deal damage $2$, etc.
In both cases, you lose.
출처
ICPC > Regionals > Europe > Southwestern European Regional Contest > SWERC 2025 H번