| # 1037_E. Trips |
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| ## Problem Description |
| There are n persons who initially don't know each other. On each morning, two of them, who were not friends before, become friends. |
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| We want to plan a trip for every evening of m days. On each trip, you have to select a group of people that will go on the trip. For every person, one of the following should hold: |
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| * Either this person does not go on the trip, |
| * Or at least k of his friends also go on the trip. |
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| Note that the friendship is not transitive. That is, if a and b are friends and b and c are friends, it does not necessarily imply that a and c are friends. |
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| For each day, find the maximum number of people that can go on the trip on that day. |
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| Input |
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| The first line contains three integers n, m, and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ 2 ⋅ 10^5, 1 ≤ k < n) — the number of people, the number of days and the number of friends each person on the trip should have in the group. |
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| The i-th (1 ≤ i ≤ m) of the next m lines contains two integers x and y (1≤ x, y≤ n, x≠ y), meaning that persons x and y become friends on the morning of day i. It is guaranteed that x and y were not friends before. |
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| Output |
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| Print exactly m lines, where the i-th of them (1≤ i≤ m) contains the maximum number of people that can go on the trip on the evening of the day i. |
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| Examples |
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| Input |
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| 4 4 2 |
| 2 3 |
| 1 2 |
| 1 3 |
| 1 4 |
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| Output |
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| 0 |
| 0 |
| 3 |
| 3 |
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| Input |
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| 5 8 2 |
| 2 1 |
| 4 2 |
| 5 4 |
| 5 2 |
| 4 3 |
| 5 1 |
| 4 1 |
| 3 2 |
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| Output |
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| 0 |
| 0 |
| 0 |
| 3 |
| 3 |
| 4 |
| 4 |
| 5 |
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| Input |
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| 5 7 2 |
| 1 5 |
| 3 2 |
| 2 5 |
| 3 4 |
| 1 2 |
| 5 3 |
| 1 3 |
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| Output |
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| 0 |
| 0 |
| 0 |
| 0 |
| 3 |
| 4 |
| 4 |
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| Note |
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| In the first example, |
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| * 1,2,3 can go on day 3 and 4. |
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| In the second example, |
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| * 2,4,5 can go on day 4 and 5. |
| * 1,2,4,5 can go on day 6 and 7. |
| * 1,2,3,4,5 can go on day 8. |
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| In the third example, |
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| * 1,2,5 can go on day 5. |
| * 1,2,3,5 can go on day 6 and 7. |
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| ## Contest Information |
| - **Contest ID**: 1037 |
| - **Problem Index**: E |
| - **Points**: 2250.0 |
| - **Rating**: 2200 |
| - **Tags**: graphs |
| - **Time Limit**: {'seconds': 2, 'nanos': 0} seconds |
| - **Memory Limit**: 256000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
