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94 lines
2.1 KiB
HTML
94 lines
2.1 KiB
HTML
<p>You are given two integers <code>n</code> and <code>k</code>.</p>
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<p>Initially, you start with an array <code>a</code> of <code>n</code> integers where <code>a[i] = 1</code> for all <code>0 <= i <= n - 1</code>. After each second, you simultaneously update each element to be the sum of all its preceding elements plus the element itself. For example, after one second, <code>a[0]</code> remains the same, <code>a[1]</code> becomes <code>a[0] + a[1]</code>, <code>a[2]</code> becomes <code>a[0] + a[1] + a[2]</code>, and so on.</p>
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<p>Return the <strong>value</strong> of <code>a[n - 1]</code> after <code>k</code> seconds.</p>
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<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 4, k = 5</span></p>
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<p><strong>Output:</strong> <span class="example-io">56</span></p>
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<p><strong>Explanation:</strong></p>
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<table border="1">
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<tbody>
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<tr>
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<th>Second</th>
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<th>State After</th>
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</tr>
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<tr>
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<td>0</td>
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<td>[1,1,1,1]</td>
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</tr>
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<tr>
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<td>1</td>
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<td>[1,2,3,4]</td>
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</tr>
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<tr>
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<td>2</td>
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<td>[1,3,6,10]</td>
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</tr>
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<tr>
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<td>3</td>
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<td>[1,4,10,20]</td>
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</tr>
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<tr>
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<td>4</td>
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<td>[1,5,15,35]</td>
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</tr>
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<tr>
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<td>5</td>
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<td>[1,6,21,56]</td>
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</tr>
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</tbody>
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</table>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 5, k = 3</span></p>
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<p><strong>Output:</strong> <span class="example-io">35</span></p>
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<p><strong>Explanation:</strong></p>
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<table border="1">
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<tbody>
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<tr>
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<th>Second</th>
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<th>State After</th>
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</tr>
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<tr>
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<td>0</td>
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<td>[1,1,1,1,1]</td>
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</tr>
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<tr>
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<td>1</td>
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<td>[1,2,3,4,5]</td>
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</tr>
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<tr>
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<td>2</td>
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<td>[1,3,6,10,15]</td>
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</tr>
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<tr>
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<td>3</td>
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<td>[1,4,10,20,35]</td>
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</tr>
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</tbody>
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</table>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n, k <= 1000</code></li>
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</ul>
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