{"problem":{"name":"D. Nate and Dimension-Hopping Money","description":{"content":"One Wednesday evening, Nate went out drinking milk tea with his friends, spending $x$% of his money on that day. On Thursday, he checked his wallet and watched in confusion as $y$% of his money vanis","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10205D"},"statements":[{"statement_type":"Markdown","content":"One Wednesday evening, Nate went out drinking milk tea with his friends, spending $x$% of his money on that day.\n\nOn Thursday, he checked his wallet and watched in confusion as $y$% of his money vanished before his very eyes!\n\nHe then remembers that on Tuesday, a similar event transpired as he checked his wallet and watched money magically appear in his wallet!\n\nRealizing that the amount of money that appeared in his wallet on Tuesday is the exact same amount that he lost on Thursday, he deduced that the portion of money he lost on Thursday somehow went back in time and got transferred to his wallet on Tuesday!\n\nThis makes managing his finances confusing, and so he wants your help.\n\nIf he had $n$ Philippine pesos in his wallet on Monday, how much money would he have on each of the five weekdays this week?\n\nThe input consists of a line containing three space-separated integers $n$, $x$, and $y$. The first integer, $n$, is the amount of money he had on Monday. The second integer, $x$, is the percentage of money in his wallet he had spent on Wednesday. The third integer, $y$, is the percentage of money in his wallet on Thursday that got sent back in time.\n\n*Constraints*\n\n$1 <= n <= 10^8$\n\n $1 <= x <= 100$\n\n $1 <= y <= 100$\n\nOutput five space-separated integers: the amount of money Nate had on Monday, Tuesday, Wednesday, Thursday, and Friday, in that order. \n\nThe answer will be accepted if it is within $10^(-4)$ of the correct answer.\n\n## Input\n\nThe input consists of a line containing three space-separated integers $n$, $x$, and $y$. The first integer, $n$, is the amount of money he had on Monday. The second integer, $x$, is the percentage of money in his wallet he had spent on Wednesday. The third integer, $y$, is the percentage of money in his wallet on Thursday that got sent back in time.*Constraints*$1 <= n <= 10^8$ $1 <= x <= 100$ $1 <= y <= 100$\n\n## Output\n\nOutput five space-separated integers: the amount of money Nate had on Monday, Tuesday, Wednesday, Thursday, and Friday, in that order. The answer will be accepted if it is within $10^(-4)$ of the correct answer.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case:  \n- Let $ n, m \\in \\mathbb{Z} $ denote the number of piles for the red and white players, respectively.  \n- Let $ A = (a_1, a_2, \\dots, a_n) $ be the multiset of pile sizes for the red player.  \n- Let $ B = (b_1, b_2, \\dots, b_m) $ be the multiset of pile sizes for the white player.  \n\n**Constraints**  \n1. $ 1 \\le T \\le 100 $  \n2. $ 1 \\le n, m \\le 100 $  \n3. $ 1 \\le a_i \\le 10^9 $ for all $ i \\in \\{1, \\dots, n\\} $  \n4. $ 1 \\le b_i \\le 10^9 $ for all $ i \\in \\{1, \\dots, m\\} $  \n\n**Objective**  \nDetermine if the red player (who moves first) can force a win under the following rules:  \n- Players alternate turns, with red going first.  \n- On each turn, a player may remove any positive number of pieces from **exactly one** of their own piles.  \n- The first player to remove **all** of their own pieces wins.  \n\nThe red player wins if and only if the **nim-sum** (XOR) of their pile sizes is **non-zero**.  \nThat is, output \"Yes\" if $ \\bigoplus_{i=1}^n a_i \\ne 0 $, otherwise \"No\".","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10205D","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}