Problem: We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.

The i-th edge connects Vertex U_i and Vertex V_i. The time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).

Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible. Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.

Constraints

* 1 \leq N \leq 100 000
* 1 \leq M \leq 200 000
* 1 \leq S, T \leq N
* S \neq T
* 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
* 1 \leq D_i \leq 10^9 (1 \leq i \leq M)
* If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
* U_i \neq V_i (1 \leq i \leq M)
* D_i are integers.
* The given graph is connected.

Input

Input is given from Standard Input in the following format:


N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M


Output

Print the answer.

Examples

Input

4 4
1 3
1 2 1
2 3 1
3 4 1
4 1 1


Output

2


Input

3 3
1 3
1 2 1
2 3 1
3 1 2


Output

2


Input

8 13
4 2
7 3 9
6 2 3
1 6 4
7 6 9
3 8 9
1 2 2
2 8 12
8 6 9
2 5 5
4 2 18
5 3 7
5 1 515371567
4 8 6


Output

6

Solution (in PYTHON3):

Solution:
from heapq import heappop, heappush
import sys

MOD, INF = 1000000007, float('inf')


def solve(s, t, links):
    q = [(0, 0, s, -1, 0), (0, 0, t, -1, 1)]
    visited_fwd, visited_bwd = [INF] * n, [INF] * n
    patterns_fwd, patterns_bwd = [0] * (n + 1), [0] * (n + 1)
    patterns_fwd[-1] = patterns_bwd[-1] = 1
    collision_nodes, collision_links = set(), set()
    limit = 0
    while q:
        cost, cost_a, v, a, is_bwd = heappop(q)
        if is_bwd:
            visited_self = visited_bwd
            visited_opp = visited_fwd
            patterns_self = patterns_bwd
        else:
            visited_self = visited_fwd
            visited_opp = visited_bwd
            patterns_self = patterns_fwd

        relax_flag = False
        cost_preceding = visited_self[v]
        if cost_preceding == INF:
            visited_self[v] = cost
            relax_flag = True
        elif cost > cost_preceding:
            continue

        patterns_self[v] += patterns_self[a]

        cost_opp = visited_opp[v]
        if cost_opp != INF:
            limit = cost + cost_opp
            if cost == cost_opp:
                collision_nodes.add(v)
            else:
                collision_links.add((v, a) if is_bwd else (a, v))
            break

        if relax_flag:
            for u, du in links[v].items():
                nc = cost + du
                if visited_self[u] < nc:
                    continue
                heappush(q, (nc, cost, u, v, is_bwd))

    collision_time = limit / 2
    while q:
        cost, cost_a, v, a, is_bwd = heappop(q)
        if cost > limit:
            break
        visited_self = visited_bwd if is_bwd else visited_fwd
        if visited_self[v] == INF:
            visited_self[v] = cost
        if is_bwd:
            if cost == collision_time:
                patterns_bwd[v] += patterns_bwd[a]
            continue
        if cost_a == collision_time:
            collision_nodes.add(a)
        elif cost == collision_time:
            collision_nodes.add(v)
            patterns_fwd[v] += patterns_fwd[a]
        else:
            collision_links.add((a, v))

    shortest_count = 0
    collision_count = 0

    for v in collision_nodes:
        if visited_fwd[v] == visited_bwd[v]:
            r = patterns_fwd[v] * patterns_bwd[v]
            shortest_count += r
            shortest_count %= MOD
            collision_count += r * r
            collision_count %= MOD

    for u, v in collision_links:
        if visited_fwd[u] + visited_bwd[v] + links[u][v] == limit:
            r = patterns_fwd[u] * patterns_bwd[v]
            shortest_count += r
            shortest_count %= MOD
            collision_count += r * r
            collision_count %= MOD

    return (shortest_count ** 2 - collision_count) % MOD


n, m = map(int, input().split())
s, t = map(int, input().split())
s -= 1
t -= 1
links = [{} for _ in range(n)]
for uvd in sys.stdin.readlines():
    u, v, d = map(int, uvd.split())
    # for _ in range(m):
    #     u, v, d = map(int, input().split())
    u -= 1
    v -= 1
    links[u][v] = d
    links[v][u] = d
print(solve(s, t, links))