///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

template <typename TT, typename T>
void incr_m(map<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(V<ll> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(V<t2> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(V<t3> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(V<t4> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(V<ll> &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

template <typename T>
void _debug_print(T x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

template <typename TT, typename T>
void _debug_print(const map<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
#if DEBUG
    struct tm *tm = localtime(&tv.tv_sec);
#endif
    debug_printf("-- %s %02d:%02d:%02d.%06ld\n",
                  prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}

#define MOD   (1000000007LL)
// #define MOD   (998244353LL)

ll mod_mlt(ll x, ll y, ll mod)
{
    ll ret = 0LL;
    x %= mod;

    while (y) {
        if (y & 1LL) {
            ret += x;
            ret %= mod;
        }
        y >>= 1;
        x <<= 1;
        x %= mod;
    }

    return ret;
}

// O(log(exp))
ll mod_pow(ll base, ll exp, ll mod)
{
    ll ret = 1LL;

    for ( ; exp; ) {
        if (exp & 1LL) {
            ret *= base;
            ret %= mod;
        }
        base = (base * base) % mod;
        exp >>= 1;
    }

    return ret;
}

// O(log(mod))
ll mod_inv(ll x, ll mod)
{
    // available only when mod is prime
    return mod_pow(x, mod - 2LL, mod);
}

ull mod_combination(ll x, ll y, ll mod)
{
    if (y > x / 2LL) y = x - y;

    ll ret = 1;

    for (ll i = 0LL; i < y; ++i) {
        ret = (ret * x--) % mod;
        ret = (ret * mod_inv(i + 1LL, mod)) % mod;
    }

    return ret;
}

void make_perms(ll perms[], ll perm_invs[], ll size, ll mod)
{
    perms[0] = 1LL;
    srep (i, 1, size) {
        perms[i] = perms[i-1] * i;
        perms[i] %= mod;
    }

    perm_invs[size-1] = mod_inv(perms[size-1], mod);
    rrep (i, size-1) {
        perm_invs[i] = perm_invs[i+1LL] * (i+1LL);
        perm_invs[i] %= mod;
    }
}

///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

S ll cnts_s[100005] = {};
S ll costs_s[100005];
S ll cnts_t[100005] = {};
S ll costs_t[100005];

void f(ll cnts[], ll costs[], const V<t2> edges[], ll s)
{
    priority_queue_incr<t3> q;
    S bool looped[100005];
    memset(looped, 0, sizeof(looped));

    cnts[0] = 1;
    q.push(t3(0, 0, s));

    while (q.size()) {
        auto item = q.top(); q.pop();
        ll cost = get<0>(item);
        ll pv = get<1>(item);
        ll v = get<2>(item);

        if (costs[v] >= 0 && costs[v] != cost) continue;
        if (costs[v] < 0) costs[v] = cost;

        cnts[v] += cnts[pv];
        cnts[v] %= MOD;

        if (looped[v]) continue;
        looped[v] = true;

        for (auto nitem : edges[v]) {
            ll nd = get<0>(nitem);
            ll nv = get<1>(nitem);
            if (costs[nv] >= 0 && costs[nv] < cost+nd) continue;
            q.push(t3(cost+nd, v, nv));
        }
    }
}

ll g(ll s, ll t, ll u, ll v, ll d, ll fullcost)
{
    ll leftcost = fullcost / 2LL - !(fullcost & 1LL);
    ll rightcost = fullcost / 2LL + 1LL;
    if (costs_s[u] > leftcost) return 0;
    if (costs_s[v] < rightcost) return 0;
    if (costs_t[v] > leftcost) return 0;
    if (costs_t[u] < rightcost) return 0;
    if (costs_s[u] + d != costs_s[v]) return 0;
    if (costs_t[v] + d != costs_t[u]) return 0;
    if (costs_s[u] + d + costs_t[v] != fullcost) return 0;

    ll ret = 1;
    ret *= cnts_s[u];
    ret %= MOD;
    ret *= cnts_s[u];
    ret %= MOD;
    ret *= cnts_t[v];
    ret %= MOD;
    ret *= cnts_t[v];
    ret %= MOD;

    debug_printf("g : s=%lld t=%lld u=%lld v=%lld d=%lld\n", s, t, u, v, d);
    return ret;
}

void _main()
{
    ll n; llin(n);
    ll m; llin(m);
    ll s; llin(s);
    ll t; llin(t);
    S V<t3> uvdlist; llinl3(uvdlist, m);

    S V<t2> edges[100005];
    for (auto uvd : uvdlist) {
        ll u = get<0>(uvd);
        ll v = get<1>(uvd);
        ll d = get<2>(uvd);
        edges[u].pb(t2(d, v));
        edges[v].pb(t2(d, u));
    }

    rep (i, 100005) costs_s[i] = -1;
    f(cnts_s, costs_s, edges, s);
    debug_printf("---- cnts_s\n");
    debug_print(cnts_s, n+1);
    debug_printf("---- costs_s\n");
    debug_print(costs_s, n+1);

    rep (i, 100005) costs_t[i] = -1;
    f(cnts_t, costs_t, edges, t);
    debug_printf("---- cnts_t\n");
    debug_print(cnts_t, n+1);
    debug_printf("---- costs_t\n");
    debug_print(costs_t, n+1);

    ll ans = cnts_s[t] * cnts_t[s];
    ans %= MOD;
    debug_printf("---- ans 1 = %lld\n", ans);

    ll fullcost = costs_s[t];
    assert(costs_s[t] == costs_t[s]);

    if (!(fullcost & 1LL)) {
        ll halfcost = fullcost / 2LL;
        srep (v, 1, n+1) {
            if (costs_s[v] == halfcost && costs_t[v] == halfcost) {
                ll decr = 1;
                decr *= cnts_s[v];
                decr %= MOD;
                decr *= cnts_s[v];
                decr %= MOD;
                decr *= cnts_t[v];
                decr %= MOD;
                decr *= cnts_t[v];
                decr %= MOD;
                ans -= decr;
                if (ans < 0) ans += MOD;
            }
        }
    }
    debug_printf("---- ans 2 = %lld\n", ans);

    for (auto uvd : uvdlist) {
        ll u = get<0>(uvd);
        ll v = get<1>(uvd);
        ll d = get<2>(uvd);
        ans -= g(s, t, u, v, d, fullcost);
        if (ans < 0) ans += MOD;
        ans -= g(s, t, v, u, d, fullcost);
        if (ans < 0) ans += MOD;
    }

    debug_printf("---- ans\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////


Measured memory_bytes: 28984