Simple Game

면접 대비

시간 제한1초메모리 제한1024 MB

요약

등차수열의 2n개 항을 서로소인 정수 n쌍으로 짝지어 출력하거나, 불가능하면 No를 출력한다.

난이도: 보통10점 중 6점
유형: 수학, 정수론, 그리디
정답자: 아직 제출이 없습니다

문제

Let $s$ be an arithmetic sequence consisting of $2n$ integers, where the first term is denoted as $a$ and the common difference as $b$ . In other words, $s = \[a, a+b, a+2b, \ldots, a+(2n-1)b]$ .

You should perform a sequence of $n$ operations, where each operation involves selecting two coprime integers from $s$ and erasing them. Once an integer is erased from $s$ , it cannot be selected again for any subsequent operations.

Find any sequence of operations satisfying the above conditions, or report that such a sequence does not exist.

입력

The first line contains three integers $n, a, b$ . ( $1 \leq n \leq 10^5$ , $1 \leq a, b \leq 10^9$ )

출력

If no such sequence of operations exists, print No.

Otherwise, print Yes, followed by $n$ lines. On each line, print the two integers selected from $s$ for the corresponding operation.

If there are multiple possible answers, you may print any.

힌트

Two integers are said to be coprime if the only positive integer that divides both of them is $1$ .

예제3

예제 1
입력
```
2 1 1
```
예상 출력
```
Yes
1 4
2 3
```
예제 2
입력
```
4 4 6
```
예상 출력
```
No
```

예제 3

입력

3 995069485 940582184

예상 출력

Yes
3816816037 4757398221
5697980405 1935651669
2876233853 995069485