Problem:
Score : 700 points

Problem Statement

Takahashi found an undirected connected graph with N vertices and M edges. The vertices are numbered 1 through N. The i-th edge connects vertices a_i and b_i, and has a weight of c_i.

He will play Q rounds of a game using this graph. In the i-th round, two vertices S_i and T_i are specified, and he will choose a subset of the edges such that any vertex can be reached from at least one of the vertices S_i or T_i by traversing chosen edges.

For each round, find the minimum possible total weight of the edges chosen by Takahashi.

Constraints

1 ≦ N ≦ 4,000

1 ≦ M ≦ 400,000

1 ≦ Q ≦ 100,000

1 ≦ a_i,b_i,S_i,T_i ≦ N

1 ≦ c_i ≦ 10^{9}

a_i \neq b_i

S_i \neq T_i

The given graph is connected.

Partial Scores

In the test set worth 200 points, Q = 1.

In the test set worth another 300 points, Q ≦ 3000.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Q
S_1 T_1
S_2 T_2
:
S_Q T_Q

Output

Print Q lines. The i-th line should contain the minimum possible total weight of the edges chosen by Takahashi.

Sample Input 1

4 3
1 2 3
2 3 4
3 4 5
2
2 3
1 4

Sample Output 1

8
7

We will examine each round:

In the 1-st round, choosing edges 1 and 3 achieves the minimum total weight of 8.

In the 2-nd round, choosing edges 1 and 2 achieves the minimum total weight of 7.

Sample Input 2

4 6
1 3 5
4 1 10
2 4 6
3 2 2
3 4 5
2 1 3
1
2 3

Sample Output 2

8

This input satisfies the additional constraints for both partial scores.

Solution in PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

INF = 10**7
class PPUnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n
        self.time = [INF] * n
        self.number_time = [[0] for _ in [None] * n]
        self.number_dots = [[1] for _ in [None] * n]

    def find(self, x, t):
        while self.time[x] <= t:
            x = self.parents[x]
        return x

    def union(self, x, y, t):
        x = self.find(x, t)
        y = self.find(y, t)
        if x == y:
            return 0
        if self.parents[x] > self.parents[y]:
            x, y = y, x
        self.parents[x] += self.parents[y]
        self.parents[y] = x
        self.number_time[x] += [t]
        self.number_dots[x] += [-self.parents[x]]
        self.time[y] = t
        return 1

    def size(self, x, y, t):
        x = self.find(x, t)
        y = self.find(y, t)
        a = self.number_dots[x][bisect_left(self.number_time[x], t) - 1]
        if x != y:
            a += self.number_dots[y][bisect_left(self.number_time[y], t) - 1]
        return a

    def same(self, x, y, t = 0):
        if x == y:
            return t
        if self.time[x] == self.time[y] == INF:
            return -1
        if self.time[x] > self.time[y]:
            x, y = y, x
        return self.same(self.parents[x], y, self.time[x])

(n, m), *q = [[*map(int, o.split())] for o in open(0)]
UF = PPUnionFind(n)
E = sorted(q[:m], key = lambda t: t[2])
ans = 0
for a, b, c in E:
    if UF.union(a - 1, b - 1, c):
        ans += c
for s, t in q[m+1:]:
    print(ans - UF.same(s - 1, t - 1))