Simple Game

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.

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

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.

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