Codeforces Round 921 (Div. 1)

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ContestId
Name
Phase
Frozen
Duration (Seconds)
Relative Time
Start Time
1924 Codeforces Round 921 (Div. 1) FINISHED False 7200 30813263 Jan. 27, 2024, 2:45 p.m.

Problems

Solved$
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Name
Type
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Community Tag
Rating
( 445 ) E Paper Cutting Again PROGRAMMING combinatorics probabilities

B'There is a rectangular sheet of paper with initial height n and width m . Let the current height and width be h and w respectively. We introduce a xy -coordinate system so that the four corners of the sheet are (0, 0), (w, 0), (0, h) , and (w, h) . The sheet can then be cut along the lines x = 1,2, ldots,w-1 and the lines y = 1,2, ldots,h-1 . In each step, the paper is cut randomly along any one of these h+w-2 lines. After each vertical and horizontal cut, the right and bottom piece of paper respectively are discarded. Find the expected number of steps required to make the area of the sheet of paper strictly less than k . It can be shown that this answer can always be expressed as a fraction dfrac{p}{q} where p and q are coprime integers. Calculate p cdot q^{-1} bmod (10^9+7) . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 57000 ). Description of the test cases follows. The first line of each test case contains 3 integers n , m , and k ( 1 <= n, m <= 10^6 , 2 <= k <= 10^{12} ). It is guaranteed that the sum of n and the sum of m over all test cases do not exceed 10^6 . For each test case, print one integer -- the answer to the problem. For the first test case, the area is already less than 10 so no cuts are required. For the second test case, the area is exactly 8 so any one of the 4 possible cuts would make the area strictly less than 8 . For the third test case, the final answer is frac{17}{6} = 833 ,333 ,342 bmod (10^9+7) . For the fourth test case, the final answer is frac{5}{4} = 250 ,000 ,003 bmod (10^9+7) . '...

Tutorials

Codeforces Round 921 (Div. 1, Div. 2) Editorial

Submissions

Submission Id
Author(s)
Index
Submitted
Verdict
Language
Test Set
Tests Passed
Time taken (ms)
Memory Consumed (bytes)
Tags
Rating
243669245 alireza_kaviani E Jan. 27, 2024, 7:10 p.m. OK GNU C++17 TESTS 50 155 16076800
243643653 hos.lyric E Jan. 27, 2024, 4:22 p.m. OK GNU C++17 TESTS 50 156 32358400
243676875 radoslav11 E Jan. 27, 2024, 8:12 p.m. OK GNU C++17 TESTS 50 202 25190400
243647040 potato167 E Jan. 27, 2024, 4:28 p.m. OK GNU C++17 TESTS 50 685 48435200
243642725 Elegia E Jan. 27, 2024, 4:21 p.m. OK GNU C++17 (64) TESTS 50 62 24064000
243649183 244mhq E Jan. 27, 2024, 4:32 p.m. OK GNU C++17 (64) TESTS 50 108 32051200
243655474 Rebelz E Jan. 27, 2024, 4:43 p.m. OK GNU C++17 (64) TESTS 50 109 32051200
243667873 hitonanode E Jan. 27, 2024, 6:59 p.m. OK GNU C++17 (64) TESTS 50 109 38502400
243649002 -Eternity- E Jan. 27, 2024, 4:32 p.m. OK GNU C++17 (64) TESTS 50 124 32051200
243664858 Crystally E Jan. 27, 2024, 6:43 p.m. OK GNU C++17 (64) TESTS 50 124 64102400
243669011 hitonanode E Jan. 27, 2024, 7:08 p.m. OK GNU C++17 (64) TESTS 50 140 39116800
243699222 xuanxuan001 E Jan. 28, 2024, 2:56 a.m. OK GNU C++17 (64) TESTS 50 156 15974400
243699262 luogu_bot1 E Jan. 28, 2024, 2:57 a.m. OK GNU C++17 (64) TESTS 50 187 15974400
243697360 orzdevinwang E Jan. 28, 2024, 2:26 a.m. OK GNU C++17 (64) TESTS 50 187 24064000
243695709 your_submissions_ E Jan. 28, 2024, 1:59 a.m. OK GNU C++20 (64) TESTS 50 77 7987200
243623598 A_G E Jan. 27, 2024, 3:51 p.m. OK GNU C++20 (64) TESTS 50 77 7987200
243683383 AmirAli-Asgari E Jan. 27, 2024, 9:26 p.m. OK GNU C++20 (64) TESTS 50 77 32051200
243665026 kotatsugame E Jan. 27, 2024, 6:44 p.m. OK GNU C++20 (64) TESTS 50 78 8396800
243625417 maroonrk E Jan. 27, 2024, 3:54 p.m. OK GNU C++20 (64) TESTS 50 93 33587200
243665303 AmazingTalker_Frank E Jan. 27, 2024, 6:46 p.m. OK GNU C++20 (64) TESTS 50 124 32051200
243642282 cnnfls_csy E Jan. 27, 2024, 4:20 p.m. OK GNU C++20 (64) TESTS 50 124 32051200
243635575 maspy E Jan. 27, 2024, 4:09 p.m. OK GNU C++20 (64) TESTS 50 124 41779200
243630255 jiangly E Jan. 27, 2024, 4:01 p.m. OK GNU C++20 (64) TESTS 50 124 50585600
243706048 superguymj E Jan. 28, 2024, 4:32 a.m. OK GNU C++20 (64) TESTS 50 171 48128000
243641109 FastFreeTask E Jan. 27, 2024, 4:18 p.m. OK Kotlin 1.7 TESTS 50 577 11264000
243648905 chinerist E Jan. 27, 2024, 4:32 p.m. OK PyPy 3-64 TESTS 50 311 27852800
243652079 sansen E Jan. 27, 2024, 4:37 p.m. OK Rust 2021 TESTS 50 77 27545600

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