516_E. Drazil and His Happy Friends_10299
Drazil has many friends. Some of them are happy and some of them are unhappy. Drazil wants to make all his friends become happy. So he invented the following plan.

There are n boys and m girls among his friends. Let's number them from 0 to n - 1 and 0 to m - 1 separately. In i-th day, Drazil invites <image>-th boy and <image>-th girl to have dinner together (as Drazil is programmer, i starts from 0). If one of those two people is happy, the other one will also become happy. Otherwise, those two people remain in their states. Once a person becomes happy (or if it is happy originally), he stays happy forever.

Drazil wants to know on which day all his friends become happy or to determine if they won't become all happy at all.

Input

The first line contains two integer n and m (1 ≤ n, m ≤ 109).

The second line contains integer b (0 ≤ b ≤ min(n, 105)), denoting the number of happy boys among friends of Drazil, and then follow b distinct integers x1, x2, ..., xb (0 ≤ xi < n), denoting the list of indices of happy boys.

The third line conatins integer g (0 ≤ g ≤ min(m, 105)), denoting the number of happy girls among friends of Drazil, and then follow g distinct integers y1, y2, ... , yg (0 ≤ yj < m), denoting the list of indices of happy girls.

It is guaranteed that there is at least one person that is unhappy among his friends.

Output

Print the number of the first day that all friends of Drazil become happy. If this day won't come at all, you print -1.

Examples

Input

2 3
0
1 0


Output

4


Input

2 4
1 0
1 2


Output

-1


Input

2 3
1 0
1 1


Output

2


Input

99999 100000
2 514 415
2 50216 61205


Output

4970100515

Note

By <image> we define the remainder of integer division of i by k.

In first sample case: 

  * On the 0-th day, Drazil invites 0-th boy and 0-th girl. Because 0-th girl is happy at the beginning, 0-th boy become happy at this day. 
  * On the 1-st day, Drazil invites 1-st boy and 1-st girl. They are both unhappy, so nothing changes at this day. 
  * On the 2-nd day, Drazil invites 0-th boy and 2-nd girl. Because 0-th boy is already happy he makes 2-nd girl become happy at this day. 
  * On the 3-rd day, Drazil invites 1-st boy and 0-th girl. 0-th girl is happy, so she makes 1-st boy happy. 
  * On the 4-th day, Drazil invites 0-th boy and 1-st girl. 0-th boy is happy, so he makes the 1-st girl happy. So, all friends become happy at this moment. 
n, m = (int(x) for x in input().split())
happy_boys = [0 for _ in range(n)]
happy_girls = [0 for _ in range(m)]
boys = [int(x) for x in input().split()]
girls = [int(x) for x in input().split()]
if boys[0]:
    for i in range(1, len(boys)):
        happy_boys[boys[i]] = 1

if girls[0]:
    for i in range(1, len(girls)):
        happy_girls[girls[i]] = 1
# print (happy_boys)
# print (happy_girls)
add_val = max(n, m)
days_left = m * n + 1
cur_day = 0
while cur_day < days_left:
    if happy_boys[cur_day % n] ^ happy_girls[cur_day % m]:
        days_left += add_val
        # print(happy_boys)
        # print(happy_girls)
        # print("")
        happy_boys[cur_day % n] = happy_girls[cur_day % m] = 1
        # print(happy_boys)
        # print(happy_girls)
    cur_day += 1
if all(happy_boys) and all(happy_girls):
    print("Yes")
else:
    print("No")

2 3
1 0
1 1
 2 3
0
1 0
 2 4
1 0
1 2
 99999 100000
2 514 415
2 50216 61205
 3 5
0
5 4 3 2 1 0
 5 12
0
3 0 8 4
 98 49
33 0 51 52 6 57 10 12 63 15 16 19 20 21 72 73 74 76 77 78 30 31 81 33 83 37 38 39 40 92 44 45 95 97
15 4 5 7 9 11 13 17 18 22 26 35 36 41 42 47
 6 54
1 5
14 13 49 31 37 44 2 15 51 52 22 28 10 35 47
 4 5
3 0 1 3
4 0 1 3 4
 100 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
 41 2
1 33
0
 52 91
13 26 1 3 43 17 19 32 46 33 48 23 37 50
25 78 26 1 40 2 67 42 4 56 30 70 84 32 20 85 59 8 86 34 73 23 10 88 24 11
 816 688
23 434 388 225 277 775 76 720 339 561 754 400 221 677 317 762 373 198 126 170 158 217 202 224
30 213 619 430 587 223 367 203 467 180 324 643 53 406 651 130 126 499 74 346 590 335 435 258 593 356 495 101 345 521 35
 66 66
24 2 35 3 36 4 5 10 45 14 48 18 51 19 21 55 22 23 24 25 26 63 31 65 32
21 0 1 37 6 40 7 8 42 45 13 15 16 50 53 23 24 60 28 62 63 31
 654 44
15 500 322 152 140 176 342 311 643 391 440 373 312 374 382 231
17 12 4 16 18 26 41 14 33 43 29 34 3 39 19 24 1 7
 4 1
1 3
0
 1 1
1 0
0
 36 100
10 0 32 4 5 33 30 18 14 35 7
29 60 32 20 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 67 75 35 95 43 79 3 27
 50 49
1 49
0
 55 79
5 51 27 36 45 53
30 15 28 0 5 38 3 34 30 35 1 32 12 27 42 39 69 33 10 63 16 29 76 19 60 70 67 31 78 68 45
 26 52
8 0 14 16 17 7 9 10 11
15 39 15 2 41 42 30 17 18 31 6 21 35 48 50 51
 39 87
16 18 15 30 33 21 9 3 31 16 10 34 20 35 8 26 23
36 33 75 81 24 42 54 78 39 57 60 30 36 63 4 76 25 1 40 73 22 58 49 85 31 74 59 20 44 83 65 23 41 71 47 14 35
 66 66
26 0 54 6 37 43 13 25 38 2 32 56 20 50 39 27 51 9 64 4 16 17 65 11 5 47 23
15 6 24 43 49 25 20 14 63 27 3 58 52 53 11 41
 20 20
9 0 3 4 6 7 8 10 12 13
10 1 2 5 9 11 14 15 16 18 19
 50 50
0
0
 76 72
29 4 64 68 20 8 12 50 42 46 0 70 11 37 75 47 45 29 17 19 73 9 41 31 35 67 65 39 51 55
25 60 32 48 42 8 6 9 7 31 19 25 5 33 51 61 67 55 49 27 29 53 39 65 35 13
 100 40
25 61 42 2 3 25 46 66 68 69 49 9 10 50 91 72 92 33 73 53 14 15 55 96 36 39
12 0 22 3 23 4 6 27 11 35 37 38 39
 5 5
4 4 3 2 1
5 4 2 1 3 0
 69 72
18 58 46 52 43 1 55 16 7 4 38 68 14 32 53 41 29 2 59
21 22 43 55 13 70 4 7 31 10 23 56 44 62 17 50 53 5 41 11 65 32
 91 98
78 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89
84 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89 91 92 93 94 95 96
 3 20
0
1 19
 30 44
3 8 26 28
6 2 30 38 26 8 6
 5 7
1 0
1 0
 24 60
4 0 2 19 23
15 12 24 49 2 14 3 52 28 5 6 19 32 33 34 35
 96 36
34 84 24 0 48 85 13 61 37 62 38 86 75 3 16 64 40 28 76 53 5 17 42 6 7 91 67 55 68 92 57 11 71 35 59
9 1 14 15 17 18 30 6 8 35
 80 40
27 0 41 44 45 6 47 8 10 52 13 14 16 17 18 59 21 62 23 64 26 68 29 32 75 37 78 39
13 2 3 9 11 15 20 25 27 30 31 33 34 36
 76 28
10 24 13 61 45 29 57 41 21 37 11
2 12 9
 37 91
3 10 21 33
2 89 3
 98 98
23 6 81 90 28 38 51 23 69 13 95 15 16 88 58 10 26 42 44 54 92 27 45 39
18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57
 66 99
23 33 35 36 38 8 10 44 11 45 46 47 50 19 54 22 55 23 58 59 27 61 30 65
32 33 67 69 4 70 38 6 39 7 74 42 9 43 12 13 14 15 81 82 84 85 20 87 89 90 24 58 59 27 95 97 31
 100 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
 100 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
50 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
 7 72
1 4
3 49 32 28
 27 31
4 25 5 19 20
26 5 28 17 2 1 0 26 23 12 29 6 4 25 19 15 13 20 24 8 27 22 30 3 10 9 7
 90 25
26 55 30 35 20 15 26 6 1 41 81 76 46 57 17 12 67 77 27 47 62 8 43 63 3 48 19
9 10 16 21 7 17 12 13 19 9
 5 5
0
5 1 2 4 3 0
 100 100
45 50 1 4 5 55 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 84 36 37 38 39 40 41 42 44 45 46 48 98 49
34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49
 2 8
0
7 0 2 3 4 5 6 7
 100 1
1 99
0
 3 50
0
1 49
 100 50
31 52 54 8 60 61 62 63 64 16 19 21 73 25 76 77 79 30 81 32 33 34 37 88 39 40 91 42 94 95 96 98
18 0 1 3 5 6 7 9 15 18 20 22 24 28 35 36 43 47 49
 16 88
6 5 14 2 0 12 7
30 21 64 35 79 74 39 63 44 81 73 0 27 33 69 12 86 46 20 25 55 52 7 58 23 5 60 32 41 50 82
 100 50
30 50 54 7 8 59 60 61 62 63 64 15 16 18 19 20 22 73 27 79 83 86 87 89 42 93 94 45 46 97 98
20 1 2 3 5 6 17 21 24 25 26 28 30 31 32 34 35 38 40 41 49
 5 2
4 0 1 2 3
2 0 1
 75 75
19 48 3 5 67 23 8 70 45 63 36 38 56 15 10 37 52 11 9 27
21 13 9 45 28 59 36 30 43 5 38 27 40 50 17 41 71 8 51 63 1 33
 100 99
1 99
0
 79 23
35 31 62 14 9 46 18 68 69 42 13 50 77 23 76 5 53 40 16 32 74 54 38 25 45 39 26 37 66 78 3 48 10 17 56 59
13 16 0 8 6 18 14 21 11 20 4 15 13 22
 242 894
21 65 23 226 163 221 107 66 114 122 126 81 216 153 3 154 172 176 75 177 18 129
50 201 278 7 234 743 868 699 529 240 40 798 751 321 281 411 283 333 705 471 477 761 308 207 185 498 850 187 372 361 161 856 353 786 400 461 484 43 589 310 451 639 682 218 376 288 645 827 6 351 73
 5 2
4 4 3 2 1
0
 2 5
2 0 1
4 0 1 2 3
 90 30
27 15 16 2 32 78 49 64 65 50 6 66 21 22 82 23 39 84 85 10 86 56 27 87 13 58 44 74
7 19 4 20 24 25 12 27
 75 30
18 46 47 32 33 3 34 35 21 51 7 9 54 39 72 42 59 29 14
8 0 17 5 6 23 26 27 13
 271 268
4 154 146 231 61
26 203 53 86 28 56 257 4 17 189 182 57 78 197 64 20 74 186 33 85 127 24 60 245 9 119 115
 65 75
15 25 60 12 62 37 22 47 52 3 63 58 13 14 49 34
18 70 10 2 52 22 47 72 57 38 48 13 73 3 19 4 74 49 34
 99 84
66 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83 84 86 87 89 90 92 93 95 96 98
56 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83
 75 90
60 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74
72 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 47 48 49 50 52 53 54 55 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 75 77 78 79 80 82 83 84 85 87 88 89
 75 75
33 30 74 57 23 19 42 71 11 44 29 58 43 48 61 63 13 27 50 17 18 70 64 39 12 32 36 10 40 51 49 1 54 73
8 43 23 0 7 63 47 74 28
 50 50
14 7 8 12 16 18 22 23 24 28 30 35 40 46 49
35 0 1 2 3 4 5 6 9 10 11 13 14 15 17 19 20 21 25 26 27 29 31 32 33 34 36 37 38 39 41 43 44 45 47 48
 98 98
43 49 1 51 3 53 4 55 56 8 9 10 60 11 12 61 64 16 65 17 19 20 21 72 24 74 25 77 78 31 34 35 36 37 87 88 89 42 92 43 44 94 46 96
34 50 2 52 5 54 9 62 63 15 18 68 70 22 72 75 26 27 77 30 81 82 83 35 36 37 87 88 89 90 41 93 95 96 48
 2 3
1 0
2 0 2
 40 40
23 0 2 3 4 5 7 11 15 16 17 18 19 22 25 28 29 30 31 32 34 35 36 37
16 1 6 8 9 10 12 13 14 20 21 23 24 26 27 38 39
 559980448 895457224
35 338103844 411015076 425824139 8380281 119965274 321731919 208245319 89429868 348155671 523593389 138589444 547297581 376660793 92034247 354190817 177495097 326596224 232785610 286800032 410409837 387409647 300083687 434506566 547591790 159772046 221529075 516651168 238650818 159674251 381198888 129927193 165545973 91840116 243694210 548098149
4 791267773 56796078 159535284 66343130
 999999999 1000000000
0
1 0
 1000000000 999999999
0
1 1
 999999998 1000000000
1 0
1 1
 5880582 100615605
33 994430 2580881 208833 773217 5288222 4144306 1283201 4501728 3876492 4261396 1313993 1567121 1408932 5225554 2622889 3029881 1790677 5350621 1743001 3413796 5100735 3105904 1969283 453573 429283 4544410 2070808 3695158 1066291 2639099 4258365 908486 3326551
24 33537185 77594259 11768849 19360698 8271602 21242033 71331508 20826471 34871621 76880162 39454121 2931759 33110806 10569027 87973893 100244502 61064650 65786830 50736147 52591097 40751690 63206622 34597611 29092629
 129271212 589710419
24 43866614 67144145 61869108 79320931 73649599 64006357 20169679 78909956 720584 18425931 4273621 28680377 91318841 89188553 109864283 215413 21031455 24685200 70869298 14789609 114474057 70281672 104353114 33212786
8 531065576 451960506 137324569 422241517 425985526 125660027 338384637 341330468
 999999999 1000000000
0
1 999999999
 999999998 1000000000
1 0
0
 631552432 574185227
2 137997956 49349887
7 305792529 514447648 232873322 88421704 213346056 71435572 465303282
 98 49
33 0 51 52 6 57 10 12 63 15 16 19 20 26 72 73 74 76 77 78 30 31 81 33 83 37 38 39 40 92 44 45 95 97
15 4 5 7 9 11 13 17 18 22 26 35 36 41 42 47
 4 10
3 0 1 3
4 0 1 3 4
 101 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
 654 44
15 500 322 152 140 176 342 311 643 391 440 373 312 374 382 231
17 12 4 8 18 26 41 14 33 43 29 34 3 39 19 24 1 7
 36 100
10 0 32 4 5 33 30 18 14 35 7
29 60 32 20 4 16 69 5 38 50 46 74 94 18 82 2 66 22 42 55 51 91 67 75 35 95 43 79 3 49
 55 79
5 51 27 36 45 53
30 15 28 0 5 38 3 34 30 35 1 32 12 27 22 39 69 33 10 63 16 29 76 19 60 70 67 31 78 68 45
 39 87
16 18 15 30 33 21 9 3 31 16 10 34 20 35 8 26 23
36 33 75 81 24 42 54 78 39 57 60 30 36 63 4 76 25 1 40 73 22 58 49 85 31 26 59 20 44 83 65 23 41 71 47 14 35
 76 72
29 4 64 68 20 8 12 50 42 46 0 70 11 37 75 47 45 29 17 19 73 9 41 31 35 67 65 39 51 55
25 60 32 48 42 8 6 9 7 31 19 35 5 33 51 61 67 55 49 27 29 53 39 65 35 13
 100 40
25 61 42 2 3 25 46 51 68 69 49 9 10 50 91 72 92 33 73 53 14 15 55 96 36 39
12 0 22 3 23 4 6 27 11 35 37 38 39
 66 99
23 33 35 36 38 9 10 44 11 45 46 47 50 19 54 22 55 23 58 59 27 61 30 65
32 33 67 69 4 70 38 6 39 7 74 42 9 43 12 13 14 15 81 82 84 85 20 87 89 90 24 58 59 27 95 97 31
 27 31
4 25 5 19 20
26 5 28 17 3 1 0 26 23 12 29 6 4 25 19 15 13 20 24 8 27 22 30 3 10 9 7
 90 25
26 55 30 35 20 15 26 6 1 41 81 76 46 57 5 12 67 77 27 47 62 8 43 63 3 48 19
9 10 16 21 7 17 12 13 19 9
 16 88
6 5 14 2 0 12 7
30 21 64 2 79 74 39 63 44 81 73 0 27 33 69 12 86 46 20 25 55 52 7 58 23 5 60 32 41 50 82
 100 99
1 76
0
 242 894
21 65 23 226 163 190 107 66 114 122 126 81 216 153 3 154 172 176 75 177 18 129
50 201 278 7 234 743 868 699 529 240 40 798 751 321 281 411 283 333 705 471 477 761 308 207 185 498 850 187 372 361 161 856 353 786 400 461 484 43 589 310 451 639 682 218 376 288 645 827 6 351 73
 271 268
4 154 146 231 61
26 203 53 108 28 56 257 4 17 189 182 57 78 197 64 20 74 186 33 85 127 24 60 245 9 119 115
 6 54
1 5
14 13 49 31 37 44 2 15 51 52 2 28 10 35 47
 52 91
13 26 1 3 43 17 19 32 46 33 48 23 37 50
25 78 26 1 40 2 67 42 3 56 30 70 84 32 20 85 59 8 86 34 73 23 10 88 24 11
 816 688
23 434 388 225 277 775 76 720 339 561 754 400 221 677 317 762 373 198 126 170 158 217 202 224
30 213 619 430 587 223 367 203 467 180 324 643 53 406 651 130 204 499 74 346 590 335 435 258 593 356 495 101 345 521 35
 66 66
24 2 35 3 36 4 5 10 45 14 48 18 51 19 21 55 22 23 24 25 26 63 31 65 32
21 0 1 37 6 40 7 8 42 45 13 15 16 50 53 23 24 60 28 62 63 50
 26 52
8 0 14 9 17 7 9 10 11
15 39 15 2 41 42 30 17 18 31 6 21 35 48 50 51
 66 66
26 1 54 6 37 43 13 25 38 2 32 56 20 50 39 27 51 9 64 4 16 17 65 11 5 47 23
15 6 24 43 49 25 20 14 63 27 3 58 52 53 11 41
 20 20
9 0 3 4 6 7 8 17 12 13
10 1 2 5 9 11 14 15 16 18 19
 91 98
78 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 10 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89
84 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 61 63 64 65 66 67 68 70 71 72 73 74 75 77 78 79 80 81 82 84 85 86 87 88 89 91 92 93 94 95 96
 5 10
1 0
1 0
 24 60
4 0 2 19 23
15 12 24 2 2 14 3 52 28 5 6 19 32 33 34 35
 96 36
34 84 24 0 48 85 13 61 37 62 38 86 75 3 16 64 40 28 76 53 5 17 42 6 7 23 67 55 68 92 57 11 71 35 59
9 1 14 15 17 18 30 6 8 35
 80 40
27 0 41 44 45 6 47 8 10 52 13 14 16 17 18 14 21 62 23 64 26 68 29 32 75 37 78 39
13 2 3 9 11 15 20 25 27 30 31 33 34 36
 76 28
10 24 13 61 45 29 57 41 21 37 12
2 12 9
 14 91
3 10 21 33
2 89 3
 98 98
23 6 81 90 28 38 51 23 69 13 95 15 27 88 58 10 26 42 44 54 92 27 45 39
18 20 70 38 82 72 61 37 78 74 23 15 56 59 35 93 64 28 57
 100 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 182 96 97
 100 100
50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
50 50 51 52 53 54 55 56 57 58 59 60 50 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
 100 100
45 50 1 4 5 34 7 8 10 60 61 62 63 14 65 66 17 18 20 21 22 24 25 27 78 28 29 30 31 82 83 33 84 36 37 38 39 40 41 42 44 45 46 48 98 49
34 50 1 2 52 3 54 56 7 9 59 61 14 16 67 18 69 22 73 24 76 79 81 82 84 35 36 38 39 90 43 44 45 47 49
 2 50
0
1 49
 100 50
31 52 54 8 60 61 62 63 104 16 19 21 73 25 76 77 79 30 81 32 33 34 37 88 39 40 91 42 94 95 96 98
18 0 1 3 5 6 7 9 15 18 20 22 24 28 35 36 43 47 49
 100 50
30 50 54 7 8 59 60 61 62 63 64 15 16 18 19 20 22 73 27 79 83 86 87 89 42 29 94 45 46 97 98
20 1 2 3 5 6 17 21 24 25 26 28 30 31 32 34 35 38 40 41 49
 75 75
19 48 3 5 67 23 8 70 45 63 36 38 56 15 10 37 52 11 9 27
21 13 9 45 28 59 36 30 43 5 38 27 40 60 17 41 71 8 51 63 1 33
 90 30
27 15 16 2 32 78 49 64 65 50 6 66 21 22 82 23 39 84 85 10 86 56 27 87 13 58 44 74
7 19 3 20 24 25 12 27
 75 30
18 46 47 32 33 3 34 35 21 51 7 9 54 39 72 42 59 29 14
8 0 17 6 6 23 26 27 13
 65 75
15 25 60 12 62 37 22 47 52 3 63 58 13 14 49 34
18 70 10 4 52 22 47 72 57 38 48 13 73 3 19 4 74 49 34
 99 84
66 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83 84 86 87 89 90 92 93 95 96 98
56 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 47 48 50 51 53 54 56 57 59 99 62 63 65 66 68 69 71 72 74 75 77 78 80 81 83

Yes
 Yes
 No
 4970100515
 Yes
 Yes
 No
 No
 Yes
 No
 Yes
 No
 No
 No
 Yes
 Yes
 Yes
 Yes
 Yes
 Yes
 No
 Yes
 No
 No
 No
 Yes
 Yes
 Yes
 No
 No
 Yes
 No
 Yes
 Yes
 No
 Yes
 No
 Yes
 No
 Yes
 No
 Yes
 Yes
 Yes
 Yes
 Yes
 No
 Yes
 Yes
 Yes
 No
 Yes
 Yes
 Yes
 No
 Yes
 Yes
 Yes
 Yes
 Yes
 No
 No
 Yes
 No
 No
 No
 No
 No
 No
 Yes
 No
 46816415967044267
 999999998000000001
 999999998000000002
 499999998000000003
 36843517882409
 8389164312799597
 999999999000000000
 -1
 -1
 -1
 16
 200
 2615
 697
 420
 242
 618
 228
 227
 76
 344
 187
 9877
 9196
 10997
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
 -1
