{"problem":{"name":"Maximize GCD","description":{"content":"Given is a sequence of $N$ positive integers: $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence at least zero and at most $K$ times: *   choose $i\\in {1,2,\\ldots,N}$ ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc126_c"},"statements":[{"statement_type":"Markdown","content":"Given is a sequence of $N$ positive integers: $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence at least zero and at most $K$ times:\n\n*   choose $i\\in {1,2,\\ldots,N}$ and add $1$ to $A_i$.\n\nFind the maximum possible value of $\\gcd(A_1, A_2, \\ldots, A_N)$ after your operations.\n\n## Constraints\n\n*   $2\\leq N\\leq 3\\times 10^5$\n*   $1\\leq K\\leq 10^{18}$\n*   $1 \\leq A_i\\leq 3\\times 10^5$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc126_c","tags":[],"sample_group":[["3 6\n3 4 9","5\n\nOne way to achieve $\\gcd(A_1, A_2, A_3) = 5$ is as follows.\n\n*   Do the operation with $i = 1$ twice, with $i = 2$ once, and with $i = 3$ once, for a total of four times, which is not more than $K=6$.\n*   Now we have $A_1 = 5$, $A_2 = 5$, $A_3 = 10$, for which $\\gcd(A_1, A_2, A_3) = 5$."],["3 4\n30 10 20","10\n\nDoing no operation achieves $\\gcd(A_1, A_2, A_3) = 10$."],["5 12345\n1 2 3 4 5","2472"]],"created_at":"2026-03-03 11:01:14"}}