Tennis Game

시간 제한1초메모리 제한1024 MB

요약

한 세트를 이기려면 최소 K게임을 따내고 상대보다 2게임 앞서야 할 때, S세트 경기가 정확히 N게임으로 끝날 수 있는지 판정한다.

난이도: 보통10점 중 5점
유형: 수학, 정수론
정답자: 아직 제출이 없습니다

문제

Tennis is a racket sport that is played by two opposing players on S sets. Each set consists of at least K games. A set is won by a player if that player wins at least K games and at least 2 games more than the opponent. Once a set is won, the set is ended and the match continues to a new set (if any) where both players start from 0 game won for that new set.

For example, let K = 6, then a set can be ended with any of the following.

P1 (Player 1) wins 6 games while P2 (Player 2) wins 3 games → P1 wins the set.
P1 wins 7 games while P2 wins 9 games → P2 wins the set.

On the other hand, a set cannot be ended with any of the following.

P1 wins 6 games while P2 wins 5 games → no player wins at least 2 games more than the opponent.
P1 wins 0 game while P2 wins 5 games → no player wins K = 6 games.
P1 wins 7 games while P2 wins 0 games → the set is already ended when P1 won the first 6 games.
P1 wins 8 games while P2 wins 5 games → the set must already be ended before it reaches this state, e.g., the set can be ended at 7 − 5, 6 − 4, 6 − 3, etc.

You are given K, S and N, determine whether there could be such a tennis match with S sets to ends exactly with N games. If there is such a tennis match, then output “YES” (without quotes) in a single line, otherwise, output “NO” (without quotes) in a single line.

For example, let K = 4, S = 2, and N = 14. It is possible to have such a tennis match. One the possibilities is as follows.

Set 1: P1 wins 6 games while P2 wins 4 games.
Set 2: P1 wins 4 games while P2 wins 0 games.

There are a total of N = 6 + 4 + 4 + 0 = 14 games on S = 2 sets where each set is won if a player won at least K = 4 games and at least 2 games more than the opponent.

입력

Input contains three integers K S N (2 ≤ K ≤ 109; 1 ≤ S, N ≤ 109) in a line representing the minimum number of games to win a set, the total number of sets, and the total number of games, respectively.

출력

Output in a line a string “YES” or “NO” (without quotes) whether it is possible to have such a tennis match.

예제3

예제 1
입력
```
4 2 14
```
예상 출력
```
YES
```
예제 2
입력
```
3 1 2
```
예상 출력
```
NO
```
예제 3
입력
```
6 5 181
```
예상 출력
```
YES
```