#include <bits/stdc++.h>

using namespace std;

// tourist's modular-arithmetic class
template<typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template<typename T>
class Modular {
public:
    using Type = typename decay<decltype(T::value)>::type;

    constexpr Modular() : value() {}

    template<typename U>
    Modular(const U &x) {
      value = normalize(x);
    }

    template<typename U>
    static Type normalize(const U &x) {
      Type v;
      if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
      else v = static_cast<Type>(x % mod());
      if (v < 0) v += mod();
      return v;
    }

    const Type &operator()() const { return value; }

    template<typename U>
    explicit operator U() const { return static_cast<U>(value); }

    constexpr static Type mod() { return T::value; }

    Modular &operator+=(const Modular &other) {
      if ((value += other.value) >= mod()) value -= mod();
      return *this;
    }

    Modular &operator-=(const Modular &other) {
      if ((value -= other.value) < 0) value += mod();
      return *this;
    }

    template<typename U>
    Modular &operator+=(const U &other) { return *this += Modular(other); }

    template<typename U>
    Modular &operator-=(const U &other) { return *this -= Modular(other); }

    Modular &operator++() { return *this += 1; }

    Modular &operator--() { return *this -= 1; }

    Modular operator++(int) {
      Modular result(*this);
      *this += 1;
      return result;
    }

    Modular operator--(int) {
      Modular result(*this);
      *this -= 1;
      return result;
    }

    Modular operator-() const { return Modular(-value); }

    template<typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type &operator*=(const Modular &rhs) {
#ifdef _WIN32
      uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
      uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
      asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
      );
      value = m;
#else
      value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
      return *this;
    }

    template<typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
    operator*=(const Modular &rhs) {
      int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
      value = normalize(value * rhs.value - q * mod());
      return *this;
    }

    template<typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type &operator*=(const Modular &rhs) {
      value = normalize(value * rhs.value);
      return *this;
    }

    Modular &operator/=(const Modular &other) { return *this *= Modular(inverse(other.value, mod())); }

    template<typename U>
    friend const Modular<U> &abs(const Modular<U> &v) { return v; }

    template<typename U>
    friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

    template<typename U>
    friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

    template<typename U>
    friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
    Type value;
};


template<typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }

template<typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }

template<typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }

template<typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }

template<typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

template<typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }

template<typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }

template<typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

template<typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

template<typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

template<typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template<typename T>
bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template<typename T>
string to_string(const Modular<T> &number) {
  return to_string(number());
}

template<typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template<typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

struct fast_ios {
    fast_ios() {
      cin.tie(nullptr);
      ios::sync_with_stdio(false);
      cout << fixed << setprecision(10);
    };
} fast_ios_;

#define LSON(x) ((x) * 2)
#define RSON(x) ((x) * 2 + 1)

template<typename A, typename B>
bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template<typename A, typename B>
bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

int cas;

ostream &kase() {
  return cout << "Case #" << ++cas << ": ";
}

#if __cplusplus < 201402L
template<class Iterator>
std::reverse_iterator<Iterator> make_reverse_iterator(Iterator it) {
    return std::reverse_iterator<Iterator>(it);
}
#endif

template<typename iter_t>
struct iter_pair {
    iter_t _beg, _end;

    iter_t begin() { return _beg; }

    iter_t end() { return _end; }
};

template<class cont>
iter_pair<reverse_iterator<decltype(begin(declval<cont>()))>>
reverse(cont &&r) {
  return {make_reverse_iterator(end(r)), make_reverse_iterator(begin(r))};
}

template<typename T>
void dprintln(const T &t) { cout << t << endl; } // for debug use
template<typename T, typename ...Args>
void dprintln(const T &t, const Args &...rest) {
  cout << t << ' ';
  dprintln(rest...);
}

template<typename T>
void println(const T &t) { cout << t << '\n'; }


template<typename T, typename ...Args>
void println(const T &t, const Args &...rest) {
  cout << t << ' ';
  println(rest...);
}

template<typename T>
void println(const vector<T> &vec) {
  if (!vec.empty()) {
    cout << vec[0];
    for (size_t i = 1; i < vec.size(); ++i)
      cout << ' ' << vec[i];
  }
  cout << '\n';
}

template<typename T>
void print(const T &t) { cout << t << ' '; }

template<typename T, typename ...Args>
void print(const T &t, const Args &...rest) {
  cout << t << ' ';
  print(rest...);
}

// this overload is chosen when there's only one argument
template<class T>
void scan(T &t) { cin >> t; }

template<class T, class ...Args>
void scan(T &a, Args &...rest) {
  cin >> a;
  scan(rest...);
}

template<typename T>
istream &operator>>(istream &stream, vector<T> &vec) {
  for (auto &x : vec) stream >> x;
  return stream;
}

using ull = unsigned long long;
using ll = long long;
using ul = unsigned long;
using vl = vector<ll>;
using vi = vector<int>;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pip = pair<int, pii>;
using pll = pair<ll, ll>;
using vb = vector<bool>;
using vpii = vector<pii>;
using ldb = long double;

template<typename int_t>
inline int_t lowbit(int_t x) { return x & -x; }

#define rng(i, a, b) for(int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define rep(n) for(int _iter_##n = 0, _num_##n = (int)n; _iter_##n < _num_##n; ++_iter_##n)
#define stp(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(x, cont) for (const auto &x: cont)
#define For(x, cont) for (auto &x: cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UP(i, l, r) for(i = decltype(i)(l); i <= decltype(i)(r); ++i)
#define DOWN(i, r, l) for (i = decltype(i)(r); i >= decltype(i)(l); --i)
template<typename T, typename Comp = less<T>>
using pq = priority_queue<T, vector<T>, Comp>;
#define popcnt(x) __builtin_popcountll((x))
#define SET(arr, v) memset(arr, (v), sizeof (arr))
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define UB(cont, x) int(upper_bound(all(cont), x) - begin(cont))
#define AI(name, n, m) vv<int> name(n, vi(m));
#define AL(name, n, m) vv<ll> name(size_t(n), vl(size_t(m)));
#define AT(T, n, m, a)  vector<vector<T>> a(n, vector<T>(m))
const int dx[] = {0, 0, -1, 1}, dy[] = {-1, 1, 0, 0};
const int dx8[] = {-1, -1, -1, 0, 0, 1, 1, 1}, dy8[] = {-1, 0, 1, -1, 1, -1, 0, 1};
auto bet = [](const ll x, const ll y, const ll i) {
  return x <= i && i <= y;
};

template<typename T1, typename T2>
T1 ceil(T1 x, T2 y) { // y >= 1，是整数。需要注意 x + y - 1 是否会溢出
  return (x + y - 1) / y;
}

inline int h_bit(unsigned long long x) {
  return (int) sizeof(unsigned long long) * 8 - 1 - __builtin_clzll(x);
}

int pow2(int x) { // power of 2
  return int(1U << h_bit((ull) x)) + (x != lowbit(x));
}

template<typename T>
struct BIT {
    vector<T> a;
    function<T(T, T)> bin_op;
    const T init;

    explicit BIT(int n, function<T(T, T)> bin_op, T init = T()) : bin_op(bin_op), init(init) {
      a.assign(n + 1, init);
    }

    T prefix(int x) {
      auto res = init;
      while (x) {
        res = bin_op(a[x], res);
        x -= x & -x;
      }
      return res;
    }

    void modify(int x, T v) {
      while (x < (int) a.size()) {
        a[x] = bin_op(a[x], v);
        x += x & -x;
      }
    }

    void clear() {
      fill(a.begin(), a.end(), init);
    }
};

vi get_prime(int n) {
  vi minp((ul) n + 1), p;
  for (int i = 2; i <= n; i++) {
    if (!minp[i]) {
      minp[i] = i;
      p.pb(i);
    }
    FOR(x, p) {
      if (x <= minp[i] && x * i <= n)
        minp[x * i] = x;
      else break;
    }
  }
  return p;
}

// alias templates
template<typename T> using vv = vector<vector<T>>;
template<typename T1, typename T2 = T1> using vp = vector<pair<T1, T2>>;
template<typename T, int n> using va = vector<array<T, n>>;

//order_of_key (k) : Number of items strictly smaller than k .
//find_by_order(k) : K-th element in a set (counting from zero).
#ifdef __GNUC__

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

template<typename T, typename comp = less<T>>
using rank_tree = __gnu_pbds::tree<
        T,
        __gnu_pbds::null_type,
        comp,
        __gnu_pbds::rb_tree_tag,
        __gnu_pbds::tree_order_statistics_node_update>;
#endif

//并查集
struct UnionFind {
    vi par, sz;
    int n_tree;

    explicit UnionFind(int n) : par(n), sz(n, 1), n_tree(n) { //0-indexed
      rng (i, 0, n) par[i] = i;
    }

    int n_cluster() const {
      return n_tree;
    }

    int size(int x) {
      return sz[root(x)];
    }

    int root(int x) {
      return x == par[x] ? x : par[x] = root(par[x]);
    }

    bool unite(int x, int y) {
      int rx = root(x), ry = root(y);
      if (rx != ry) {
        par[rx] = ry;
        --n_tree;
        sz[ry] += sz[rx];
        return true;
      }
      return false;
    }
    bool is_root(int x) const {
      return par[x] == x;
    }
};

template<typename T, typename Compare = std::less<T>>
struct SparseTable {
    size_t n{}; // 0-indexed
    vv<T> a;

    template<typename ptr_t>
    SparseTable(ptr_t beg, ptr_t end):n(end - beg) {
      a.resize((size_t) h_bit(n) + 1); // 注意：不能写成 h_bit(n)
      a[0].assign(beg, end);
      rng (i, 0, SZ(a) - 1) {
        a[i + 1].resize(n);
        rng(j, 0, n - (1u << i)) {
          a[i + 1][j] = min(a[i][j], a[i][j + (1u << i)], Compare());
        }
        rng(j, n - (1u << i), n) {
          a[i + 1][j] = a[i][j];
        }
      }
    }

    using idx_t = long;

    T query(idx_t l, idx_t r) { // l <=  r
      int i = h_bit(r - l + 1ul);
      return min(a[i][l], a[i][r + 1 - (1u << i)], Compare());
    }
};


vi get_popcnt(int n) {
  vi res((ul) n + 1);
  rng (i, 0, n) {
    if (i * 2 <= n) res[i * 2] = res[i];
    if ((i & 1) == 0) res[i + 1] = res[i] + 1;
  }
  return res;
}

vi get_mu(int n) {
  assert(n > 0);
  vi mu(n + 1);
  vi min_p(n + 1);
  vi prime;
  mu[1] = 1;
  rng (i, 2, n + 1) {
    if (!min_p[i]) {
      prime.pb(i);
      min_p[i] = i;
      mu[i] = -1;
    }
    FOR (p, prime) {
      if (p > min_p[i]) {
        break;
      }
      int t = p * i;
      if (t > n) break;
      min_p[t] = p;
      mu[t] = p == min_p[i] ? 0 : -mu[i];
    }
  }
  return mu;
}

// debug code by tourist
string to_string(const string &s) {
  return '"' + s + '"';
}

string to_string(const char *s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

template<typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

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;
}

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
// end DEBUG

template<typename T>
struct Binom {
    vector<T> fact, inv_fact;

    explicit Binom(int n) : fact(n + 1), inv_fact(n + 1) {
      fact[0] = 1;
      up (i, 1, n) fact[i] = fact[i - 1] * i;
      inv_fact[n] = 1 / fact[n];
      down (i, n, 1) {
        inv_fact[i - 1] = inv_fact[i] * i;
      }
    }

    T get_binom(int x, int y) const {
      assert(x <= SZ(fact) - 1);
      assert(x >= 0 && y >= 0);
      if (x < y) return 0;
      return fact[x] * inv_fact[y] * inv_fact[x - y];
    }

    T get_fact(int n) const {
      assert(n < SZ(fact));
      return fact[n];
    }
};

//https://codeforces.com/blog/entry/22072
struct HLD {
    HLD(int n, const int *heavy_son, const int *fa, const int *depth) : top(n + 1), pos(n + 1), depth(depth), fa(fa) {
      int index = 0;
      // 节点编号从1开始
      for (int i = 1; i <= n; i++) {
        if (i != heavy_son[fa[i]]) {
          for (int j = i; j != 0; j = heavy_son[j]) {
            top[j] = i;
            pos[j] = ++index; // pos从1开始
          }
        }
      }
    }

    template<typename BinOpr>
    //返回值是 LCA(u,v)
    int process_path(int u, int v, BinOpr op, bool value_on_edge = false) const {
      while (top[u] != top[v]) {
        if (depth[top[u]] < depth[top[v]]) swap(u, v);
        op(pos[top[u]], pos[u]);
        u = fa[top[u]];
      }
      if (depth[u] > depth[v]) swap(u, v);
      op(pos[u] + value_on_edge, pos[v]);
      return u;
    }

    vector<int> top, pos;
    const int *depth, *fa;
};

template<typename T>
T get_mid(T l, T r) {
  assert(l <= r);
  return l + (r - l) / 2;
}

template<typename T>
int get_bit(T a, int i) {
  return a >> i & 1;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
 */
constexpr int md = 1000000007;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
//////////////////^"^///////////////////////////////////


int main() {
#if defined LOCAL && !defined DUIPAI
  ifstream in("main.in");
  cin.rdbuf(in.rdbuf());
//    ofstream out("main.out");
//    cout.rdbuf(out.rdbuf());
#endif
  int n, m, s, t;
  scan(n, m, s, t);
  --s, --t;
  vv<pii> g(n);
  rep (m) {
    int u, v, d;
    scan(u, v, d);
    --u, --v;
    g[u].eb(v, d);
    g[v].eb(u, d);
  }

  auto dijkstra = [&g](int s, vl& d) {
    pq<pli, greater<>> que;
    d[s] = 0;
    que.ep(0, s);
    while (!que.empty()) {
      auto p = que.top();
      que.pop();
      int u = p.second;
      if (d[u] != p.first) continue;
      FOR (e, g[u]) {
        if (chkmin(d[e.first], d[u] + e.second)) {
          que.ep(d[e.first], e.first);
        }
      }
    }
  };

  vl d_s(n, LLONG_MAX), d_t(n, LLONG_MAX);
  dijkstra(s, d_s);
  dijkstra(t, d_t);

  vi v(n);
  rng (i, 0, n) {
    v[i] = i;
  }
  sort(all(v), [&](int x, int y){return d_s[x] < d_s[y];});

  vector<Mint> dp_s(n), dp_t(n);
  dp_s[s] = 1;
  FOR (x, v) {
    if (d_s[x] != LLONG_MAX) {
      FOR (e, g[x]) {
        if (d_s[e.first] == d_s[x] + e.second) {
          dp_s[e.first] += dp_s[x];
        }
      }
    }
  }

  dp_t[t] = 1;
  FOR (x, reverse(v)) {
    if (dp_s[x] != LLONG_MAX) {
      FOR (e, g[x]) {
        if (d_s[e.first] == d_s[x] + e.second) {
          dp_t[x] += dp_t[e.first];
        }
      }
    }
  }

  Mint ans = 0;
  ll D = d_s[t];
  if (D % 2 == 0) {
    rng (i, 0, n) {
      if (d_s[i] == D / 2) {
        ans += dp_s[i] * dp_s[i] * dp_t[i] * dp_t[i];
      }
    }
  }

  rng (x, 0, n) {
    FOR (e, g[x]) {
      int y = e.first;
      if (d_s[x] < (D + 1) / 2 && d_t[y] < (D + 1) / 2 && d_s[x] + d_t[y] + e.second == D) {
        ans += dp_s[x] * dp_s[x] * dp_t[y] * dp_t[y];
      }
    }
  }
  println(dp_s[t] * dp_s[t] - ans);



#if defined LOCAL && !defined DUIPAI
  cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " s.\n";
#endif
  return 0;
}



Measured memory_bytes: 13524