| # 754_E. Dasha and cyclic table |
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| ## Problem Description |
| Dasha is fond of challenging puzzles: Rubik's Cube 3 × 3 × 3, 4 × 4 × 4, 5 × 5 × 5 and so on. This time she has a cyclic table of size n × m, and each cell of the table contains a lowercase English letter. Each cell has coordinates (i, j) (0 ≤ i < n, 0 ≤ j < m). The table is cyclic means that to the right of cell (i, j) there is the cell <image>, and to the down there is the cell <image>. |
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| Dasha has a pattern as well. A pattern is a non-cyclic table of size r × c. Each cell is either a lowercase English letter or a question mark. Each cell has coordinates (i, j) (0 ≤ i < r, 0 ≤ j < c). |
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| The goal of the puzzle is to find all the appearance positions of the pattern in the cyclic table. |
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| We say that the cell (i, j) of cyclic table is an appearance position, if for every pair (x, y) such that 0 ≤ x < r and 0 ≤ y < c one of the following conditions holds: |
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| * There is a question mark in the cell (x, y) of the pattern, or |
| * The cell <image> of the cyclic table equals to the cell (x, y) of the pattern. |
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| Dasha solved this puzzle in no time, as well as all the others she ever tried. Can you solve it?. |
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| Input |
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| The first line contains two integers n and m (1 ≤ n, m ≤ 400) — the cyclic table sizes. |
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| Each of the next n lines contains a string of m lowercase English characters — the description of the cyclic table. |
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| The next line contains two integers r and c (1 ≤ r, c ≤ 400) — the sizes of the pattern. |
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| Each of the next r lines contains a string of c lowercase English letter and/or characters '?' — the description of the pattern. |
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| Output |
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| Print n lines. Each of the n lines should contain m characters. Each of the characters should equal '0' or '1'. |
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| The j-th character of the i-th (0-indexed) line should be equal to '1', in case the cell (i, j) is an appearance position, otherwise it should be equal to '0'. |
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| Examples |
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| Input |
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| 5 7 |
| qcezchs |
| hhedywq |
| wikywqy |
| qckrqzt |
| bqexcxz |
| 3 2 |
| ?? |
| yw |
| ?q |
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| Output |
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| 0000100 |
| 0001001 |
| 0000000 |
| 0000000 |
| 0000000 |
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| Input |
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| 10 10 |
| fwtoayylhw |
| yyaryyjawr |
| ywrdzwhscy |
| hnsyyxiphn |
| bnjwzyyjvo |
| kkjgseenwn |
| gvmiflpcsy |
| lxvkwrobwu |
| wyybbcocyy |
| yysijsvqry |
| 2 2 |
| ?? |
| yy |
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| Output |
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| 1000100000 |
| 0000000001 |
| 0001000000 |
| 0000010000 |
| 0000000000 |
| 0000000000 |
| 0000000000 |
| 0100000010 |
| 1000000001 |
| 0000010000 |
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| Input |
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| 8 6 |
| ibrgxl |
| xqdcsg |
| okbcgi |
| tvpetc |
| xgxxig |
| igghzo |
| lmlaza |
| gpswzv |
| 1 4 |
| gx?? |
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| Output |
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| 000100 |
| 000001 |
| 000000 |
| 000000 |
| 010001 |
| 000000 |
| 000000 |
| 000000 |
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| ## Contest Information |
| - **Contest ID**: 754 |
| - **Problem Index**: E |
| - **Points**: 2500.0 |
| - **Rating**: 2600 |
| - **Tags**: bitmasks, brute force, fft, strings, trees |
| - **Time Limit**: {'seconds': 6, 'nanos': 0} seconds |
| - **Memory Limit**: 512000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
