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avoidcollision Batch , stdin/stdout

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avoidcollision.html

Title

Problem Statement

We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.

The i-th edge connects Vertex Ui and Vertex Vi. The time it takes to traverse this edge is Di minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).

Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible. Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 109 + 7.

Constraints

  • 1 ≤ N ≤ 100 000
  • 1 ≤ M ≤ 200 000
  • 1 ≤ S, T ≤ N
  • S ≠ T
  • 1 ≤ Ui, Vi ≤ N (1 ≤ i ≤ M)
  • 1 ≤ Di ≤ 109 (1 ≤ i ≤ M)
  • If i ≠ j, then (Ui, Vi) ≠ (Uj, Vj) and (Ui, Vi) ≠ (Vj, Uj).
  • Ui ≠ Vi (1 ≤ i ≤ M)
  • Di are integers.
  • The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
S T
U1 V1 D1
U2 V2 D2
:
UM VM DM

Output

Print the answer.

Sample Input 1

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

Sample Output 1

2

There are two ways to choose shortest paths that satisfies the condition:

  • Takahashi chooses the path 1 \rightarrow 2 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 4 \rightarrow 1.
  • Takahashi chooses the path 1 \rightarrow 4 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 2 \rightarrow 1.

Sample Input 2

3 3
1 3
1 2 1
2 3 1
3 1 2

Sample Output 2

2

Sample Input 3

3 3
1 3
1 2 1
2 3 1
3 1 2

Sample Output 3

2

Sample Input 4

8 13
4 2
7 3 9
6 2 3
1 6 4
7 6 9
3 8 9
1 2 2
2 8 12
8 6 9
2 5 5
4 2 18
5 3 7
5 1 515371567
4 8 6

Sample Output 4

6

Tags

AtCoder, Graph Theory

Subtasks and Limits

Subtask Score #TC Time Memory Scoring
1100181s256MBMinimum
2041s256MBMinimum

Judge Compile Command

g++-8 ans.cpp -o avoidcollision -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512

Accepted Submissions

subIDUserTimeMax Time

Past Submissions

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mrJudge 09.05.20
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