#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define lfs <<fixed<<setprecision(10)<<
#define test cout<<"test"<<endl;
#define fi first
#define se second
#define MP make_pair
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = n; i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = n - 1; i >= (ll)(m); i--)
using ll = long long;
using ld = long double;
const ll MOD = 1e9+7;
//const ll MOD = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T>
void chmin(T &a,T b){if(a>b)a=b;}
template<typename T>
void chmax(T &a,T b){if(a<b)a=b;}
void pmod(ll &a,ll b){a=(a+b)%MOD;}
void pmod(ll &a,ll b,ll c){a=(b+c)%MOD;}
void qmod(ll &a,ll b){a=(a*b)%MOD;}
void qmod(ll &a,ll b,ll c){a=(b*c)%MOD;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>
void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>
void debug(vector<vector<T>>v,ll h,ll w){for(ll i=0;i<h;i++)
{cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>v,ll h,ll w){for(ll i=0;i<h;i++)
{for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>
void debug(vector<T>v,ll n){if(n!=0)cout<<v[0];
for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>
vector<vector<T>>vec(ll x, ll y, T w){
  vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
template<typename T>
vector<ll>dx={1,0,-1,0,1,1,-1,-1};
vector<ll>dy={0,1,0,-1,1,-1,1,-1};
template<typename T>
vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>
auto make_v(size_t a,Ts... ts){
  return vector<decltype(make_v(ts...))>(a,make_v(ts...));
}
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 >;


ll MAX_V = 2e5 + 5;
struct edge {
  ll to,cost;
  edge(ll x,ll y):to(x),cost(y){};
};

//<最短距離, 頂点の番号>using P = pair<ll, ll>;
vector<vector<struct edge>> G(MAX_V); //隣接リスト
vector<ll> d(MAX_V); //各頂点への最短距離
vector<modint>cnt(MAX_V);
void dijkstra(ll s) {
    priority_queue<P, vector<P>, greater<P> > que;
    fill(ALL(d), INF);
    fill(ALL(cnt),0);
    d[s] = 0;
    cnt[s]=1;
    que.push(P(0, s));
    while (!que.empty()) {
        P p = que.top();
        que.pop();
        ll v = p.second;
        if (d[v] < p.first) continue;

        for (ll i=0; i<G[v].size(); i++) {
            struct edge e = G[v][i];
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to], e.to));
                cnt[e.to]=cnt[v];
            }
            else if(d[e.to] == d[v] + e.cost){
              cnt[e.to]+=cnt[v];
            }
        }
    }
}

int main(){
  cin.tie(NULL);
  ios_base::sync_with_stdio(false);
  ll res=0,res1=INF,res2=-INF,buf=0;
  bool judge = true;
  ll n,m,s,t;cin>>n>>m>>s>>t;
  s--;t--;
  for(ll i=0;i<m;i++){
    ll u,v,c;
    cin>>u>>v>>c;
    u--;v--;
    struct edge e ={v,c};
    G[u].push_back(e);
    e ={u,c};
    G[v].push_back(e);
  }
  dijkstra(s);
  auto cnt1=cnt;
  auto d1=d;
  dijkstra(t);
  auto cnt2=cnt;
  auto d2=d;
  ll limit=d1[t];
  modint ret=cnt1[t]*cnt2[s];
  rep(i,0,n){
    if(d1[i]+d2[i]==limit){
      if(d1[i]==d2[i]){
        ret-=(cnt1[i]*cnt2[i])*(cnt1[i]*cnt2[i]);
      }
      else if(d1[i]<d2[i]){
        
        for(ll j=0;j<G[i].size();j++){
          ll y=G[i][j].to;
          if(d1[y]+d2[y]==limit&&d1[y]>d2[y]&&G[i][j].cost==d1[y]-d1[i]){
            ret-=(cnt1[i]*cnt2[y])*(cnt1[i]*cnt2[y]);
          }
        }
      }
    }
  }
  //debug(d1,n);
  //debug(cnt1,n);
  //debug(d2,n);
  //debug(cnt2,n);
  cout<<ret<<endl;
  return 0;
}

Measured memory_bytes: 22740