import java.io.BufferedReader
import java.io.InputStreamReader
import java.util.*

val DEBUG = false

val P = 1000000007L

//data class FiniteField(val x: Long) {
//  val p = 1000000007L
//  operator fun plus(o: FiniteField) = FiniteField((x + o.x) % p)
//  operator fun minus(o: FiniteField) = FiniteField((x + p - o.x) % p)
//  operator fun times(o: FiniteField) = FiniteField((x * o.x) % p)
//}

data class Edge(val from: Int, val to: Int, val cost: Long)

data class State(val v: Int, val cost: Long)

fun compareState(s1: State, s2: State): Int {
  if (s1.cost > s2.cost) return 1
  if (s1.cost < s2.cost) return -1
  return 0
}

fun main(args: Array<String>) {
  val inputReader = BufferedReader(InputStreamReader(System.`in`))
  val (n, m) = inputReader.readLine()!!.split(" ").map(String::toInt)
  val (sRaw, tRaw) = inputReader.readLine()!!.split(" ").map(String::toInt)
  val s = sRaw - 1
  val t = tRaw - 1
  val graph = Array(n, { mutableListOf<Edge>() })
  repeat(m) {
    val (uRaw, vRaw, dInt) = inputReader.readLine()!!.split(" ").map(String::toInt)
    val u = uRaw - 1
    val v = vRaw - 1
    val d = dInt.toLong()
    graph[u].add(Edge(u, v, d))
    graph[v].add(Edge(v, u, d))
  }

  // Dijkstra from s
  val pq = PriorityQueue<State>(11, { s1: State, s2: State -> compareState(s1, s2) })
  val dist = LongArray(n, { -1L })
  pq.add(State(s, 0L))
  while (pq.isNotEmpty()) {
    val state = pq.poll()!!
    if (dist[state.v] >= 0) continue
    dist[state.v] = state.cost
    for (e in graph[state.v]) {
      if (dist[e.to] < 0) {
        pq.add(State(e.to, state.cost + e.cost))
      }
    }
  }
  if (DEBUG) println("dist: ${dist.toList()}")

  val sGraph = Array(n, { mutableListOf<Int>() })
  val tGraph = Array(n, { mutableListOf<Int>() })

  val stack = Stack<Int>()
  stack.push(t)
  val visited = BooleanArray(n)
  while (stack.isNotEmpty()) {
    val v = stack.pop()!!
    if (visited[v]) continue
    visited[v] = true
    if (DEBUG) println("v: $v")
    for (e in graph[v]) {
      if (dist[v] == dist[e.to] + e.cost) {
        tGraph[v].add(e.to)
        sGraph[e.to].add(v)
        stack.push(e.to)
      }
    }
  }
//  for (v in 0 until n) {
//    for (e in graph[v]) {
//      if (dist[v] + e.cost == dist[e.to]) {
//        tGraph[e.to].add(v)
//        sGraph[v].add(e.to)
//      }
//    }
//  }
  if (DEBUG) println("sGraph: ${sGraph.toList()}")
  if (DEBUG) println("tGraph: ${tGraph.toList()}")

//  val sCount = Array(n, { FiniteField(0) })
//  sCount[s] = FiniteField(1)
//  val sSorted = dist.withIndex().sortedBy { it.value }.map { it.index }
//  fillCount(s, sGraph, sSorted, sCount)
//  if (DEBUG) println("sCount: ${sCount.toList()}")
//
//  val tCount = Array(n, { FiniteField(0) })
//  tCount[t] = FiniteField(1)
//  val tSorted = sSorted.reversed()
//  fillCount(t, tGraph, tSorted, tCount)
//  if (DEBUG) println("tCount: ${tCount.toList()}")
//
//  var ans = sCount[t] * tCount[s]
//  if (DEBUG) println("ans STEP 1: $ans")
//  val totalDist = dist[t]
//  // Meet on vertex
//  for (v in 0 until n) {
//    if (dist[v] * 2 == totalDist) {
//      ans -= sCount[v] * sCount[v] * tCount[v] * tCount[v]
//    }
//  }
//  if (DEBUG) println("ans STEP 2: $ans")
//
//  // Meet on edge
//  for (v in 0 until n) {
//    for (e in graph[v]) {
//      if (dist[v] + e.cost == dist[e.to] && dist[v] * 2 < totalDist && dist[e.to] * 2 > totalDist) {
//        ans -= sCount[v] * sCount[v] * tCount[e.to] * tCount[e.to]
//      }
//    }
//  }
//  if (DEBUG) println("ans STEP 3: $ans")

  val sCount = LongArray(n, { 0L })
  sCount[s] = 1L
  val sSorted = dist.withIndex().sortedBy { it.value }.map { it.index }
  fillCount(s, sGraph, sSorted, sCount)
  if (DEBUG) println("sCount: ${sCount.toList()}")

  val tCount = LongArray(n, { 0L })
  tCount[t] = 1L
  val tSorted = sSorted.reversed()
  fillCount(t, tGraph, tSorted, tCount)
  if (DEBUG) println("tCount: ${tCount.toList()}")

  var ans = sCount[t] * tCount[s]
  if (DEBUG) println("ans STEP 1: $ans")
  val totalDist = dist[t]
  // Meet on vertex
  for (v in 0 until n) {
    if (dist[v] * 2 == totalDist) {
      val f1 = sCount[v] * sCount[v] % P
      val f2 = tCount[v] * tCount[v] % P
      val delta = f1 * f2 % P
      ans = (ans + P - delta) % P
    }
  }
  if (DEBUG) println("ans STEP 2: $ans")

  // Meet on edge
  for (v in 0 until n) {
    for (e in graph[v]) {
      if (dist[v] + e.cost == dist[e.to] && dist[v] * 2 < totalDist && dist[e.to] * 2 > totalDist) {
        val f1 = sCount[v] * sCount[v] % P
        val f2 = tCount[e.to] * tCount[e.to] % P
        val delta = f1 * f2 % P
        ans = (ans + P - delta) % P
      }
    }
  }
  if (DEBUG) println("ans STEP 3: $ans")

  println(ans)
}

fun fillCount(r: Int, graph: Array<MutableList<Int>>, tSorted: List<Int>, count: LongArray) {
  for (v in tSorted) {
    for (u in graph[v]) {
      count[u] = (count[u] + count[v]) % P
    }
  }
}

Measured memory_bytes: 177708