{"raw_statement":[{"iden":"problem statement","content":"There is a shogi (Japanese chess) board with $H$ rows and $W$ columns, and one king piece. The square at the $i$\\-th row from the top and $j$\\-th column from the left of the board is represented as $(i, j)$.  \nInitially, the king is placed at $(A, B)$. You perform the following operation exactly $T$ times.\n\n*   Move the king to one of the eight adjacent squares of the current square. More precisely, if the king is at square $(i, j)$, move the king to one of $(i+1,j+1), (i+1,j), (i+1,j-1), (i,j+1), (i,j-1), (i-1,j+1), (i-1,j), (i-1,j-1)$. The king cannot leave the board.\n\nFind the number, modulo $998244353$, of operation sequences such that the king is at $(C, D)$ after completing all $T$ operations. Two operation sequences are considered different if and only if there exists an integer $i$ $(1 \\leq i \\leq T)$ such that the king's position after the $i$\\-th operation is different."},{"iden":"constraints","content":"*   $2 \\leq H \\leq 3 \\times 10^5$\n*   $2 \\leq W \\leq 3 \\times 10^5$\n*   $1 \\leq T \\leq 3 \\times 10^5$\n*   $1 \\leq A \\leq H$\n*   $1 \\leq B \\leq W$\n*   $1 \\leq C \\leq H$\n*   $1 \\leq D \\leq W$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$H$ $W$ $T$ $A$ $B$ $C$ $D$"},{"iden":"sample input 1","content":"3 4 3 2 1 3 4"},{"iden":"sample output 1","content":"5\n\nThere are five operation sequences that satisfy the conditions in the problem statement. The king's movements corresponding to each operation sequence are as follows.\n\n*   $(2, 1) \\to (1, 2) \\to (2, 3) \\to (3, 4)$\n*   $(2, 1) \\to (2, 2) \\to (2, 3) \\to (3, 4)$\n*   $(2, 1) \\to (2, 2) \\to (3, 3) \\to (3, 4)$\n*   $(2, 1) \\to (3, 2) \\to (2, 3) \\to (3, 4)$\n*   $(2, 1) \\to (3, 2) \\to (3, 3) \\to (3, 4)$"},{"iden":"sample input 2","content":"202 123 456 20 25 7 20"},{"iden":"sample output 2","content":"167373259"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}