Square root of 1 in mod 1e300

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Problem

Print the specified 300 digit number x according to the hints below,
though these hints may not uniquely determine the value of x for each case.

Hint 1: The square of x is equal to 1 in mod 10<sup>300</sup>.
Hint 2: The last three ditigs of x will be given as input.

-- tails

Options

exec is denied

now post-mortem time, all source codes will be revealed

Sample input:_

Sample output:

604375146618424928110766602983870727725667231901941561316236180836680951044276307718174243403123136593503653142226854524673706961790023941104078370652478992085606212570656397248761889074006370471472192093985361783660394122980219875666980838272377998885153153538207781991786760045215487480163574218751

Sample input:_

Sample output:

395624853381575071889233397016129272274332768098058438683763819163319048955723692281825756596876863406496346857773145475326293038209976058895921629347521007914393787429343602751238110925993629528527807906014638216339605877019780124333019161727622001114846846461792218008213239954784512519836425781249

Sample input:_

Sample output:

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Ranking

Ruby _

Rank	User	Size	Time	Date	Statistics
1	mitchs	41	0.0649	2015/09/20 22:50:56	0B / 21B / 19B
2	mitchs (luck)	42	0.0656	2015/09/15 10:42:56	0B / 23B / 16B
3	gmk	62	0.0634	2015/09/17 22:56:48	0B / 34B / 27B

Perl _

Rank	User	Size	Time	Date	Statistics
1	tails	50	0.2197	2015/09/17 00:23:29	0B / 28B / 21B
2	mitchs	50	2.6227	2015/09/22 10:29:07	0B / 31B / 18B
3	llhuii	53	2.0464	2015/09/17 02:24:37	0B / 25B / 27B
4	angel	76	0.4425	2015/09/25 19:51:28	0B / ?B / ?B
5	mitchs (tails)	49	2.6142	2015/09/25 22:13:42	0B / 31B / 17B

Python _

Rank	User	Size	Time	Date	Statistics
1	mitchs (alt)	45	0.1159	2015/09/20 22:38:12	0B / 27B / 15B
2	xsot	47	0.1120	2015/09/25 10:48:30	0B / 28B / 16B
3	llhuii	52	0.1394	2015/09/16 01:18:42	0B / 30B / 21B
4	xsot (luck)	58	0.1940	2015/09/24 20:25:41	0B / 30B / 26B
5	gmk	61	0.1149	2015/09/17 23:17:59	0B / 35B / 26B
6	mitchs	67	0.3984	2015/09/12 07:55:43	0B / 41B / 21B
7	xnor	76	0.0968	2015/09/15 10:12:47	0B / ?B / ?B
8	rolf	135	0.3387	2015/09/12 04:25:44	0B / 69B / 40B

Python3 _

Rank	User	Size	Time	Date	Statistics
1	mitchs (luck)	51	0.1760	2015/09/25 05:11:26	0B / 26B / 23B
2	xsot (luck)	53	0.1670	2015/09/25 20:14:56	0B / 27B / 24B
3	mitchs	54	0.1618	2015/09/20 22:40:57	0B / 30B / 22B
4	llhuii	61	0.2785	2015/09/16 01:27:09	0B / 33B / 28B

PARI/GP _

Rank	User	Size	Time	Date	Statistics
1	mitchs	44	0.0481	2015/09/12 12:14:50	0B / 28B / 16B
2	llhuii	45	0.0571	2015/09/17 02:25:20	0B / 27B / 18B

Haskell _

Rank	User	Size	Time	Date	Statistics
1	henkma	65	0.1105	2015/09/17 20:32:57	0B / 40B / 20B

Maxima _

Rank	User	Size	Time	Date	Statistics
1	mitchs	57	0.7826	2015/09/22 09:57:46	0B / 32B / 25B

sed _

Rank	User	Size	Time	Date	Statistics
1	tails	357	0.0462	2015/09/25 09:17:15	0B / 332B / 23B

dc _

Rank	User	Size	Time	Date	Statistics
1	tails	28	0.0528	2015/09/17 00:30:40	0B / 18B / 10B

Whitespace _

Rank	User	Size	Time	Date	Statistics
1	mitchs	134	0.0452	2015/09/24 05:34:17	0B / 0B / 0B

Befunge _

Rank	User	Size	Time	Date	Statistics
1	test1	703	0.0143	2015/09/25 15:31:09	0B / ?B / ?B
2	test1	380	0.0133	2015/09/28 16:31:17	0B / ?B / ?B

GolfScript _

Rank	User	Size	Time	Date	Statistics
1	tails	19	0.4808	2015/09/24 23:40:29	0B / 6B / 13B
2	mitchs	19	0.4406	2015/09/24 23:50:52	0B / 5B / 14B

gs2 _

Rank	User	Size	Time	Date	Statistics
1	mitchs	14	0.3314	2015/09/20 22:57:17	4B / 6B / 4B
2	mitchs (xsot)	13	0.5555	2015/09/25 23:02:19	5B / 4B / 4B

FlogScript _

Rank	User	Size	Time	Date	Statistics
1	mitchs	30	0.3950	2015/09/24 06:27:26	0B / 13B / 14B

goruby _

Rank	User	Size	Time	Date	Statistics
1	mitchs	34	0.0905	2015/09/20 23:03:43	0B / 18B / 12B

Groovy _

Rank	User	Size	Time	Date	Statistics
1	gmk	73	3.0758	2015/09/16 23:58:01	0B / 45B / 28B

Language Ranking_

Rank	Lang	User	Size	Score
1	gs2	mitchs (xsot)	13	10000
2	GolfScript	tails	19	6842
3	dc	tails	28	4642
4	FlogScript	mitchs	30	4333
5	goruby	mitchs	34	3823
6	Ruby	mitchs	41	3170
7	PARI/GP	mitchs	44	2954
8	Python	mitchs (alt)	45	2888
9	Perl	mitchs (tails)	49	2653
10	Python3	mitchs (luck)	51	2549
11	Maxima	mitchs	57	2280
12	Haskell	henkma	65	2000
13	Groovy	gmk	73	1780
14	Whitespace	mitchs	134	970
15	sed	tails	357	364
16	Befunge	test1	380	342

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