#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using PII = pair<ll, ll>;
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
template<typename T> void chmin(T &a, const T &b) { a = min(a, b); }
template<typename T> void chmax(T &a, const T &b) { a = max(a, b); }
struct FastIO {FastIO() { cin.tie(0); ios::sync_with_stdio(0); }}fastiofastio;
#ifdef DEBUG_ 
#include "../program_contest_library/memo/dump.hpp"
#else
#define dump(...)
#endif
const ll INF = 1LL<<60;

template<ll MOD>
struct modint {
    ll x;
    modint(): x(0) {}
    modint(ll y) : x(y>=0 ? y%MOD : y%MOD+MOD) {}
    static constexpr ll mod() { return MOD; }
    // e乗
    modint pow(ll e) {
        ll a = 1, p = x;
        while(e > 0) {
            if(e%2 == 0) {p = (p*p) % MOD; e /= 2;}
            else {a = (a*p) % MOD; e--;}
        }
        return modint(a);
    }
    modint inv() const {
        ll a=x, b=MOD, u=1, y=1, v=0, z=0;
        while(a) {
            ll q = b/a;
            swap(z -= q*u, u);
            swap(y -= q*v, v);
            swap(b -= q*a, a);
        }
        return z;
    }
    // Comparators
    bool operator <(modint b) { return x < b.x; }
    bool operator >(modint b) { return x > b.x; }
    bool operator<=(modint b) { return x <= b.x; }
    bool operator>=(modint b) { return x >= b.x; }
    bool operator!=(modint b) { return x != b.x; }
    bool operator==(modint b) { return x == b.x; }
    // Basic Operations
    modint operator+(modint r) const { return modint(*this) += r; }
    modint operator-(modint r) const { return modint(*this) -= r; }
    modint operator*(modint r) const { return modint(*this) *= r; }
    modint operator/(modint r) const { return modint(*this) /= r; }
    modint &operator+=(modint r) {
        if((x += r.x) >= MOD) x -= MOD;
        return *this;
    }
    modint &operator-=(modint r) {
        if((x -= r.x) < 0) x += MOD;
        return *this;
    }
    modint &operator*=(modint r) {
    #if !defined(_WIN32) || defined(_WIN64)
        x = x * r.x % MOD; return *this;
    #endif
        unsigned long long y = x * r.x;
        unsigned xh = (unsigned) (y >> 32), xl = (unsigned) y, d, m;
        asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (MOD)
        );
        x = m;
        return *this;
    }
    modint &operator/=(modint r) { return *this *= r.inv(); }
    // increment, decrement
    modint operator++() { x++; return *this; }
    modint operator++(signed) { modint t = *this; x++; return t; }
    modint operator--() { x--; return *this; }
    modint operator--(signed) { modint t = *this; x--; return t; }
    // 平方剰余のうち一つを返す なければ-1
    friend modint sqrt(modint a) {
        if(a == 0) return 0;
        ll q = MOD-1, s = 0;
        while((q&1)==0) q>>=1, s++;
        modint z=2;
        while(1) {
            if(z.pow((MOD-1)/2) == MOD-1) break;
            z++;
        }
        modint c = z.pow(q), r = a.pow((q+1)/2), t = a.pow(q);
        ll m = s;
        while(t.x>1) {
            modint tp=t;
            ll k=-1;
            FOR(i, 1, m) {
                tp *= tp;
                if(tp == 1) { k=i; break; }
            }
            if(k==-1) return -1;
            modint cp=c;
            REP(i, m-k-1) cp *= cp;
            c = cp*cp, t = c*t, r = cp*r, m = k;
        }
        return r.x;
    }

    template<class T>
    friend modint operator*(T l, modint r) { return modint(l) *= r; }
    template<class T>
    friend modint operator+(T l, modint r) { return modint(l) += r; }
    template<class T>
    friend modint operator-(T l, modint r) { return modint(l) -= r; }
    template<class T>
    friend modint operator/(T l, modint r) { return modint(l) /= r; }
    template<class T>
    friend bool operator==(T l, modint r) { return modint(l) == r; }
    template<class T>
    friend bool operator!=(T l, modint r) { return modint(l) != r; }
    // Input/Output
    friend ostream &operator<<(ostream& os, modint a) { return os << a.x; }
    friend istream &operator>>(istream& is, modint &a) { 
        is >> a.x;
        a.x = ((a.x%MOD)+MOD)%MOD;
        return is;
    }
    friend string to_frac(modint v) {
        static map<ll, PII> mp;
        if(mp.empty()) {
            mp[0] = mp[MOD] = {0, 1};
            FOR(i, 2, 1001) FOR(j, 1, i) if(__gcd(i, j) == 1) {
                mp[(modint(i) / j).x] = {i, j};
            }
        }
        auto itr = mp.lower_bound(v.x);
        if(itr != mp.begin() && v.x - prev(itr)->first < itr->first - v.x) --itr;
        string ret = to_string(itr->second.first + itr->second.second * ((int)v.x - itr->first));
        if(itr->second.second > 1) {
            ret += '/';
            ret += to_string(itr->second.second);
        }
        return ret;
    }
};
using mint = modint<1000000007>;

int main(void) {
    ll n, m, s, t;
    cin >> n >> m >> s >> t;
    s--, t--;
    vector<vector<PII>> g(n);
    vector<ll> a(m), b(m), c(m);
    REP(i, m) {
        cin >> a[i] >> b[i] >> c[i];
        a[i]--, b[i]--;
        g[a[i]].emplace_back(b[i], c[i]);
        g[b[i]].emplace_back(a[i], c[i]);
    }

    // sからt
    vector<ll> dist1(n, INF);
    vector<mint> cnt1(n);
    cnt1[s] = 1;
    dist1[s] = 0;
    priority_queue<PII, vector<PII>, greater<PII>> que;
    que.push({0, s});
    while(que.size()) {
        PII p = que.top(); que.pop();
        if(dist1[p.second] < p.first) continue;
        for(auto to: g[p.second]) {
            if(dist1[to.first] > dist1[p.second] + to.second) {
                dist1[to.first] = dist1[p.second] + to.second;
                cnt1[to.first] = cnt1[p.second];
                que.push({dist1[to.first], to.first});
            } else if(dist1[to.first] == dist1[p.second] + to.second) {
                cnt1[to.first] += cnt1[p.second];
            }
        }
    }

    // tからs
    vector<ll> dist2(n, INF);
    vector<mint> cnt2(n);
    cnt2[t] = 1;
    dist2[t] = 0;
    que.push({0, t});
    while(que.size()) {
        PII p = que.top(); que.pop();
        if(dist2[p.second] < p.first) continue;
        for(auto to: g[p.second]) {
            if(dist2[to.first] > dist2[p.second] + to.second) {
                dist2[to.first] = dist2[p.second] + to.second;
                cnt2[to.first] = cnt2[p.second];
                que.push({dist2[to.first], to.first});
            } else if(dist2[to.first] == dist2[p.second] + to.second) {
                cnt2[to.first] += cnt2[p.second];
            }
        }
    }

    dump(dist1);
    dump(cnt1);
    dump(dist2);
    dump(cnt2);

    const ll D = dist1[t];
    mint ret = cnt1[t] * cnt2[s];
    REP(i, n) if(dist1[i] == dist2[i]) ret -= cnt1[i]*cnt1[i]*cnt2[i]*cnt2[i];
    REP(i, m) {
        ll u = a[i], v = b[i];
        if(dist1[u]*2 < D && dist1[v]*2 > D && dist1[u]+c[i] == dist1[v] && dist1[u]+dist2[v]+c[i]==D) {
            dump(u, v, cnt1[u], cnt2[v]);
            ret -= cnt1[u]*cnt1[u]*cnt2[v]*cnt2[v];
        }
        swap(u, v);
        if(dist1[u]*2 < D && dist1[v]*2 > D && dist1[u]+c[i] == dist1[v] && dist1[u]+dist2[v]+c[i]==D) {
            dump(u, v, cnt1[u], cnt2[v]);
            ret -= cnt1[u]*cnt1[u]*cnt2[v]*cnt2[v];
        }
    }
    cout << ret << endl;

    return 0;
}

Measured memory_bytes: 21752