输入描述:

The first line of input contains a single integer n (2 ≤ n ≤ 100000).

The next n - 1 lines contains two space-separated integers each, ui, vi (1 ≤ ui ≠ vi ≤ n), describing an edge of the tree connecting ui and vi.

The last line contains a single integer D (1 ≤ D ≤ n).

It is guaranteed that the input graph is a tree.

输出描述:

Output a single integer, the number of subsets of nodes with diameter D. Since the answer might be large, output it modulo 109 + 7.

4
2 3
1 3
3 4
2

8

For the first sample, the subsets are {1, 2}, {1, 4}, {2, 4}, {1, 2, 3}, {1, 3, 4}, {2, 3, 4}, {1, 2, 4}, {1, 2, 3, 4}.

4
2 3
1 3
3 4
1

3

For the second sample, the subsets are {1, 3}, {2, 3}, {3, 4}.