Problem Description

Given a positive integer $k$, there are $k$ queries. In each query, three positive integers $n_i, e_i, d_i$ are given. Find two positive integers $p_i, q_i$ such that $n_i = p_i \times q_i$ and $e_i \times d_i = (p_i - 1)(q_i - 1) + 1$.

Input Format

The first line contains a positive integer $k$, meaning there are $k$ queries.

The next $k$ lines each contain three positive integers $n_i, d_i, e_i$ on the $i$-th line.

Output Format

Output $k$ lines. Each line contains two positive integers $p_i, q_i$ as the answer.

To make the output consistent, you should ensure that $p_i \leq q_i$.

If there is no solution, output NO.

10
770 77 5
633 1 211
545 1 499
683 3 227
858 3 257
723 37 13
572 26 11
867 17 17
829 3 263
528 4 109

2 385
NO
NO
NO
11 78
3 241
2 286
NO
NO
6 88

Hint

Sample #2

See decode/decode2.in and decode/decode2.ans in the attachment.

Sample #3

See decode/decode3.in and decode/decode3.ans in the attachment.

Sample #4

See decode/decode4.in and decode/decode4.ans in the attachment.

Constraints

Let $m = n - e \times d + 2$.

It is guaranteed that for $100\%$ of the testdata, $1 \leq k \leq {10}^5$. For any $1 \leq i \leq k$, $1 \leq n_i \leq {10}^{18}$, $1 \leq e_i \times d_i \leq {10}^{18}$, and $1 \leq m \leq {10}^9$.

::cute-table{tuack}

Translated by ChatGPT 5