{"problem":{"name":"NEQ","description":{"content":"Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \\cdots, A_{N}$ and $B_1, B_2, \\cdots, B_{N}$, that satisfy all of the following conditions: ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc172_e"},"statements":[{"statement_type":"Markdown","content":"Count the pairs of length-$N$ sequences consisting of integers between $1$ and $M$ (inclusive), $A_1, A_2, \\cdots, A_{N}$ and $B_1, B_2, \\cdots, B_{N}$, that satisfy all of the following conditions:\n\n*   $A_i \\neq B_i$, for every $i$ such that $1\\leq i\\leq N$.\n*   $A_i \\neq A_j$ and $B_i \\neq B_j$, for every $(i, j)$ such that $1\\leq i < j\\leq N$.\n\nSince the count can be enormous, print it modulo $(10^9+7)$.\n\n## Constraints\n\n*   $1\\leq N \\leq M \\leq 5\\times10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc172_e","tags":[],"sample_group":[["2 2","2\n\n$A_1=1,A_2=2,B_1=2,B_2=1$ and $A_1=2,A_2=1,B_1=1,B_2=2$ satisfy the conditions."],["2 3","18"],["141421 356237","881613484"]],"created_at":"2026-03-03 11:01:14"}}