{"raw_statement":[{"iden":"problem statement","content":"There is a $H \\times W$\\-square grid with $H$ horizontal rows and $W$ vertical columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and $j$\\-th column from the left.\nThe grid has a rook, initially on $(x_1, y_1)$. Takahashi will do the following operation $K$ times.\n\n*   Move the rook to a square that shares the row or column with the square currently occupied by the rook. Here, it must move to a square different from the current one.\n\nHow many ways are there to do the $K$ operations so that the rook will be on $(x_2, y_2)$ in the end? Since the answer can be enormous, find it modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq H, W \\leq 10^9$\n*   $1 \\leq K \\leq 10^6$\n*   $1 \\leq x_1, x_2 \\leq H$\n*   $1 \\leq y_1, y_2 \\leq W$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$ $K$\n$x_1$ $y_1$ $x_2$ $y_2$"},{"iden":"sample input 1","content":"2 2 2\n1 2 2 1"},{"iden":"sample output 1","content":"2\n\nWe have the following two ways.\n\n*   First, move the rook from $(1, 2)$ to $(1, 1)$. Second, move it from $(1, 1)$ to $(2, 1)$.\n*   First, move the rook from $(1, 2)$ to $(2, 2)$. Second, move it from $(2, 2)$ to $(2, 1)$."},{"iden":"sample input 2","content":"1000000000 1000000000 1000000\n1000000000 1000000000 1000000000 1000000000"},{"iden":"sample output 2","content":"24922282\n\nBe sure to find the count modulo $998244353$."},{"iden":"sample input 3","content":"3 3 3\n1 3 3 3"},{"iden":"sample output 3","content":"9"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}