410537: GYM104037 B Decode

Mutitestcases.

You're given three positive integers $$$n_i, e_i, d_i$$$, print two positive integers $$$p_i, q_i$$$, meet $$$n_i = p_i \times q_i$$$ and $$$e_i \times d_i = (p_i - 1)(q_i - 1) + 1$$$.

Read from file "decode.in"

First line an integer $$$t$$$ — number of testcases.

Following $$$t$$$ lines, $$$i$$$th contains three integers $$$n_i, d_i, e_i$$$.

Output to file "decode.out"

Output $$$t$$$ lines, two integers $$$p_i, q_i$$$ as your answer. Note $$$p_i\leq q_i$$$ should hold.

If there are no solutions, pring '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

$$$$$$1\leq t\leq 10^5,1\leq n_i\leq 10^{18},1\leq d_i\times e_i\leq 10^{18},1\leq n_i−e_i\times d_i+2\leq 10^9$$$$$$