You are given a weighted tree with $n$ vertices. In this tree:

• $d(u, v)$ represents the weight of the minimum edge on the simple path from vertex $u$ to vertex $v$.

Your task is to handle $q$ queries of the form $(u, k)$, count the number of vertices $v$ for which $d(u, v) = k$.

Input

• The first line contains two integers $n,q$.
• The next $n - 1$ lines, each line contains three integers $u, v, w$, there is an edge of weight $w$ between $u$ and $v$.
• The next $q$ lines, each line contains two integers $u, k$, a query.

Output

• Print an integer is the answer for each query.

Constraints

• $1 \le n,q \le 10^5$.
• $1 \le u, v \le n$.
• $1 \le w, k \le n$.

Example

Input:

4 2
1 2 1
2 3 2
2 4 3
3 2
2 1

Output:

2
1