Jenny loves experimenting with trees. Her favorite tree has nodes connected by edges, and each edge is unit in length. She wants to cut a subtree (i.e., a connected part of the original tree) of radius from this tree by performing the following two steps:
- Choose a node, , from the tree.
- Cut a subtree consisting of all nodes which are not further than units from node .
For example, the blue nodes in the diagram below depict a subtree centered at that has radius :
Given , , and the definition of Jenny's tree, find and print the number of different subtrees she can cut out. Two subtrees are considered to be different if they are not isomorphic.
Input Format
The first line contains two space-separated integers denoting the respective values of and .
Each of the next subsequent lines contains two space-separated integers, and , describing a bidirectional edge in Jenny's tree having length .
Constraints
Subtasks
For of the max score:
Output Format
Print the total number of different possible subtrees.
Sample Input 0
7 1
1 2
1 3
1 4
1 5
2 6
2 7
Sample Output 0
3
Explanation 0
In the diagram below, blue nodes denote the possible subtrees:
The last subtrees are considered to be the same (i.e., they all consist of two nodes connected by one edge), so we print as our answer.
Sample Input 1
7 3
1 2
2 3
3 4
4 5
5 6
6 7
Sample Output 1
4
Explanation 1
In the diagram below, blue nodes denote the possible subtrees:
Here, we have four possible different subtrees.