G. Counting Shortcuts
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an undirected connected graph with $$$n$$$ vertices and $$$m$$$ edges. The graph contains no loops (edges from a vertex to itself) and multiple edges (i.e. no more than one edge between each pair of vertices). The vertices of the graph are numbered from $$$1$$$ to $$$n$$$.

Find the number of paths from a vertex $$$s$$$ to $$$t$$$ whose length differs from the shortest path from $$$s$$$ to $$$t$$$ by no more than $$$1$$$. It is necessary to consider all suitable paths, even if they pass through the same vertex or edge more than once (i.e. they are not simple).

Graph consisting of $$$6$$$ of vertices and $$$8$$$ of edges

For example, let $$$n = 6$$$, $$$m = 8$$$, $$$s = 6$$$ and $$$t = 1$$$, and let the graph look like the figure above. Then the length of the shortest path from $$$s$$$ to $$$t$$$ is $$$1$$$. Consider all paths whose length is at most $$$1 + 1 = 2$$$.

  • $$$6 \rightarrow 1$$$. The length of the path is $$$1$$$.
  • $$$6 \rightarrow 4 \rightarrow 1$$$. Path length is $$$2$$$.
  • $$$6 \rightarrow 2 \rightarrow 1$$$. Path length is $$$2$$$.
  • $$$6 \rightarrow 5 \rightarrow 1$$$. Path length is $$$2$$$.

There is a total of $$$4$$$ of matching paths.

Input

The first line of test contains the number $$$t$$$ ($$$1 \le t \le 10^4$$$) —the number of test cases in the test.

Before each test case, there is a blank line.

The first line of test case contains two numbers $$$n, m$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le 2 \cdot 10^5$$$) —the number of vertices and edges in the graph.

The second line contains two numbers $$$s$$$ and $$$t$$$ ($$$1 \le s, t \le n$$$, $$$s \neq t$$$) —the numbers of the start and end vertices of the path.

The following $$$m$$$ lines contain descriptions of edges: the $$$i$$$th line contains two integers $$$u_i$$$, $$$v_i$$$ ($$$1 \le u_i,v_i \le n$$$) — the numbers of vertices that connect the $$$i$$$th edge. It is guaranteed that the graph is connected and does not contain loops and multiple edges.

It is guaranteed that the sum of values $$$n$$$ on all test cases of input data does not exceed $$$2 \cdot 10^5$$$. Similarly, it is guaranteed that the sum of values $$$m$$$ on all test cases of input data does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single number — the number of paths from $$$s$$$ to $$$t$$$ such that their length differs from the length of the shortest path by no more than $$$1$$$.

Since this number may be too large, output it modulo $$$10^9 + 7$$$.

Example
Input
4

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

6 8
6 1
1 4
1 6
1 5
1 2
5 6
4 6
6 3
2 6

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

8 18
5 1
2 1
3 1
4 2
5 2
6 5
7 3
8 4
6 4
8 7
1 4
4 7
1 6
6 7
3 8
8 5
4 5
4 3
8 2
Output
2
4
1
11