Problem K
Free Food — Problem Statistics

Back to problem description

Submissions	10921
Accepted submissions	6725
Submission ratio	61.58%
Authors	6313
Full solves [?]	5962
Full solve Ratio	94.44%

#	User	Runtime	Language	Date
1	Chenzhang Hu	0.08 s	Bash	2024-04-08 15:49:23
2	Manish shrestha	0.11 s	Bash	2025-04-15 10:39:41

#	User	Runtime	Language	Date
1	Hidden user	0.02 s	C#	2018-12-13 03:04:00
2	Joseph Russell	0.02 s	C#	2018-12-16 19:01:52
3	李陆屿	0.02 s	C#	2018-12-22 16:34:16
4	Hans Maulwurf	0.02 s	C#	2018-12-23 13:35:40
5	Duelene Olson	0.02 s	C#	2019-01-01 01:50:10
6	Brandon Story	0.02 s	C#	2019-01-01 23:07:38
7	Дмитро Рудий	0.02 s	C#	2019-01-24 12:09:33
8	Eric Bäckhage	0.02 s	C#	2019-02-02 09:53:51
9	Marek Bina	0.02 s	C#	2019-02-15 09:21:06
10	Csaba Varga	0.02 s	C#	2019-03-09 13:32:04

#	User	Runtime	Language	Date
1	Francisco Romero	0.01 s	COBOL	2021-12-24 01:12:49

#	User	Runtime	Language	Date
1	wibi	0.01 s	Common Lisp	2020-08-25 18:58:52
2	David Cawthon	0.02 s	Common Lisp	2019-04-11 03:39:38
3	Nicholas Lantz	0.02 s	Common Lisp	2019-05-01 19:49:43
4	Hidden user	0.02 s	Common Lisp	2019-05-24 06:38:38

#	User	Runtime	Language	Date
1	Jacob Harris Cryer Kragh	0.04 s	F#	2022-06-05 19:05:50
2	Emil Jessen	0.07 s	F#	2020-09-23 21:00:33
3	Patrick Bahr	0.08 s	F#	2021-02-23 13:01:26

#	User	Runtime	Language	Date
1	Suka Isnaini	0.00 s	Go	2023-12-12 20:40:52
2	Jimmy Nejtron	0.00 s	Go	2024-12-11 09:08:33
3	Andreas	0.01 s	Go	2025-10-07 14:47:21
4	Santiago Andaluz Ruiz	0.02 s	Go	2020-06-29 01:05:41
5	Eric Martin	0.07 s	Go	2018-12-26 18:08:08
6	Krzysztof Gibuła	0.07 s	Go	2019-01-11 20:06:11
7	Mik Achu	0.07 s	Go	2019-03-11 17:02:46
8	Theo Coyne Morgan	0.07 s	Go	2019-03-25 19:20:37
9	Andriy Zyevakov	0.07 s	Go	2019-04-17 08:22:23
10	Jürgen Lehmann	0.08 s	Go	2019-10-22 13:43:02

#	User	Runtime	Language	Date
1	Sebastian Banert	0.00 s	Haskell	2023-09-05 15:05:21
2	Morten Clausen	0.01 s	Haskell	2018-12-31 17:50:45
3	Tom Magnusson	0.01 s	Haskell	2019-02-07 18:30:13
4	Micah Stairs	0.01 s	Haskell	2019-03-11 01:56:13
5	Cooper Bell	0.01 s	Haskell	2019-05-01 19:06:41
6	Hidden user	0.01 s	Haskell	2019-08-13 15:20:15
7	Aurélien Pepin	0.01 s	Haskell	2019-08-16 15:21:58
8	Intrets	0.01 s	Haskell	2019-08-20 02:18:55
9	Andrés Marzal Varó	0.01 s	Haskell	2020-09-27 10:51:54
10	Jan Hrček	0.01 s	Haskell	2020-10-18 12:26:30

#	User	Runtime	Language	Date
1	Bala Krishna	0.04 s	Java	2024-08-16 15:50:44
2	Lim Shao Qi	0.04 s	Java	2024-10-20 14:37:53
3	Donald Trump	0.04 s	Java	2024-12-16 19:48:42
4	Markus	0.04 s	Java	2025-10-29 20:41:33
5	Eyleifur Bjarkason	0.05 s	Java	2018-12-14 01:59:47
6	John Ladera	0.05 s	Java	2018-12-14 02:48:14
7	José Vander Meulen	0.05 s	Java	2018-12-14 13:40:39
8	Bjørn Dons	0.05 s	Java	2018-12-14 20:05:48
9	Laurens Versluis	0.05 s	Java	2018-12-20 20:21:07
10	Lee Heng Sheng	0.05 s	Java	2024-04-27 11:42:18

#	User	Runtime	Language	Date
1	Hidden user	0.05 s	JavaScript (Node.js)	2024-08-10 17:08:38
2	Jerry Hu	0.06 s	JavaScript (Node.js)	2019-01-26 01:21:46
3	Dennis Svedberg	0.06 s	JavaScript (Node.js)	2019-02-03 13:05:22
4	Gurpartap Singh Bhatti	0.06 s	JavaScript (Node.js)	2019-02-14 02:49:33
5	José Lucas	0.06 s	JavaScript (Node.js)	2019-03-06 17:03:41
6	Sander Hellesø	0.06 s	JavaScript (Node.js)	2019-04-16 17:33:02
7	Daniel Roeven	0.06 s	JavaScript (Node.js)	2019-05-02 20:35:29
8	Tomáš Necky Necuda	0.07 s	JavaScript (Node.js)	2019-02-11 13:55:48
9	Peter Hairatidis	0.09 s	JavaScript (Node.js)	2023-04-11 23:29:02
10	Oliver Bredenberg	0.40 s	JavaScript (Node.js)	2019-08-28 15:07:17

#	User	Runtime	Language	Date
1	Christian Pilegaard Cederquist	0.02 s	JavaScript (SpiderMonkey)	2022-11-12 21:21:11
2	Shishir	0.02 s	JavaScript (SpiderMonkey)	2025-01-28 17:23:28
3	Nguyễn Hùng Cường	0.03 s	JavaScript (SpiderMonkey)	2018-12-13 02:28:51
4	Bjørn Chr. Soltvedt	0.03 s	JavaScript (SpiderMonkey)	2018-12-14 17:38:11
5	Jeremy Loh	0.03 s	JavaScript (SpiderMonkey)	2019-01-04 15:15:56
6	Bernard Perrin	0.03 s	JavaScript (SpiderMonkey)	2019-01-18 19:54:35
7	Rolands	0.03 s	JavaScript (SpiderMonkey)	2020-05-24 22:00:30
8	Peter Menyes	0.03 s	JavaScript (SpiderMonkey)	2021-03-08 21:02:18
9	Nicklas Utgaard	0.03 s	JavaScript (SpiderMonkey)	2021-04-18 19:14:35
10	Fredrik Möller	0.03 s	JavaScript (SpiderMonkey)	2021-04-27 16:52:33

#	User	Runtime	Language	Date
1	Hidden user	0.51 s	Julia	2025-04-13 07:40:11
2	Timothy Gaede	0.54 s	Julia	2024-03-21 06:42:40
3	Danny Robinson	0.57 s	Julia	2023-06-21 16:12:20

#	User	Runtime	Language	Date
1	Albert Pala	0.13 s	Kotlin	2021-06-29 19:48:04
2	Johnny Baloney	0.14 s	Kotlin	2022-01-14 16:45:47
3	Robert Berggren	0.17 s	Kotlin	2020-06-12 14:24:18
4	Hidden user	0.18 s	Kotlin	2019-12-15 21:04:38
5	James WIlliams	0.19 s	Kotlin	2020-09-30 06:49:09
6	Adam Rankin	0.19 s	Kotlin	2023-05-10 01:14:37
7	Adam Koprowski	0.20 s	Kotlin	2020-09-08 10:18:03
8	Dayan Ruben Gonzalez	0.20 s	Kotlin	2020-10-08 06:33:17
9	Richard Li	0.20 s	Kotlin	2021-02-06 19:07:58
10	Aidan Dagnall	0.20 s	Kotlin	2022-09-30 12:18:31

#	User	Runtime	Language	Date
1	Enzo Crance	0.00 s	OCaml	2019-02-13 23:22:51
2	Fredrik Eriksson	0.01 s	OCaml	2024-10-16 20:09:34

#	User	Runtime	Language	Date
1	Hidden user	0.00 s	Odin	2025-04-27 17:50:20

#	User	Runtime	Language	Date
1	Ingemar Ragnemalm	0.00 s	Pascal	2019-01-01 22:12:45
2	Oleg Smelov	0.00 s	Pascal	2019-02-24 22:13:47
3	高梓軒4D16 Ko Tsz Hin	0.00 s	Pascal	2020-01-23 17:46:43
4	Hidden user	0.00 s	Pascal	2020-02-12 17:24:15
5	David Connolly	0.00 s	Pascal	2021-10-06 23:40:49

#	User	Runtime	Language	Date
1	Renate Fiala-Lundström	0.01 s	PHP	2021-05-06 17:03:18
2	Muhammad Asyraf bin Akop	0.03 s	PHP	2022-05-13 04:22:05

#	User	Runtime	Language	Date
1	Hakan Kjellerstrand	0.03 s	Prolog	2023-01-26 20:38:57
2	Philip Cramer	0.13 s	Prolog	2024-10-09 22:42:24

#	User	Runtime	Language	Date
1	Godmar Back	0.03 s	Python 2	2018-12-13 21:29:07
2	Catalin Popa	0.03 s	Python 2	2018-12-14 22:24:11
3	Johann Ly	0.03 s	Python 2	2018-12-16 23:39:55
4	Alex Van Keulen	0.03 s	Python 2	2018-12-17 18:37:15
5	Jeff Thomas	0.03 s	Python 2	2018-12-22 15:42:39
6	Andrei Stoica	0.03 s	Python 2	2018-12-27 23:47:23
7	Omar Abdelaziz	0.03 s	Python 2	2019-01-27 10:16:06
8	Hidden user	0.03 s	Python 2	2019-02-07 02:34:36
9	Daryl Vogel	0.03 s	Python 2	2019-02-10 02:31:29
10	Erik Tjøswold	0.03 s	Python 2	2019-02-11 19:30:20

#	User	Runtime	Language	Date
1	Phirasit Charoenchitseriwong	0.02 s	Python 3	2018-12-13 02:30:24
2	Rimba Erlangga	0.02 s	Python 3	2018-12-13 07:23:01
3	Ryan Chew	0.02 s	Python 3	2018-12-13 08:26:26
4	Raynold Ng	0.02 s	Python 3	2018-12-13 11:20:40
5	Daniel Widjaja	0.02 s	Python 3	2018-12-13 11:28:40
6	Vincent Tandya	0.02 s	Python 3	2018-12-13 11:34:13
7	Nicholas Rianto Putra	0.02 s	Python 3	2018-12-13 15:30:23
8	Faza Fahleraz	0.02 s	Python 3	2018-12-13 15:36:45
9	Alexander Ursu	0.02 s	Python 3	2018-12-14 04:05:52
10	Hakan Celik	0.02 s	Python 3	2018-12-14 08:01:08

#	User	Runtime	Language	Date
1	Laurent Voisin	0.04 s	Ruby	2019-08-04 11:46:08
2	Miorel Palii	0.05 s	Ruby	2018-12-30 03:10:01
3	Stefan Kennedy	0.05 s	Ruby	2019-01-18 14:41:01
4	Hidden user	0.05 s	Ruby	2019-02-14 15:08:46
5	Hadi Qovaizi	0.05 s	Ruby	2021-06-18 16:06:27
6	Régis Hanol	0.05 s	Ruby	2022-01-13 09:18:32
7	TobiasZ	0.05 s	Ruby	2022-01-20 20:09:22
8	Hidden user	0.06 s	Ruby	2019-04-05 23:03:20
9	Davi Guimarães Leite	0.06 s	Ruby	2019-04-05 23:03:42
10	Victor Souza	0.06 s	Ruby	2019-04-05 23:08:27

#	User	Runtime	Language	Date
1	Joe Blower	0.00 s	Zig	2025-06-01 02:22:38
2	Grettir Heimisson	0.00 s	Zig	2025-10-28 10:26:47

#	User	Length	Language	Date
1	Chenzhang Hu	33	Bash	2025-09-12 20:55:20
2	Manish shrestha	520	Bash	2025-04-15 10:39:41

#	User	Length	Language	Date
1	Martin Blom	140	C	2023-10-21 16:51:29
2	Illa Somasekhar	251	C	2018-12-15 18:38:47
3	Wesley Stephanak	269	C	2019-02-03 22:40:47
4	Stanley Wisely	273	C	2021-01-30 12:52:30
5	Nagata Parama Aptana	275	C	2021-02-26 09:14:33
6	Jasper Chang張銜容	290	C	2021-07-11 05:35:37
7	Solar Solar	299	C	2021-12-28 17:41:47
8	MADHUMITHA K	300	C	2025-04-12 18:04:21
9	Mahammad Imran	306	C	2019-01-03 03:59:43
10	Juan Trilnardo Defrin	313	C	2020-09-12 12:45:10

#	User	Length	Language	Date
1	Marek Bina	405	C#	2019-02-15 09:21:06
2	Esty Crow	464	C#	2023-01-12 03:37:05
3	Anthony Ye	464	C#	2023-01-15 18:07:34
4	Bryce Goddard	493	C#	2020-05-21 00:19:15
5	Mads Orfelt	497	C#	2025-05-25 10:33:47
6	Bjarke Brodin	504	C#	2020-08-30 21:53:04
7	Leslie Yip	506	C#	2022-07-15 12:10:48
8	Josh Bryant	506	C#	2023-11-20 14:38:28
9	李陆屿	529	C#	2018-12-22 16:34:16
10	Дмитро Рудий	538	C#	2019-01-24 12:09:33

#	User	Length	Language	Date
1	Yeo Swe Hon	137	C++	2024-07-08 20:23:02
2	Frans Meulenbroeks	142	C++	2024-10-25 12:24:21
3	Ricardo Fagundes	205	C++	2019-05-23 15:38:44
4	Jonathan Loh	207	C++	2020-03-06 05:34:26
5	Garrepally Tejas	208	C++	2022-12-10 02:47:07
6	Luis Murillo	214	C++	2019-03-17 07:37:48
7	Friðrik Njálsson	217	C++	2019-07-03 08:33:18
8	206-11-鄭香禹	218	C++	2021-11-19 00:34:22
9	Paul Wild	220	C++	2023-03-04 02:37:39
10	Đỗ Minh	225	C++	2020-03-29 19:26:57

#	User	Length	Language	Date
1	Francisco Romero	1126	COBOL	2021-12-24 01:12:49

#	User	Length	Language	Date
1	wibi	218	Common Lisp	2020-08-25 18:58:52
2	David Cawthon	258	Common Lisp	2019-04-11 03:39:38
3	Nicholas Lantz	267	Common Lisp	2019-05-01 19:49:43
4	Hidden user	274	Common Lisp	2019-05-24 06:38:38

#	User	Length	Language	Date
1	Jacob Harris Cryer Kragh	343	F#	2022-06-05 19:05:50
2	Emil Jessen	943	F#	2020-09-23 21:00:33
3	Patrick Bahr	1898	F#	2021-02-23 13:01:26

#	User	Length	Language	Date
1	Hidden user	248	Go	2021-12-15 13:34:12
2	Ainun Nazieb	282	Go	2020-09-24 17:01:33
3	Theo Coyne Morgan	286	Go	2019-03-25 19:20:37
4	James Leopold	309	Go	2021-11-22 08:04:23
5	Andriy Zyevakov	316	Go	2019-04-17 08:22:23
6	dick move	320	Go	2021-05-30 20:49:17
7	Chris Vilches	338	Go	2021-12-17 07:35:05
8	Andreas	367	Go	2025-10-07 14:47:21
9	Santiago Andaluz Ruiz	383	Go	2020-06-29 01:05:41
10	Suka Isnaini	389	Go	2023-12-12 20:40:52

#	User	Length	Language	Date
1	BlackcapCoder	180	Haskell	2019-05-01 02:38:52
2	Fran Cruz Zamorano	219	Haskell	2018-12-23 22:52:26
3	Thomas Hügel	232	Haskell	2023-05-25 14:08:08
4	Daniel Cabral	246	Haskell	2022-11-22 11:16:37
5	Cooper Bell	264	Haskell	2019-05-01 19:06:41
6	Sebastian Banert	264	Haskell	2023-09-05 15:05:21
7	Klas af Geijerstam	269	Haskell	2019-01-30 22:58:39
8	Mason Barnhill	305	Haskell	2023-05-19 01:52:54
9	Brent Yorgey	316	Haskell	2020-11-10 14:37:07
10	Micah Stairs	324	Haskell	2019-03-11 01:56:13

#	User	Length	Language	Date
1	Sabrina Mori	371	Java	2020-03-18 20:00:47
2	Auburn Ford	373	Java	2019-02-19 00:49:47
3	Matthew Simionato	374	Java	2025-05-29 14:55:53
4	Hidden user	375	Java	2019-11-20 02:59:10
5	Lim Ting Kai	377	Java	2023-06-08 07:16:23
6	Jason Liu	378	Java	2023-05-13 20:22:39
7	Natalie Longtin	382	Java	2019-01-17 20:38:13
8	Hidden user	384	Java	2020-02-04 14:06:50
9	Jacob Steinebronn	387	Java	2019-10-10 00:07:35
10	Marc Fong	397	Java	2020-07-31 11:09:36

#	User	Length	Language	Date
1	Karim Dridi	409	JavaScript (Node.js)	2022-01-14 00:38:35
2	Chris Wong	494	JavaScript (Node.js)	2021-02-08 16:05:51
3	José Lucas	502	JavaScript (Node.js)	2019-03-06 17:03:41
4	Howard Tin Chi Chan	529	JavaScript (Node.js)	2021-02-01 00:01:27
5	Gurpartap Singh Bhatti	533	JavaScript (Node.js)	2019-02-14 02:49:33
6	Peter Kedemo	536	JavaScript (Node.js)	2019-12-22 15:54:14
7	Dennis Svedberg	545	JavaScript (Node.js)	2019-02-03 13:05:22
8	Hidden user	550	JavaScript (Node.js)	2023-02-06 05:36:20
9	Ali	564	JavaScript (Node.js)	2021-12-20 05:41:52
10	Hovhannes Kantuni	610	JavaScript (Node.js)	2021-03-02 01:05:44

#	User	Length	Language	Date
1	Christian Pilegaard Cederquist	95	JavaScript (SpiderMonkey)	2022-11-12 21:07:46
2	Jimmy Gustafsson	110	JavaScript (SpiderMonkey)	2024-06-12 22:28:45
3	Bjørn Chr. Soltvedt	188	JavaScript (SpiderMonkey)	2018-12-14 17:38:11
4	Zach Tschetter	227	JavaScript (SpiderMonkey)	2023-04-22 20:58:25
5	Peter Menyes	228	JavaScript (SpiderMonkey)	2021-03-08 21:02:18
6	Evan Magill	243	JavaScript (SpiderMonkey)	2024-04-19 18:25:09
7	Bernard Perrin	244	JavaScript (SpiderMonkey)	2019-01-18 19:54:35
8	Nguyễn Hùng Cường	254	JavaScript (SpiderMonkey)	2018-12-13 02:28:51
9	Casey Smith	261	JavaScript (SpiderMonkey)	2019-05-24 16:58:23
10	Shishir	262	JavaScript (SpiderMonkey)	2025-01-28 17:23:28

#	User	Length	Language	Date
1	Danny Robinson	85	Julia	2023-06-21 16:12:20
2	Hidden user	141	Julia	2025-04-13 07:40:11
3	Timothy Gaede	897	Julia	2024-03-21 06:42:40

#	User	Length	Language	Date
1	axl	225	Kotlin	2019-08-06 14:07:33
2	Bendik Solheim	319	Kotlin	2019-03-12 20:16:10
3	Lars-Petter Hansen	319	Kotlin	2021-01-12 10:08:39
4	Marit van Dijk	338	Kotlin	2019-01-26 20:18:41
5	Adam Koprowski	339	Kotlin	2020-09-08 10:18:03
6	Jonathan Soo	342	Kotlin	2019-06-21 07:54:38
7	Zaw Myat	345	Kotlin	2024-01-28 11:29:53
8	Connor MacKinnon	351	Kotlin	2023-04-11 23:40:37
9	Mike Poland	353	Kotlin	2019-07-21 17:47:26
10	Marianne Grov	358	Kotlin	2019-03-11 15:45:30

#	User	Length	Language	Date
1	Enzo Crance	392	OCaml	2019-02-13 23:22:51
2	Fredrik Eriksson	397	OCaml	2024-10-16 20:09:34

#	User	Length	Language	Date
1	Hidden user	411	Odin	2025-04-27 17:50:20

#	User	Length	Language	Date
1	Ingemar Ragnemalm	319	Pascal	2019-01-01 22:12:45
2	Hidden user	352	Pascal	2020-02-12 17:24:15
3	高梓軒4D16 Ko Tsz Hin	383	Pascal	2020-01-23 17:46:43
4	Oleg Smelov	473	Pascal	2019-02-24 22:13:47
5	David Connolly	980	Pascal	2021-10-06 23:40:49

#	User	Length	Language	Date
1	Renate Fiala-Lundström	291	PHP	2021-05-06 17:03:18
2	Muhammad Asyraf bin Akop	627	PHP	2022-05-13 04:22:05

#	User	Length	Language	Date
1	Hakan Kjellerstrand	331	Prolog	2023-01-26 20:38:57
2	Philip Cramer	728	Prolog	2024-10-09 22:42:24

#	User	Length	Language	Date
1	Hidden user	101	Python 2	2025-04-15 11:04:18
2	Thomas Feld	117	Python 2	2019-08-22 12:31:48
3	Andreas Björklund	138	Python 2	2020-03-09 20:57:21
4	Johan Lyts	139	Python 2	2019-03-07 22:09:24
5	Guan Yang Ze	142	Python 2	2019-08-27 17:39:15
6	Justin Su	150	Python 2	2019-10-02 00:44:07
7	Hidden user	154	Python 2	2019-02-07 02:34:36
8	Lars Lindgren	156	Python 2	2019-02-16 21:52:55
9	Jesper Öqvist	161	Python 2	2019-02-19 14:14:16
10	Conor McCauley	162	Python 2	2019-03-19 11:07:12

#	User	Length	Language	Date
1	Kevin Gomez	76	Python 3	2025-05-18 05:28:24
2	Avery	81	Python 3	2025-08-01 10:51:18
3	Clement Oh	86	Python 3	2023-05-24 15:36:42
4	lbm364dl	89	Python 3	2024-10-06 15:26:29
5	David Allemang	97	Python 3	2020-01-28 01:01:23
6	Jacob Raymond	98	Python 3	2020-01-28 01:01:41
7	Yeo Swe Hon	106	Python 3	2024-07-08 20:19:51
8	Francisco Carvajal	110	Python 3	2023-06-22 02:38:44
9	Alexandre Charland	111	Python 3	2024-08-23 21:49:22
10	Hidden user	113	Python 3	2020-10-05 14:49:24

#	User	Length	Language	Date
1	Thomas Feld	49	Ruby	2022-11-09 10:33:24
2	Russell Ng	58	Ruby	2025-12-04 18:39:17
3	Régis Hanol	78	Ruby	2022-01-13 09:18:32
4	Noah Hessen Bjerke	114	Ruby	2022-11-24 01:33:58
5	Hidden user	117	Ruby	2019-02-14 15:08:46
6	Alexander Bilde Pedersen	126	Ruby	2023-05-29 22:43:50
7	Macdara mac an tSionnaigh	139	Ruby	2019-10-22 23:10:58
8	Miorel Palii	144	Ruby	2018-12-30 03:10:01
9	Eugen Neagoe	157	Ruby	2023-06-14 14:38:17
10	Stefan Kennedy	163	Ruby	2019-01-18 14:41:01

#	User	Length	Language	Date
1	Vincent Lagerros	215	Rust	2024-09-27 20:08:22
2	Emil Dichmann	368	Rust	2025-09-01 12:25:17
3	Raphaël Baulant	442	Rust	2021-02-01 01:24:15
4	Raphaël Gauthier	504	Rust	2021-01-20 16:12:34
5	Bas Dirks	527	Rust	2021-12-30 20:47:45
6	Léana Renon	534	Rust	2021-02-23 17:43:19
7	Kok Dith	537	Rust	2021-08-03 09:50:31
8	Antoine Bauri	554	Rust	2022-02-09 16:23:54
9	Marine Gendry	562	Rust	2025-10-08 13:47:24
10	Viktor Sieger	600	Rust	2020-06-18 23:18:36

#	User	Length	Language	Date
1	Joe Blower	1060	Zig	2025-06-01 02:22:38
2	Grettir Heimisson	2729	Zig	2025-10-28 10:26:47

Solution running time distribution