{"problem":{"name":"Odd Sum Rectangles","description":{"content":"We have a grid with $(2^N - 1)$ rows and $(2^M-1)$ columns. You are asked to write $0$ or $1$ in each of these squares. Let $a_{i,j}$ be the number written in the square at the $i$\\-th row from the to","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"hitachi2020_e"},"statements":[{"statement_type":"Markdown","content":"We have a grid with $(2^N - 1)$ rows and $(2^M-1)$ columns. You are asked to write $0$ or $1$ in each of these squares. Let $a_{i,j}$ be the number written in the square at the $i$\\-th row from the top and the $j$\\-th column from the left.\nFor a quadruple of integers $(i_1, i_2, j_1, j_2)$ such that $1\\leq i_1 \\leq i_2\\leq 2^N-1, 1\\leq j_1 \\leq j_2\\leq 2^M-1$, let $S(i_1, i_2, j_1, j_2) = \\displaystyle \\sum_{r=i_1}^{i_2}\\sum_{c=j_1}^{j_2}a_{r,c}$. Then, let the _oddness_ of the grid be the number of quadruples $(i_1, i_2, j_1, j_2)$ such that $S(i_1, i_2, j_1, j_2)$ is odd.\nFind a way to fill in the grid that maximizes its oddness.\n\n## Constraints\n\n*   $N$ and $M$ are integers between $1$ and $10$ (inclusive).\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":"hitachi2020_e","tags":[],"sample_group":[["1 2","111\n\nFor this grid, $S(1, 1, 1, 1)$, $S(1, 1, 2, 2)$, $S(1, 1, 3, 3)$, and $S(1, 1, 1, 3)$ are odd, so it has the oddness of $4$.\nWe cannot make the oddness $5$ or higher, so this is one of the ways that maximize the oddness."]],"created_at":"2026-03-03 11:01:14"}}