Counting Shortcuts solution codeforces

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).

$Counting Shortcuts solution codeforces$ Graph consisting of

6

of vertices and

8

of edgesFor 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

t

1

. Consider all paths whose length is at most

1 + 1 = 2

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

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

Input Counting Shortcuts solution codeforces

The first line of test contains the number $t$ ( $1 \leq t \leq 10^{4}$ ) —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 $n, m$ ( $2 \leq n \leq 2 \cdot 10^{5}$ , $1 \leq m \leq 2 \cdot 10^{5}$ ) —the number of vertices and edges in the graph.

The second line contains two numbers $s$ and $t$ ( $1 \leq s, t \leq n$ , $s \neq t$ ) —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 $u_{i}$ , $v_{i}$ ( $1 \leq u_{i}, v_{i} \leq n$ ) — 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 Counting Shortcuts solution codeforces

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

Copy

output

Copy Counting Shortcuts solution codeforces

Counting Shortcuts solution codeforces

Input Counting Shortcuts solution codeforces

Output Counting Shortcuts solution codeforces

Copy Counting Shortcuts solution codeforces

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