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)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, a, b) for(int i = a; i < b; i++)
#define rrep(i, a, b) for(int i = b - 1; i >= a; i--)
#define ALL(a) a.begin(), a.end()
#define pii pair<int,int>
#pragma GCC optimize("Ofast")
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define pb push_back
#define mp make_pair
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define isSquare(x) (sqrt(x)*sqrt(x) == x)
template<class T>bool chmax(T &a, const T &b) {if(a<b){a = b; return 1;} return 0; };
template<class T>bool chmin(T &a, const T &b) {if(a>b){a = b; return 1;} return 0; };
inline void IN(void){return;}
template <typename First, typename... Rest> void IN(First& first, Rest&... rest){cin >> first;IN(rest...);return;}
inline void OUT(void){cout << "\n";return;}
template <typename First, typename... Rest> void OUT(First first, Rest... rest){cout << first << " ";OUT(rest...);return;}
const double EPS = 1e-9;
const int mod = 1e9 + 7;
const int INF = 1e9;
const long long LLINF = 1e18;
long long lcm(ll a, ll b){return a * b / __gcd(a,b);}
struct IoSetup { IoSetup() {
    cin.tie(nullptr);ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
} } iosetup;
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
    os << p.first << " " << p.second;
    return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
    is >> p.first >> p.second;
    return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
    for(int i = 0; i < (int) v.size(); i++) {
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
    for(T &in : v) is >> in;
    return is;
}
template <typename T> void Exit(T first){cout << first << endl;exit(0); };
template< int mod > struct ModInt {
    int x; ModInt() : x(0) {}
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
    ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
    ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}
    ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); }return ModInt(u);}
    ModInt pow(int64_t n) const {ModInt ret(1), mul(x); while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x;}
    friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); }
    static int get_mod() { return mod; }
}; using modint = ModInt< mod >;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

template< typename T > struct edge {
   int src, to; T cost;
   edge(int to, T cost) : src(-1), to(to), cost(cost) {}
   edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
   edge &operator=(const int &x) { to = x; return *this;}
   operator int() const { return to; }
};
template< typename T > using Edges = vector< edge< T > >;
template< typename T > using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T > using Matrix = vector< vector< T > >;

template< typename T > struct dijkstra
{
        WeightedGraph< T > g;
        int s;
        int V;
        vector<int> Prev;
        vector<T> Dist;
        vector<modint> dp;

        using Pi = pair< T, int >;
        dijkstra(WeightedGraph< T > &G, int S){
            g = G;
            s = S;
            V = G.size();
            Prev.resize(V, -1);
            Dist.resize(g.size(), LLINF);
            dp.resize(V, 0);
        }


        vector< T > dist(){
            priority_queue< Pi, vector< Pi >, greater< Pi > > que;
            Dist[s] = 0;
            dp[s] = 1;
            que.emplace(Dist[s], s);
            while(!que.empty()) {
                T cost;
                int idx;
                tie(cost, idx) = que.top();
                que.pop();
                if(Dist[idx] < cost) continue;
                for(auto &e : g[idx]) {
                    auto next_cost = cost + e.cost;
                    if(Dist[e.to] < next_cost) continue;
                    else if(Dist[e.to] == next_cost){
                        dp[e.to] += dp[idx];
                        continue;
                    }
                    dp[e.to] = dp[idx];
                    Dist[e.to] = next_cost;
                    Prev[e.to] = idx;
                    que.emplace(Dist[e.to], e.to);
                }
            }
            return Dist;
        }

        // 頂点tへの最短路
        vector<int> get_path(int t){
            vector<int> path;
            for(; t != -1; t = Prev[t]) path.push_back(t);//tがsになるまで辿っていく
            reverse(path.begin(), path.end());
            return path;
        }
};
// dijkstra<int> ds(G, 1);

int main(){
    iosetup;
    int N, M; cin >> N >> M;
    int S, T;IN(S, T);S--, T--;
    WeightedGraph<ll> G(N);
    rep(i, 0, M){
        int u, v;
        ll d; cin >> u >> v >> d; u--, v--;
        G[u].push_back({v, d});
        G[v].push_back({u, d});
    }
    dijkstra<ll> distt(G, S), dista(G, T);
    auto d_T = distt.dist();
    auto d_A = dista.dist();
    ll TL = d_T[T];
    modint ans = distt.dp[T];
    ans *= ans;
    // cerr << ans << endl;
    // cerr << TL << endl;
    rep(i, 0, N){
        // cerr << i << " " << ans << endl;
        if(TL%2 == 0){
            if(TL/2 == d_T[i]) ans -= distt.dp[i] * dista.dp[i];
            else{
                for(auto nv: G[i]){
                    if(d_T[i] < TL/2 && d_A[nv.to] < TL/2 && d_T[i] + d_A[nv.to] + nv.cost == TL){
                        modint tmp = distt.dp[i] * dista.dp[nv.to];
                        ans -= tmp * tmp;
                    }
                }
            }
        }else{
            for(auto nv: G[i]){
                if(d_T[i] <= TL/2 && d_A[nv.to] <= TL/2 && d_T[i] + d_A[nv.to] + nv.cost == TL){
                    modint tmp = distt.dp[i] * dista.dp[nv.to];
                    ans -= tmp * tmp;
                }
            }
        }
    }
    cout << ans << endl;

    return 0;
}