#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include<bits/stdc++.h>
using namespace std;
#define rep(i,s,t) for(ll i = (ll)(s); i < (ll)(t); i++)
#define rrep(i,s,t) for(ll i = (ll)(s-1);(ll)(t) <= i; i--)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> Pll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
constexpr ll INF = numeric_limits<ll>::max()/4;
constexpr ll n_max = 2e5+10;
#define int ll

template <typename A, typename B>
string to_string(pair<A, B> p);
string to_string(const string &s) {return '"' + s + '"';}
string to_string(const char *c) {return to_string((string) c);}
string to_string(bool b) {return (b ? "true" : "false");}
template <size_t N>
string to_string(bitset<N> v){
    string res = "";
    for(size_t i = 0; i < N; i++) res += static_cast<char>('0' + v[i]);
    return res;
}
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for(const auto &x : v) {
        if(!first) res += ", ";
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p){return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";}

void debug_out() {cerr << endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template<class T>
bool chmax(T &a, T b){if(a < b){a = b; return true;} return false;}
template<class T>
bool chmin(T &a, T b){if(a > b){a = b; return true;} return false;}

template<std::int_fast64_t Modulus>
class modint {
    using i64 = int_fast64_t;

    public:
    i64 a;

    constexpr modint(const i64 x = 0) noexcept {
        this -> a = x % Modulus;
        if(a < 0){
            a += Modulus;
        }
    }
    constexpr int getmod() { return Modulus; }
    constexpr modint operator - () const noexcept {
        return a ? Modulus - a : 0;
    }
    constexpr const i64 &value() const noexcept {return a;}
    constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
    }
    constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
    }
    constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
    }
    constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
    }
    constexpr modint &operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if(a >= Modulus) {
            a -= Modulus;
        }
        return *this;
    }
    constexpr modint &operator-=(const modint rhs) noexcept {
        if(a < rhs.a) {
            a += Modulus;
        }
        a -= rhs.a;
        return *this;
    }
    constexpr modint &operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
    }
    constexpr modint &operator/=(modint rhs) noexcept {
        i64 a_ = rhs.a, b = Modulus, u = 1, v = 0;
        while(b){
            i64 t = a_/b;
            a_ -= t * b; swap(a_,b);
            u -= t * v; swap(u,v);
        }
        a = a * u % Modulus;
        if(a < 0) a += Modulus;
        return *this;
    }
    
    // 自前実装
    constexpr bool operator==(const modint rhs) noexcept {
        return a == rhs.a;
    }
    constexpr bool operator!=(const modint rhs) noexcept {
        return a != rhs.a;
    }
    constexpr bool operator>(const modint rhs) noexcept {
        return a > rhs.a;
    }
    constexpr bool operator>=(const modint rhs) noexcept {
        return a >= rhs.a;
    }
    constexpr bool operator<(const modint rhs) noexcept {
        return a < rhs.a;
    }
    constexpr bool operator<=(const modint rhs) noexcept {
        return a <= rhs.a;
    }
    constexpr modint& operator++() noexcept {
        return (*this) += modint(1);
    }
    // constexpr modint operator++(int) {
    //     modint tmp(*this);
    //     operator++();
    //     return tmp;
    // }
    constexpr modint& operator--() noexcept {
        return (*this) -= modint(1);
    }
    // constexpr modint operator--(int) {
    //     modint tmp(*this);
    //     operator--();
    //     return tmp;
    // }
    template<typename T>
    friend constexpr modint modpow(const modint &mt, T n) noexcept {
        if(n < 0){
            modint t = (modint(1) / mt);
            return modpow(t, -n);
        }
        modint res = 1, tmp = mt;
        while(n){
            if(n & 1)res *= tmp;
            tmp *= tmp;
            n /= 2;
        }
        return res;
    }

    friend constexpr string to_string(const modint &mt) noexcept {
        return to_string(mt.a);
    }
};

// 標準入出力対応
template<std::int_fast64_t Modulus>
std::ostream &operator<<(std::ostream &out, const modint<Modulus> &m) {
    out << m.a;
    return out;
}
template<std::int_fast64_t Modulus>
std::istream &operator>>(std::istream &in, modint<Modulus> &m) {
    ll a;
    in >> a;
    m = modint<Modulus>(a);
    return in;
}

const ll MOD = 1e9+7;
// const ll MOD = 998244353;
using mint = modint<MOD>;
template<typename T>
struct edge{
    int f,t;
    T c;
    int id;
    edge(){};
    edge(int f,int t,T c,int id = 0):f(f),t(t),c(c),id(id){};
    bool operator< (const edge &rhs) const {
        return (*this).c < rhs.c;
    }
    bool operator> (const edge &rhs) const {
        return (*this).c > rhs.c;
    }
    friend string to_string(edge<T> e){
        return "(" + to_string(e.f) + ", " + to_string(e.t) + ", " + to_string(e.c) + ")";
    }
};

template<typename T>
struct graph{
    std::vector<std::vector<edge<T> > > data;
    graph(){};
    graph(int v):data(v){};
    void resize(int n){
        data.resize(n);
    }
    void add_edge(edge<T> &e){
        data[e.f].push_back(e);
    }
    void add_edge(int f,int t,T c){
        data[f].emplace_back(f,t,c);
    }
    size_t size(){
        return data.size();
    }
    vector<edge<T>> operator[](int n){
        return data[n];
    }
    std::vector<edge<T>> make_edges(){
        std::vector<edge<T>> r;
        for(auto &i:data)std::copy(i.begin(),i.end(),std::back_inserter(r));
        return r;
    }
};

template<typename T>
std::vector<T> dijkstra(graph<T> &g,int s, vector<mint> &res){
    using state = std::pair<T,int>;
    //priority_queue
    std::priority_queue<state,std::vector<state>,std::greater<state>> q;
    q.emplace((T)0,s);
    //data init
    std::vector<T> data(g.size(),std::numeric_limits<T>::max());
    
    data[s] = (T)0;
    res[s] = 1;
    //solve
    while(!q.empty()){
        state cur = q.top();q.pop();
        T c = cur.first; int pos = cur.second;
        if(data[pos] < c)continue;
        for(auto &e : g.data[pos]){
            if(c + e.c == data[e.t]){
                res[e.t] += res[e.f];
            }
            if(c + e.c < data[e.t]){
                data[e.t] = c + e.c;
                res[e.t] = res[e.f];
                q.emplace(c + e.c, e.t);
            }
        }
    }
    return data;
};

signed main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    ll n,m; cin >> n >> m;
    ll s,t; cin >> s >> t;
    s--;t--;
    
    vector<tuple<ll, ll, ll>> v(m);
    graph<ll> g(n);
    rep(i,0,m){
        ll f,t,c; cin >> f >> t >> c;
        f--;t--;
        g.add_edge(f, t, c);
        g.add_edge(t, f, c);
        v[i] = {f, t, c};
    }

    vector<mint> sres(n), tres(n);
    auto sdij = dijkstra(g, s, sres);
    debug(sres, sdij);
    auto tdij = dijkstra(g, t, tres);
    debug(tres, tdij);


    mint ans = sres[t] * sres[t];
    ll dis = sdij[t];

    rep(i,0,n){
        if(sdij[i] + tdij[i] == dis && sdij[i] == tdij[i])
            ans -= sres[i] * sres[i] * tres[i] * tres[i];
    }
    debug(ans);
    rep(i,0,m){
        auto [f, t, c]= v[i];
        if(sdij[f] > sdij[t])swap(f, t);
        if(!(sdij[f] + c == sdij[t]))continue;
        if(sdij[f] + c + tdij[t] != dis)continue;

        if(sdij[f] - c < tdij[t] && tdij[t] < sdij[f] + c)
            ans -= sres[f] * sres[f] * tres[t] * tres[t];
        debug(f,t,c,ans);
    }

    cout << ans << "\n";

}

Measured memory_bytes: 34012