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

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 operation.

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

Input

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

Output

On the first line, print "No" if no such sequence of operations exists.

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

If there are multiple possible answers, print any one of them.

Examples

Input 1

2 1 1

Output 1

Yes
1 4
2 3

Input 2

4 4 6

Output 2

No

Input 3

3 995069485 940582184

Output 3

Yes
3816816037 4757398221
5697980405 1935651669
2876233853 995069485

Note

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