{"problem":{"name":"2A + x","description":{"content":"You are given a sequence $A = (A_1, A_2, \\ldots, A_N)$ of positive integers and a positive integer $X$. You can perform the operation below any number of times, possibly zero: *   Choose an index $i$","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc057_b"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence $A = (A_1, A_2, \\ldots, A_N)$ of positive integers and a positive integer $X$. You can perform the operation below any number of times, possibly zero:\n\n*   Choose an index $i$ ($1\\leq i\\leq N$) and a non-negative integer $x$ such that $0\\leq x\\leq X$. Change $A_i$ to $2A_i+x$.\n\nFind the smallest possible value of $\\max{A_1,A_2,\\ldots,A_N}-\\min{A_1,A_2,\\ldots,A_N}$ after your operations.\n\n## Constraints\n\n*   $2\\leq N\\leq 10^5$\n*   $1\\leq X\\leq 10^9$\n*   $1\\leq A_i\\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $X$\n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc057_b","tags":[],"sample_group":[["4 2\n5 8 12 20","6\n\nLet $(i, x)$ denote an operation that changes $A_i$ to $2A_i+x$. An optimal sequence of operations is\n\n*   $(1,0)$, $(1,1)$, $(2,2)$, $(3,0)$\n\nwhich yields $A = (21, 18, 24, 20)$, achieving $\\max{A_1,A_2,A_3,A_4}-\\min{A_1,A_2,A_3,A_4} = 6$."],["4 5\n24 25 26 27","0\n\nAn optimal sequence of operations is\n\n*   $(1,5)$, $(1,5)$, $(2,5)$, $(2,1)$, $(3,2)$, $(3,3)$, $(4,0)$, $(4,3)$\n\nwhich yields $A = (111,111,111,111)$, achieving $\\max{A_1,A_2,A_3,A_4}-\\min{A_1,A_2,A_3,A_4} = 0$."],["4 1\n24 25 26 27","3\n\nPerforming no operations achieves $\\max{A_1,A_2,A_3,A_4}-\\min{A_1,A_2,A_3,A_4} = 3$."],["10 5\n39 23 3 7 16 19 40 16 33 6","13"]],"created_at":"2026-03-03 11:01:14"}}