Description

Given a rooted tree with $n$ nodes, rooted at node $1$. Now let's start the wander from node $s$, abiding by the following rules:

• If we have gone to $u$'s parent $f$ from $u$, delete the edge $(u,f)$ immediately.
• When $u$ has no neighbor, the wander stops.

For two plans $A,B$, we call they are essentially different only when the sets of nodes they pass through are different. It can be proven that if plan $A,B$ are the same, the numbers of step that their token are also the same.

Compute the sum of the lengths of all essentially different walks, modulo $10^9+7$.

Input Format

The first line contains two integers $n$ and $s$.

The next $n-1$ lines each contains two positive integers $u$ and $v$, representing an edge $(u,v)$.

Output Format

A single integer, the sum of the lengths modulo $10^9+7$.

7 5
2 1
3 2
4 2
5 3
6 5
7 3

48

Hint

Example explanation

Consider all possible essentially different paths:

• $5,3,2,1$;

• $5,3,7,3,2,1$;

• $5,3,7,3,2,4,2,1$;

• $5,3,2,4,2,1$;

• $5,6,5,3,2,1$;

• $5,6,5,3,7,3,2,1$;

• $5,6,5,3,2,4,2,1$;

• $5,6,5,3,7,3,2,4,2,1$;

The sum is $48$.

Data Volume and Conventions

This problem is divided into subtasks. Your score in a subtask is the minimum score across all its test cases.

This problem uses subtask dependencies. You will not receive the score for a subtask unless you achieve full points on all its dependent subtasks.

Special property A: $\forall i \in [1,n),u_i=1$.
Special property B: $\forall i \in [1,n),u_i=i,v_i=i+1$.
Special property C: $s=1$.

For all of the cases, $1 \le s \le n \le 10^6$.