Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
print
D=cost_S[T-1]
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
print
D=cost_S[T-1]
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
print
D=cost_S[T-1]
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

def dp(t,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[t]=1
  cost[t]=0
  heap=[(0,t)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if hc>d/2:
      break
    if Visited[hp]:
      continue
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append((P_S[a]*P_T[b])%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append((P_S[a]*P_T[b])%mod)
Sum=0
for i in List:
  Sum=(Sum+i)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

def dp(t,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[t]=1
  cost[t]=0
  heap=[(0,t)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if hc>d/2:
      break
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append((P_S[a]*P_T[b])%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append((P_S[a]*P_T[b])%mod)
Sum=0
for i in List:
  Sum=(Sum+i)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

def dp(t,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[t]=1
  cost[t]=0
  heap=[(0,t)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if hc>d/2:
      break
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append((P_S[a]*P_T[b])%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append((P_S[a]*P_T[b])%mod)
Sum=0
for i in List:
  Sum=(Sum+i)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
    Visited[hp]=True
  return cost,P
  
cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
D=cost_S[T-1]
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append((P_S[a]*P_T[b])%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append((P_S[a]*P_T[b])%mod)
Sum=0
for i in List:
  Sum=(Sum+i)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  Visited[0]=True
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
      if c+hc>cost[p]:
        Visited[p]=True
  return cost,P
  
cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
D=cost_S[T-1]
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append((P_S[a]*P_T[b])%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append((P_S[a]*P_T[b])%mod)
Sum=0
for i in List:
  Sum=(Sum+i)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  Visited[0]=True
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]+=P[hp]
      if c+hc>cost[p]:
        Visited[p]=True
  return cost,P
  
cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
D=cost_S[T-1]
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append(P_S[a]*P_T[b]%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append(P_S[a]*P_T[b]%mod)
Sum=sum(List)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
from heapq import heapify,heappop,heappush
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(N):
  Edge.append((i,i,0))
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    for c,p in links[hp]:
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]+=P[hp]
  return cost,P
  
cost_S,P_S=dijkstra(S-1,N,Graph)
cost_T,P_T=dijkstra(T-1,N,Graph)
D=cost_S[T-1]
List=[]
for a,b,c in Edge:
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]<D/2 and cost_T[b]<D/2 and c>0:
    List.append(P_S[a]*P_T[b]%mod)
  if cost_S[a]+c+cost_T[b]==D and cost_S[a]==D/2 and cost_T[b]==D/2 and c==0:
    List.append(P_S[a]*P_T[b]%mod)
Sum=sum(List)%mod
ans=0
for i,c in enumerate(List):
  ans=(ans+(Sum-List[i])*List[i])%mod
print(ans)



      
  
  
  
  


Fixed submission:
from heapq import heapify,heappop,heappush
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
S,T=map(int,input().split())
Graph=[set() for i in range(N)]
Edge=[]
mod=10**9+7
inf=float("inf")
for i in range(M):
  a,b,c=map(int,input().split())
  Graph[a-1].add((c,b-1))
  Graph[b-1].add((c,a-1))
  Edge.append((a-1,b-1,c))
  Edge.append((b-1,a-1,c))
def dijkstra(s,n,links):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

def dp(s,n,links,d):
  Visited=[False]*n
  cost=[inf]*n
  P=[0]*n
  P[s]=1
  cost[s]=0
  heap=[(0,s)]
  heapify(heap)
  while heap:
    hc,hp=heappop(heap)
    if 2*hc>d:
      break
    if Visited[hp]:
      continue
    Visited[hp]=True
    for c,p in links[hp]:
      if Visited[p]:
        continue
      if c+hc<cost[p]:
        cost[p]=c+hc
        P[p]=P[hp]
        heappush(heap,(cost[p],p))
      elif c+hc==cost[p]:
        P[p]=(P[p]+P[hp])%mod
  return cost,P

cost_S,P_S=dijkstra(S-1,N,Graph)
D=cost_S[T-1]
cost_T,P_T=dp(T-1,N,Graph,D)
Pat=P_S[T-1]
ans=(Pat**2)%mod
for a,b,c in Edge:
  if cost_S[a]+cost_T[b]+c==D:
    if 2*cost_S[a]<D and 2*cost_T[b]<D:
      ans-=((P_S[a]*P_T[b])**2)%mod
for i in range(N):
  if 2*cost_S[i]==2*cost_T[i]==D:
    ans-=((P_S[i]*P_T[i])**2)%mod
print(ans%mod)