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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Petya and Strings</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya loves presents. His mum bought him two strings of the same size for his birthday. The strings consist of uppercase and lowercase Latin letters. Now Petya wants to compare those two strings <span class="tex-font-style-underline">lexicographically</span>. The letters' case does not matter, that is an uppercase letter is considered equivalent to the corresponding lowercase letter. Help Petya perform the comparison.</p></div><div class="input-specification"><div class="section-title">Input</div><p>Each of the first two lines contains a bought string. The strings' lengths range from <span class="tex-span">1</span> to <span class="tex-span">100</span> inclusive. It is guaranteed that the strings are of the same length and also consist of uppercase and lowercase Latin letters.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the first string is less than the second one, print "-1". If the second string is less than the first one, print "1". If the strings are equal, print "0". Note that the letters' case is not taken into consideration when the strings are compared.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>aaaa<br />aaaA<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div><div class="input"><div class="title">Input</div><pre>abs<br />Abz<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div><div class="input"><div class="title">Input</div><pre>abcdefg<br />AbCdEfF<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>If you want more formal information about the lexicographical order (also known as the "<span class="tex-font-style-underline">dictionary order</span>" or "<span class="tex-font-style-underline">alphabetical order</span>"), you can visit the following site:</p><ul><li> <span class="tex-font-style-tt">http://en.wikipedia.org/wiki/Lexicographical_order</span></li></ul></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Petya and Square</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya loves playing with squares. Mum bought him a square <span class="tex-span">2<i>n</i> × 2<i>n</i></span> in size. Petya marked a cell inside the square and now he is solving the following task.</p><p>The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal <span class="tex-font-style-bf">up to rotation</span>.</p><p>Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three space-separated integers <span class="tex-span">2<i>n</i></span>, <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span">2 ≤ 2<i>n</i> ≤ 100, 1 ≤ <i>x</i>, <i>y</i> ≤ 2<i>n</i></span>), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that <span class="tex-span">2<i>n</i></span> is even.</p><p>The coordinates of the marked cell are represented by a pair of numbers <span class="tex-span"><i>x</i></span> <span class="tex-span"><i>y</i></span>, where <span class="tex-span"><i>x</i></span> represents the number of the row and <span class="tex-span"><i>y</i></span> represents the number of the column. The rows and columns are numbered by consecutive integers from <span class="tex-span">1</span> to <span class="tex-span">2<i>n</i></span>. The rows are numbered from top to bottom and the columns are numbered from the left to the right.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If the square is possible to cut, print "<span class="tex-font-style-tt">YES</span>", otherwise print "<span class="tex-font-style-tt">NO</span>" (without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>YES<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 2 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>NO<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>A sample test from the statement and one of the possible ways of cutting the square are shown in the picture: </p><center> <img class="tex-graphics" src="https://espresso.codeforces.com/1f4eaddfc0f65100f6eb9944e60200ca4c61e857.png" style="max-width: 100.0%;max-height: 100.0%;" /> </center></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Petya and Inequiations</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya loves inequations. Help him find <span class="tex-span"><i>n</i></span> positive integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span>, such that the following two conditions are satisfied:</p><ul><li> <span class="tex-span"><i>a</i><sub class="lower-index">1</sub><sup class="upper-index">2</sup> + <i>a</i><sub class="lower-index">2</sub><sup class="upper-index">2</sup> + ... + <i>a</i><sub class="lower-index"><i>n</i></sub><sup class="upper-index">2</sup> ≥ <i>x</i></span></li><li> <span class="tex-span"><i>a</i><sub class="lower-index">1</sub> + <i>a</i><sub class="lower-index">2</sub> + ... + <i>a</i><sub class="lower-index"><i>n</i></sub> ≤ <i>y</i></span></li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three space-separated integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup>, 1 ≤ <i>x</i> ≤ 10<sup class="upper-index">12</sup>, 1 ≤ <i>y</i> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>Please do not use the %lld specificator to read or write 64-bit integers in С++. It is recommended to use cin, cout streams or the %I64d specificator.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print <span class="tex-span"><i>n</i></span> positive integers that satisfy the conditions, one integer per line. If such numbers do not exist, print a single number "-1". If there are several solutions, print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>5 15 15<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br />4<br />1<br />1<br />2<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 3 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div><div class="input"><div class="title">Input</div><pre>1 99 11<br /></pre></div><div class="output"><div class="title">Output</div><pre>11<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Petya and Divisors</div><div class="time-limit"><div class="property-title">time limit per test</div>5 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya loves looking for numbers' divisors. One day Petya came across the following problem:</p><p>You are given <span class="tex-span"><i>n</i></span> queries in the form "<span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span>". For each query Petya should count how many divisors of number <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> divide none of the numbers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i> - <i>y</i><sub class="lower-index"><i>i</i></sub></sub>, <i>x</i><sub class="lower-index"><i>i</i> - <i>y</i><sub class="lower-index"><i>i</i></sub> + 1</sub>, ..., <i>x</i><sub class="lower-index"><i>i</i> - 1</sub></span>. Help him.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains an integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">1 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>). Each of the following <span class="tex-span"><i>n</i></span> lines contain two space-separated integers <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>x</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">5</sup></span>, <span class="tex-span">0 ≤ <i>y</i><sub class="lower-index"><i>i</i></sub> ≤ <i>i</i> - 1</span>, where <span class="tex-span"><i>i</i></span> is the query's ordinal number; the numeration starts with <span class="tex-span">1</span>). </p><p>If <span class="tex-span"><i>y</i><sub class="lower-index"><i>i</i></sub> = 0</span> for the query, then the answer to the query will be the number of divisors of the number <span class="tex-span"><i>x</i><sub class="lower-index"><i>i</i></sub></span>. In this case you do not need to take the previous numbers <span class="tex-span"><i>x</i></span> into consideration.</p></div><div class="output-specification"><div class="section-title">Output</div><p>For each query print the answer on a single line: the number of positive integers <span class="tex-span"><i>k</i></span> such that <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a2f638209e8c902f97bdea6bbe47f9dcc1c7b537.png" style="max-width: 100.0%;max-height: 100.0%;" /></p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>6<br />4 0<br />3 1<br />5 2<br />6 2<br />18 4<br />10000 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br />1<br />1<br />2<br />2<br />22<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>Let's write out the divisors that give answers for the first 5 queries:</p><p>1) 1, 2, 4 </p><p>2) 3</p><p>3) 5</p><p>4) 2, 6</p><p>5) 9, 18</p></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Petya and Spiders</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Little Petya loves training spiders. Petya has a board <span class="tex-span"><i>n</i> × <i>m</i></span> in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idle or to move from current cell to some of the four side-neighboring cells (that is, one command for each of the four possible directions). Petya gives the commands so that no spider leaves the field. It is allowed for spiders to pass through each other when they crawl towards each other in opposite directions. All spiders crawl simultaneously and several spiders may end up in one cell. Petya wants to know the maximum possible number of spider-free cells after one second.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two space-separated integers <span class="tex-span"><i>n</i></span> and <span class="tex-span"><i>m</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 40, <i>n</i>·<i>m</i> ≤ 40</span>) — the board sizes.</p></div><div class="output-specification"><div class="section-title">Output</div><p>In the first line print the maximum number of cells without spiders.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>1 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>0<br /></pre></div><div class="input"><div class="title">Input</div><pre>2 3<br /></pre></div><div class="output"><div class="title">Output</div><pre>4<br /></pre></div></div></div><div class="note"><div class="section-title">Note</div><p>In the first sample the only possible answer is:</p><p><span class="tex-font-style-tt">s</span></p><p>In the second sample one of the possible solutions is: </p><pre class="verbatim"><br />rdl<br />rul<br /></pre><p><span class="tex-font-style-tt">s</span> denotes command "stay idle", <span class="tex-font-style-tt">l, r, d, u</span> denote commands "crawl left", "crawl right", "crawl down", "crawl up", correspondingly.</p></div></div></div>
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