// warm heart, wagging tail,and a smile just for you!
//                                                                     ███████████   
//                                                                   ███╬╬╬╬╬╬╬╬╬╬███
//                                                                ███╬╬╬╬╬████╬╬╬╬╬╬███
//                                            ███████████       ██╬╬╬╬╬████╬╬████╬╬╬╬╬██
//                                      █████████╬╬╬╬╬████████████╬╬╬╬╬██╬╬╬╬╬╬███╬╬╬╬╬██
//                               ████████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬██╬╬╬╬╬╬╬██
//                             ████╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬╬╬╬╬╬██
//                           ███╬╬╬█╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬███╬╬╬╬╬╬╬█████
//                         ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬████████╬╬╬╬╬██
//                       ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬╬╬╬╬███
//                     ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬██
//                 ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬████
//     █████████████╬╬╬╬╬╬╬╬██╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬██████
//   ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬██████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████╬╬╬╬╬╬╬███████████╬╬╬╬╬╬╬╬██╬╬╬██╬╬╬██
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬█╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬██
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬▓▓▓▓▓▓╬╬╬████╬╬████╬╬╬╬╬╬╬▓▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬███
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████▓▓▓▓▓▓▓╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬█████
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████████
//   ███╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██
//       ██████████████  ████╬╬╬╬╬╬███████████████████████████╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████
//                         ███████                           █████  ███████████████████  
#include "bits/stdc++.h"
using namespace std;
#define MOD 1000000007
const double EPS = 1e-9;
#define INF (1LL<<60)
#define fs first
#define sc second
#define pb push_back
#define int long long
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i = (b-1);i>=a;i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ITR(itr,mp) for(auto itr = (mp).begin(); itr != (mp).end(); ++itr)
#define RITR(itr,mp) for(auto itr = (mp).rbegin(); itr != (mp).rend(); ++itr)
#define range(i,a,b) ((a)<=(i) && (i)<(b))
#define debug(x)  cout << #x << " = " << (x) << endl;
#define SP << " " << 
typedef pair<int,int> P;
typedef vector<vector<P> > Graph;
typedef vector<int> vec;
typedef vector<vector<int>> mat;

vector<int> dijkstra(int s, Graph &G){
  priority_queue<P,vector<P>,greater<P>> que;
  int n = G.size();
  vector<int> dist(n);
  dist.assign(n,INF);
  dist[s] = 0;
  que.push(P(0,s));

  while(!que.empty()){
    P p = que.top();
    que.pop();
    int v = p.sc;
    REP(i,G[v].size()){
      if(dist[G[v][i].fs] > dist[v]+G[v][i].sc){
        dist[G[v][i].fs] = dist[v]+G[v][i].sc;
        que.push(P(dist[G[v][i].fs],G[v][i].fs));
      }
    }
  }
  return dist;
}

void add(int &a, int b){
  a = ((a+b) % MOD + MOD) % MOD;
}

inline int mul(int a, int b) {
    #if !defined(_WIN32) || defined(_WIN64)
      return (int) ((long long) a * b % MOD);
    #endif
      unsigned long long x = (long long) a * b;
      unsigned xh = (unsigned) (x >> 32), xl = (unsigned) x, d, m;
      asm(
        "divl %4; \n\t"
        : "=a" (d), "=d" (m)
        : "d" (xh), "a" (xl), "r" (MOD)
      );
      return m;
}

inline int modpow(int a, long long b) {
  int res = 1;
  while (b > 0) {
    if (b & 1) {
      res = mul(res, a);
      }
      a = mul(a, a);
      b >>= 1;
  }
  return res;
}

inline int inv(int a) {
    a %= MOD;
    if (a < 0) a += MOD;
    int b = MOD, u = 0, v = 1;
    while (a) {
      int t = b / a;
      b -= t * a; swap(a, b);
      u -= t * v; swap(u, v);
    }
    assert(b == 1);
    if (u < 0) u += MOD;
    return u;
}

signed main(){
  ios::sync_with_stdio(false);
  cin.tie(0);  
  //問題文を読む時間をケチらない！！
  //未定義動作に気を付ける！！
  //DPや二分探索の範囲に気をつける！！

  int n,m,s,t;
  cin >> n >> m >> s >> t;
  s--; t--;

  Graph edge(n);
  REP(_,m){
    int node_x,node_y,cost = 1;
    cin >> node_x >> node_y;
    cin >> cost;  // 重みなしなら削除
    node_x--; node_y--;
    edge[node_x].pb(P(node_y,cost));
    edge[node_y].pb(P(node_x,cost));
  }
  
  vec dist1 = dijkstra(s,edge), dist2 = dijkstra(t,edge);
  vector<P> tmp1(n),tmp2(n);
  REP(i,n) tmp1[i] = P(dist1[i],i), tmp2[i] = P(dist2[i],i);
  sort(tmp1.begin(),tmp1.end());
  sort(tmp2.begin(),tmp2.end());
  vec dp_s(n,0), dp_t(n,0);
  dp_s[s] = dp_t[t] = 1;
  
  int d = dist1[t]; //最短経路の距離
  REP(i,n){
    int no = tmp1[i].sc, cost = tmp1[i].fs;
    for(P to:edge[no]) if(dist1[to.fs] == cost+to.sc && dist1[to.fs]+dist2[to.fs]==d) add(dp_s[to.fs],dp_s[no]);
  }

  REP(i,n){
    int no = tmp2[i].sc, cost = tmp2[i].fs;
    for(P to:edge[no]) if(dist2[to.fs] == cost+to.sc && dist1[to.fs]+dist2[to.fs]==d) add(dp_t[to.fs],dp_t[no]);
  }

  int ans = mul(dp_s[t],dp_s[t]);
  REP(i,n) if(dist1[i]*2 == d) add(ans,-modpow(mul(dp_s[i],dp_t[i]),2));
  REP(i,n){
    for(P e:edge[i]){
      int a = i, b = e.fs, co = e.sc;
      if(dist1[a]*2 < d && dist1[b]*2 > d && dist1[a]+co == dist1[b]){
      //  cout << "*" SP a SP  b << endl;
        add(ans,-modpow(mul(dp_s[a],dp_t[b]),2));
      }
    }
  }

  //REP(i,n) cout << dp_s[i]  SP dp_t[i] << endl;
  //REP(i,n) cout << dist1[i] << endl;

  cout << ans << endl;

  return 0;
}

Measured memory_bytes: 19424