{"raw_statement":[{"iden":"problem statement","content":"Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with $H$ east-west rows and $W$ north-south columns. Let $(i,j)$ be the square at the $i$\\-th row from the north and $j$\\-th column from the west.\nSome of the squares have a lotus leaf on it and cannot be entered. The square $(i,j)$ has a lotus leaf on it if $c_{ij}$ is `@`, and it does not if $c_{ij}$ is `.`.\nIn one stroke, Snuke can move between $1$ and $K$ squares (inclusive) toward one of the four directions: north, east, south, and west. The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.\nFind the minimum number of strokes Snuke takes to travel from the square $(x_1,y_1)$ to $(x_2,y_2)$. If the travel from $(x_1,y_1)$ to $(x_2,y_2)$ is impossible, point out that fact."},{"iden":"constraints","content":"*   $1 \\leq H,W,K \\leq 10^6$\n*   $H \\times W \\leq 10^6$\n*   $1 \\leq x_1,x_2 \\leq H$\n*   $1 \\leq y_1,y_2 \\leq W$\n*   $x_1 \\neq x_2$ or $y_1 \\neq y_2$.\n*   $c_{i,j}$ is `.` or `@`.\n*   $c_{x_1,y_1} =$ `.`\n*   $c_{x_2,y_2} =$ `.`\n*   All numbers in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$H$ $W$ $K$\n$x_1$ $y_1$ $x_2$ $y_2$\n$c_{1,1}c_{1,2}$ $..$ $c_{1,W}$\n$c_{2,1}c_{2,2}$ $..$ $c_{2,W}$\n$:$\n$c_{H,1}c_{H,2}$ $..$ $c_{H,W}$"},{"iden":"sample input 1","content":"3 5 2\n3 2 3 4\n.....\n.@..@\n..@.."},{"iden":"sample output 1","content":"5\n\nInitially, Snuke is at the square $(3,2)$. He can reach the square $(3, 4)$ by making five strokes as follows:\n\n*   From $(3, 2)$, go west one square to $(3, 1)$.\n    \n*   From $(3, 1)$, go north two squares to $(1, 1)$.\n    \n*   From $(1, 1)$, go east two squares to $(1, 3)$.\n    \n*   From $(1, 3)$, go east one square to $(1, 4)$.\n    \n*   From $(1, 4)$, go south two squares to $(3, 4)$."},{"iden":"sample input 2","content":"1 6 4\n1 1 1 6\n......"},{"iden":"sample output 2","content":"2"},{"iden":"sample input 3","content":"3 3 1\n2 1 2 3\n.@.\n.@.\n.@."},{"iden":"sample output 3","content":"\\-1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}