{"raw_statement":[{"iden":"problem statement","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 $(10^9+7)$."},{"iden":"constraints","content":"*   $1\\leq N \\leq M \\leq 5\\times10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 2"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"2 3"},{"iden":"sample output 2","content":"18"},{"iden":"sample input 3","content":"141421 356237"},{"iden":"sample output 3","content":"881613484"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}