{"problem":{"name":"A. Archmage","description":{"content":"Archmage (AM for short) is a hero unit in WatercraftⅢ. He has $n$ mana *at most* and two powerful skills which enable him to show great strength in battle: Since the power of an Archmage is tremendo","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10262A"},"statements":[{"statement_type":"Markdown","content":"Archmage (AM for short) is a hero unit in WatercraftⅢ.\n\nHe has $n$ mana *at most* and two powerful skills which enable him to show great strength in battle:\n\nSince the power of an Archmage is tremendous, the upper limit of mana $n$ is always greater than or equal to $x + y$.\n\nEvery second, Archmage will summon *exactly one* Water Element (if the mana is enough, i.e., his mana won't be less than $0$ after that) or do nothing. Then no matter what he did before, he will restore $y$ mana.\n\nArchmage has $n$ mana at the end of the second $0$, and the game starts at the beginning of the second $1$.\n\nHe wants to know how many Water Elements he can summon at most before the end of the second $m$.\n\nThe input consists of multiple test cases. \n\nThe first line contains a single integer $t (1 <= t <= 10^5)$, indicating the number of test cases.\n\nEach of the next $t$ lines contains $4$ integers $n, m, x, y (1 <= m, x, y <= 10^9, x + y <= n <= 2 times 10^9)$.\n\nFor each test case, output the answer in a line.\n\nIn test case $1$, Archmage can cast spells every second, so the answer is $2$.\n\nIn test case $2$, here's a way for Archmage to cast spells $3$ times.\n\nSecond $1$: Archmage cast spells, and there is $4 -x + y = 3$ mana left.\n\nSecond $2$: Archmage cast spells, and there is $3 -x + y = 2$ mana left.\n\nSecond $3$: Archmage cast spells, and there is $2 -x + y = 1$ mana left.\n\nSecond $4$: Archmage doesn't have enough mana so he can do nothing, and there is $1 + y = 2$ mana left.\n\n## Input\n\nThe input consists of multiple test cases. The first line contains a single integer $t (1 <= t <= 10^5)$, indicating the number of test cases.Each of the next $t$ lines contains $4$ integers $n, m, x, y (1 <= m, x, y <= 10^9, x + y <= n <= 2 times 10^9)$.\n\n## Output\n\nFor each test case, output the answer in a line.\n\n[samples]\n\n## Note\n\nIn test case $1$, Archmage can cast spells every second, so the answer is $2$.In test case $2$, here's a way for Archmage to cast spells $3$ times.Second $1$: Archmage cast spells, and there is $4 -x + y = 3$ mana left.Second $2$: Archmage cast spells, and there is $3 -x + y = 2$ mana left.Second $3$: Archmage cast spells, and there is $2 -x + y = 1$ mana left.Second $4$: Archmage doesn't have enough mana so he can do nothing, and there is $1 + y = 2$ mana left.","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, let $ N, M, X, Y \\in \\mathbb{Z} $ denote:  \n- $ N $: number of rows,  \n- $ M $: number of columns,  \n- $ (X, Y) $: coordinates of Mr. Manohar’s office.  \n\nThe auto follows the path:  \n- From $ (1,1) $ to $ (1,M) $ along row 1 (eastward),  \n- Then from $ (1,M) $ to $ (N,M) $ along column $ M $ (southward).  \n\nAt $ t = 0 $, four secret agents start at $ (X, Y) $ and move in fixed directions with rebound behavior:  \n- Agent 1: North (if possible), else South.  \n- Agent 2: South (if possible), else North.  \n- Agent 3: East (if possible), else West.  \n- Agent 4: West (if possible), else East.  \n\nEach agent moves 1 cell per second; upon hitting a grid boundary, it reverses direction immediately.  \n\n**Constraints**  \n1. $ 1 \\le T \\le 1000 $  \n2. $ 2 \\le N, M \\le 10^9 $  \n3. $ 1 \\le X \\le N $, $ 1 \\le Y \\le M $  \n\n**Objective**  \nDetermine if the auto’s path intersects any secret agent at the same cell at the same time $ t \\in \\mathbb{Z}_{\\ge 0} $.  \n\nThe auto’s position at time $ t $:  \n- For $ 0 \\le t < M $: $ (1, 1 + t) $  \n- For $ M \\le t \\le M + N - 1 $: $ (1 + (t - M), M) $  \n\nLet $ A_i(t) $ denote the position of agent $ i \\in \\{1,2,3,4\\} $ at time $ t $.  \n\n**Output**  \nPrint \"Farewell\" if $ \\forall t \\in [0, M + N - 1] $, auto’s position $ \\neq A_i(t) $ for all $ i \\in \\{1,2,3,4\\} $.  \nOtherwise, print \"BestWishes\".","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10262A","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}