{"problem":{"name":"Shuffle and mod K","description":{"content":"You are given an integer sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$. You can rearrange $A$ freely. Find the maximum value that $\\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \\bmod K)$ can take after rearrangi","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc065_a"},"statements":[{"statement_type":"Markdown","content":"You are given an integer sequence $A=(A_1,A_2,\\dots,A_N)$ of length $N$.\nYou can rearrange $A$ freely. Find the maximum value that $\\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \\bmod K)$ can take after rearranging.\nHere, $x \\bmod K$ denotes the integer $y$ such that $0 \\le y < K$ and $x - y$ is a multiple of $K$. For example, $-3 \\bmod 8 = 5$, and $9 \\bmod 6 = 3$.\n\n## Constraints\n\n*   $2 \\le N \\le 2 \\times 10^5$\n*   $1 \\le K \\le 10^9$\n*   $0 \\le A_i < K$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\dots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc065_a","tags":[],"sample_group":[["3 4\n0 1 2","6\n\nOne optimal solution is to rearrange $A$ into $(2,1,0)$ to achieve $(1 - 2) \\bmod 4 + (0 - 1) \\bmod 4 = 3 + 3 = 6$."],["7 123\n11 34 56 0 32 100 78","638"]],"created_at":"2026-03-03 11:01:14"}}