155 lines
10 KiB
HTML
155 lines
10 KiB
HTML
<!DOCTYPE html>
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<html lang="ko">
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<head>
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<meta charset="UTF-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
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<title>BOJ 7393 - Offline</title>
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<style>
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:root {
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--bg: #fafaf8;
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--paper: #ffffff;
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--ink: #1e1f24;
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--muted: #6a6d75;
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--line: #d8dce3;
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--accent: #0d6e6e;
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--code-bg: #f4f6fb;
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}
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* { box-sizing: border-box; }
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body {
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margin: 0;
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background:
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radial-gradient(circle at 15% 0%, #f0efe9 0%, transparent 42%),
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radial-gradient(circle at 85% 20%, #e7f1f2 0%, transparent 38%),
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var(--bg);
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color: var(--ink);
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font-family: "Noto Sans KR", "Pretendard", "Apple SD Gothic Neo", sans-serif;
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line-height: 1.65;
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}
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main {
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max-width: 980px;
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margin: 0 auto;
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padding: 24px 16px 56px;
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}
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.header {
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background: var(--paper);
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border: 1px solid var(--line);
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border-radius: 14px;
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padding: 18px 20px;
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margin-bottom: 18px;
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}
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.header h1 { margin: 0 0 6px; font-size: 1.5rem; }
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.header p { margin: 0; color: var(--muted); font-size: 0.95rem; }
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.header a { color: var(--accent); text-decoration: none; }
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.section {
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background: var(--paper);
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border: 1px solid var(--line);
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border-radius: 14px;
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padding: 16px 18px;
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margin-bottom: 14px;
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overflow-x: auto;
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}
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h2 {
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margin: 0 0 10px;
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font-size: 1.05rem;
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color: var(--accent);
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border-bottom: 1px solid var(--line);
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padding-bottom: 8px;
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}
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pre, code {
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font-family: "JetBrains Mono", "Fira Code", monospace;
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background: var(--code-bg);
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}
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pre {
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padding: 12px;
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border-radius: 10px;
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border: 1px solid #e7ebf2;
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overflow: auto;
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}
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blockquote {
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margin: 14px 0;
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padding: 16px 16px 14px 22px;
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border-left: 4px solid var(--accent);
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border-radius: 10px;
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background: linear-gradient(90deg, #eef8f8 0%, #f9fdfd 100%);
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color: #24313a;
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font-weight: 600;
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position: relative;
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}
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blockquote::before {
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content: "“";
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position: absolute;
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left: 8px;
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top: 2px;
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font-size: 1.35rem;
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line-height: 1;
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color: #0b5f5f;
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opacity: 0.7;
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}
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blockquote > :first-child { margin-top: 0; }
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blockquote > :last-child { margin-bottom: 0; }
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q {
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color: #114f50;
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font-weight: 700;
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background: #edf8f8;
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border-radius: 6px;
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padding: 0 4px;
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}
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.math-inline math {
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font-size: 1em;
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vertical-align: middle;
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}
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.math-block {
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margin: 10px 0;
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padding: 8px 10px;
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overflow-x: auto;
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background: #f8fbff;
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border: 1px solid #e2ecf8;
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border-radius: 8px;
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}
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.math-block math {
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font-size: 1.04em;
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display: block;
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}
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table { border-collapse: collapse; width: 100%; }
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th, td { border: 1px solid var(--line); padding: 6px 8px; }
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img { max-width: 100%; height: auto; }
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</style>
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</head>
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<body>
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<main>
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<header class="header">
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<h1>Irrelevant Elements</h1>
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</header>
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<article class="section">
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<h2>문제</h2>
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<p>Young cryptoanalyst Georgie is investigating different schemes of generating random integer numbers ranging from <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn></mrow></math></span> to <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></math></span>. He thinks that standard random number generators are not good enough, so he has invented his own scheme that is intended to bring more randomness into the generated numbers.</p>
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<p>First, Georgie chooses <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> and generates <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> random integer numbers ranging from <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>0</mn></mrow></math></span> to <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></math></span>. Let the numbers generated be <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><mi>…</mi><mo>,</mo><msub><mi>a</mi><mi>n</mi></msub></mrow></math></span>. After that Georgie calculates the sums of all pairs of adjacent numbers, and replaces the initial array with the array of sums, thus getting <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span> numbers:~<span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>2</mn></msub><mo>+</mo><msub><mi>a</mi><mn>3</mn></msub><mo>,</mo><mi>…</mi><mo>,</mo><msub><mi>a</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>a</mi><mi>n</mi></msub></mrow></math></span>. Then he applies the same procedure to the new array, getting <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></math></span> numbers. The procedure is repeated until only one number is left. This number is then taken modulo <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi></mrow></math></span>. That gives the result of the generating procedure.</p>
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<p>Georgie has proudly presented this scheme to his computer science teacher, but was pointed out that the scheme has many drawbacks. One important drawback is the fact that the result of the procedure sometimes does not even depend on some of the initially generated numbers. For example, if <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></math></span> and <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi><mo>=</mo><mn>2</mn></mrow></math></span>, then the result does not depend on <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>a</mi><mn>2</mn></msub></mrow></math></span>. </p>
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<p>Now Georgie wants to investigate this phenomenon. He calls the <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>-th element of the initial array <em>irrelevant</em> if the result of the generating procedure does not depend on <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mi>a</mi><mi>i</mi></msub></mrow></math></span>. He considers various <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> and <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi></mrow></math></span> and wonders which elements are irrelevant for these parameters. Help him to find it out.</p>
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</article>
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<article class="section">
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<h2>입력</h2>
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<p>Input file contains <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> and <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi></mrow></math></span> (<span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>≤</mo><mi>n</mi><mo>≤</mo><mn>100</mn><mspace width="0.167em" /><mn>000</mn></mrow></math></span>, <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>≤</mo><mi>m</mi><mo>≤</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></math></span>).</p>
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</article>
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<article class="section">
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<h2>출력</h2>
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<p>On the first line of the output file print the number of irrelevant elements of the initial array for given <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>n</mi></mrow></math></span> and <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>m</mi></mrow></math></span>. On the second line print all such <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span> that <span class="math-inline"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>i</mi></mrow></math></span>-th element is irrelevant. Numbers on the second line must be printed in the ascending order and must be separated by spaces.</p>
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</article>
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<article class="section">
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<h2>예제 입력 1 복사</h2>
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<pre class="sampledata" id="sample-input-1">3 2
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</pre>
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</article>
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<article class="section">
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<h2>예제 출력 1 복사</h2>
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<pre class="sampledata" id="sample-output-1">1
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2
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</pre>
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</article>
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</main>
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</body>
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</html>
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