{"problem":{"name":"Frog 3","description":{"content":"There are $N$ stones, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), the height of Stone $i$ is $h_i$. Here, $h_1 < h_2 < \\cdots < h_N$ holds. There is a frog who is initially on Stone ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"dp_z"},"statements":[{"statement_type":"Markdown","content":"There are $N$ stones, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), the height of Stone $i$ is $h_i$. Here, $h_1 < h_2 < \\cdots < h_N$ holds.\nThere is a frog who is initially on Stone $1$. He will repeat the following action some number of times to reach Stone $N$:\n\n*   If the frog is currently on Stone $i$, jump to one of the following: Stone $i + 1, i + 2, \\ldots, N$. Here, a cost of $(h_j - h_i)^2 + C$ is incurred, where $j$ is the stone to land on.\n\nFind the minimum possible total cost incurred before the frog reaches Stone $N$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq C \\leq 10^{12}$\n*   $1 \\leq h_1 < h_2 < \\cdots < h_N \\leq 10^6$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $C$\n$h_1$ $h_2$ $\\ldots$ $h_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"dp_z","tags":[],"sample_group":[["5 6\n1 2 3 4 5","20\n\nIf we follow the path $1$ → $3$ → $5$, the total cost incurred would be $((3 - 1)^2 + 6) + ((5 - 3)^2 + 6) = 20$."],["2 1000000000000\n500000 1000000","1250000000000\n\nThe answer may not fit into a 32-bit integer type."],["8 5\n1 3 4 5 10 11 12 13","62\n\nIf we follow the path $1$ → $2$ → $4$ → $5$ → $8$, the total cost incurred would be $((3 - 1)^2 + 5) + ((5 - 3)^2 + 5) + ((10 - 5)^2 + 5) + ((13 - 10)^2 + 5) = 62$."]],"created_at":"2026-03-03 11:01:14"}}