Problem:
Score : 700 points

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 U_i and Vertex V_i.
The time it takes to traverse this edge is D_i 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 10^9 + 7.

Constraints

1 \leq N \leq 100 000

1 \leq M \leq 200 000

1 \leq S, T \leq N

S \neq T

1 \leq U_i, V_i \leq N (1 \leq i \leq M)

1 \leq D_i \leq 10^9 (1 \leq i \leq M)

If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).

U_i \neq V_i (1 \leq i \leq M)

D_i are integers.

The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M

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

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//#pragma comment(linker, "/STACK:102400000,102400000") 
//#include <windows.h>
//#include <unordered_map>
//#include <unordered_set>
#include <fstream>
#include <iostream>
#include <functional>
#include <algorithm>
#include <cstring>
#include <vector>
#include <string>
#include <cstdio>
#include <cmath>
#include <queue>
#include <stack>
#include <deque>
#include <ctime>
#include <list>
#include <set>
#include <map>
#include <bitset>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
#define eps 1e-10
#define LL_INF 0x3fffffffffffffff
#define INF 0x3f3f3f3f
#define mem(a, b) memset(a, b, sizeof(a))
#define pper(i,n,m) for(int i = n;i >= m; i--)
#define repp(i, n, m) for (int i = n; i <= m; i++)
#define rep(i, n, m) for (int i = n; i < m; i++)
#define sa(n) scanf("%d", &(n))
#define mp make_pair
#define ff first
#define ss second
#define pb push_back

const int maxn = 1e5 + 5;
const int dir[8][2] = { { 0,1 },{ 1,1 },{ 1,0 },{ 1,-1 },{ 0,-1 },{ -1,-1 },{ -1,0 },{ -1,1 } };
const int dir8x[8] = { -1,-1,-1,0,0,1,1,1 };
const int dir8y[8] = { -1,0,1,1,-1,-1,0,1 };
const ll mod = 1e9 + 7;
const double PI = acos(-1.0);
ll po(ll a, ll b, ll mod) { ll res = 1; a %= mod; for (; b; b >>= 1) { if (b & 1)res = res*a%mod; a = a*a%mod; }return res; }
ll gcd(ll a, ll b) { if (a == 0) { return b; } else { return gcd(b%a, a); } }

const int maxm = 2e5 + 5;
struct P {
	int to, dis;
	P() {}
	P(int _to, int _dis) : to(_to), dis(_dis) {}
	friend bool operator<(P a, P b) { return a.dis > b.dis; }
};

struct Edge {
	int u, v, dis, next;
};

int st, en;
int n, m;
int a, b, c, num;
int head[maxn];
Edge edge[maxm * 2];
ll sum1[maxn], sum2[maxn];
ll dist1[maxn], dist2[maxn];

void addEdge(int u, int v, int dis) {
	edge[num].u = u;
	edge[num].v = v;
	edge[num].dis = dis;
	edge[num].next = head[u];
	head[u] = num++;
}

void input() {
	scanf("%d%d", &n, &m);
	scanf("%d%d", &st, &en);
	num = 0;
	memset(head, -1, sizeof(head));
	for (int i = 0; i < m; i++) {
		scanf("%d%d%d", &a, &b, &c);
		addEdge(a, b, c);
		addEdge(b, a, c);
	}
}

void dijkstra(ll dist[], ll sumt[], int s) {
	fill(dist + 1, dist + 1 + n, -1);
	fill(sumt + 1, sumt + 1 + n, 0);
	priority_queue <P> q;
	while (!q.empty()) q.pop();

	dist[s] = 0; sumt[s] = 1;
	q.push(P(s, 0));

	while (!q.empty()) {
		P p = q.top(); q.pop();
		int u = p.to;
		if (p.dis > dist[u]) continue;
		for (int i = head[u]; i != -1; i = edge[i].next) {
			int v = edge[i].v;
			if (dist[v] > dist[u] + edge[i].dis || dist[v] == -1) {
				sumt[v] = sumt[u] ;
				dist[v] = dist[u] + edge[i].dis;
				q.push(P(v, dist[v]));
			}
			else if (dist[v] == dist[u] + edge[i].dis) {
				sumt[v] = (sumt[v] + sumt[u]);
			}
		}
	}
}


bool check() {
	for (int i = 0; i < num; i++) {
		int u = edge[i].u;
		int v = edge[i].v;
		if (edge[i].dis == 0 && dist1[u] + dist2[v] == dist1[n]) {
			return true;
		}
	}
	return false;
}


void solve() {
	dijkstra(dist1, sum1, st);
	ll ans = sum1[en];
	cout << ans*(ans - 1) << endl;
}

int main()
{

	input();
	solve();
	//system("pause");
	return 0;
}