Description

There are $m$ blue cards and $n$ red cards on the table, each with an integer greater than $1$ on it. You will remove some cards from the table in several steps. Each time, you may remove exactly one pair of cards: the two cards have different colors, and the greatest common divisor of the two numbers on them is greater than $1$. Question: what is the maximum number of pairs you can remove from the table?

Input Format

The first line contains an integer $T$, the number of test cases.

The format of each test case is as follows:

$m\ n$
$b_1\ b_2\ \ldots\ b_m$
$r_1\ r_2\ \ldots\ r_n$

The second line gives the numbers on the blue cards, and the third line gives the numbers on the red cards.

Output Format

For each test case, output the maximum number of pairs of cards that can be removed.

7
4 3
2 6 6 15
2 3 5
2 3
4 9
8 16 32
4 2
4 9 11 13
5 7
5 5
2 3 5 1001 1001
7 11 13 30 30
10 10
2 3 5 7 9 11 13 15 17 29
4 6 10 14 18 22 26 30 34 38
20 20
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
100 100
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
117 755 835 683 52 369 302 424 513 870
75 874 299 228 140 361 30 342 750 819
761 123 804 325 952 405 578 517 49 457
932 941 988 767 624 41 912 702 241 426
351 92 300 648 318 216 785 347 556 535
166 318 434 746 419 386 928 996 680 975
231 390 916 220 933 319 37 846 797 54
272 924 145 348 350 239 563 135 362 119
446 305 213 879 51 631 43 755 405 499
509 412 887 203 408 821 298 443 445 96
274 715 796 417 839 147 654 402 280 17
298 725 98 287 382 923 694 201 679 99
699 188 288 364 389 694 185 464 138 406
558 188 897 354 603 737 277 35 139 556
826 213 59 922 499 217 846 193 416 525
69 115 489 355 256 654 49 439 118 961

3
1
0
4
9
18
85

Hint

For $100 \%$ of the testdata: $1 \le T \le 100$, $1 \le m, n \le 500$, and each card’s number is greater than $1$ and less than ${10}^7$.

Translated by ChatGPT 5