import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
n,m = LI()
s,t = LI()
e = collections.defaultdict(list)
for _ in range(m):
u,v,d = LI()
e[u].append((v,d))
e[v].append((u,d))
def search(s,t):
d = collections.defaultdict(lambda: [inf, 0])
d[s] = [0, 1]
q = []
heapq.heappush(q, (0, s))
v = collections.defaultdict(bool)
while len(q):
k, u = heapq.heappop(q)
if v[u]:
continue
v[u] = True
if u == t:
return d
uc = d[u][1]
for uv, ud in e[u]:
if v[uv]:
continue
vd = k + ud
if d[uv][0] > vd:
d[uv] = [vd, uc]
heapq.heappush(q, (vd, uv))
elif d[uv][0] == vd:
d[uv][1] += uc
return d
d1 = search(s,t)
d2 = search(t,s)
rd = d1[t][0]
kk = rd / 2.0
r = d1[t][1] ** 2
for k in list(d1.keys()):
t,c = d1[k]
if t > kk:
continue
if t == kk:
if d2[k][0] == t:
r -= c**2 * d2[k][1]**2
continue
for uv, ud in e[k]:
if t + ud <= kk or t + ud + d2[uv][0] != rd:
continue
r -= c * d2[uv][1]
return r
print(main())