F - Huge Number of Trees
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Hermione needs to solve a tough homework problem in Arithmancy class. Professor Vector was discussing trees for some time and now he gives the problem: Say, there are n + 1 nodes numbered 0, 1, 2, ..., n. Node 0 is always the root of the tree. How many different trees can be formed using the remaining n nodes so that all leaves have the same depth and the degree of each non-leaf node is at least d? Here, depth of a node u is the number of edges we need to traverse from the root (Node 0) to reach u. A tree is different from another tree if there exists at least one pair of nodes (u, v) for which an edge between u and v is present in one tree, but absent in the other one. Hermione wants your help to write a program to solve this problem.
Note that by degree, we mean the total number of neighbors, not just the number of children.
- The first line of the input contains a positive integer, T which denotes the number of test cases.
- For each case, there is one line of input containing two integers: n and the minimum degree of each non-leaf node, d.
For each test case, print "Case i: ", and then the answer (mod 109 + 7), where i is the testcase number, 1-indexed.
- 1 ≤ T ≤ 2000
- 2 ≤ n ≤ 500
- 2 ≤ d ≤ 10
Input: 3 2 2 3 2 4 2 Output: Case 1: 1 Case 2: 1 Case 3: 13
Testcase 1: The only valid tree is shown below:
Testcase 2: The only valid tree is shown below:
Testcase 3: The 13 different valid trees are as shown below:
|Time Limit:||2 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6|
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