{"problem":{"name":"Remainder Game","description":{"content":"Aoki is playing with a sequence of numbers $a_{1}, a_{2}, ..., a_{N}$. Every second, he performs the following operation : *   Choose a positive integer $k$. For each element of the sequence $v$, Aok","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc022_c"},"statements":[{"statement_type":"Markdown","content":"Aoki is playing with a sequence of numbers $a_{1}, a_{2}, ..., a_{N}$. Every second, he performs the following operation :\n\n*   Choose a positive integer $k$. For each element of the sequence $v$, Aoki may choose to replace $v$ with its remainder when divided by $k$, or do nothing with $v$. The cost of this operation is $2^{k}$ (regardless of how many elements he changes).\n\nAoki wants to turn the sequence into $b_{1}, b_{2}, ..., b_{N}$ (the order of the elements is important). Determine if it is possible for Aoki to perform this task and if yes, find the minimum cost required.\n\n## Constraints\n\n*   $1 \\leq N \\leq 50$\n*   $0 \\leq a_{i}, b_{i} \\leq 50$\n*   All values in the input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$a_{1}$ $a_{2}$ $...$ $a_{N}$\n$b_{1}$ $b_{2}$ $...$ $b_{N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc022_c","tags":[],"sample_group":[["3\n19 10 14\n0 3 4","160\n\nHere's a possible sequence of operations :\n\n*   Choose $k = 7$. Replace $19$ with $5$, $10$ with $3$ and do nothing to $14$. The sequence is now $5, 3, 14$.\n    \n*   Choose $k = 5$. Replace $5$ with $0$, do nothing to $3$ and replace $14$ with $4$. The sequence is now $0, 3, 4$.\n    \n\nThe total cost is $2^{7} + 2^{5} = 160$."],["3\n19 15 14\n0 0 0","2\n\nAoki can just choose $k = 1$ and turn everything into $0$. The cost is $2^{1} = 2$."],["2\n8 13\n5 13","\\-1\n\nThe task is impossible because we can never turn $8$ into $5$ using the given operation."],["4\n2 0 1 8\n2 0 1 8","0\n\nAoki doesn't need to do anything here. The cost is $0$."],["1\n50\n13","137438953472\n\nBeware of overflow issues."]],"created_at":"2026-03-03 11:01:14"}}