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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

n, m = map(int, raw_input().split())
que = []
for i in xrange(m):
    a, b, c = map(int, raw_input().split())
    que.append((c, a, b))
que.sort()
p = range(n)
def root(x):
    if x!=p[x]: x=p[x]=root(p[x])
    return x
def unite(x, y):
    px = p[x]
    py = p[y]
    if px < py:
        p[py] = px
    else:
        p[px] = py
su = 0
g = [[] for i in xrange(n)]
dic = {(0, -1): 0}
for c, a, b in que:
    a -= 1; b -= 1
    if root(a) != root(b):
        unite(a, b)
        su += c
        g[a].append(b)
        g[b].append(a)
        dic[a, b] = dic[b, a] = c

nl = n.bit_length()
ps = [[0]*n for i in xrange(nl)]
cs = [[0]*n for i in xrange(nl)]
ds = [0]*n
INF = 10**9+7
def dfs(v, p, d):
    ps[0][v] = p
    cs[0][v] = dic[v,p]
    ds[v] = d
    for e in g[v]:
        if e!=p:dfs(e, v, d+1)
def init(s):
    dfs(s, -1, 0)
    for i in xrange(nl-1):
        p1 = ps[i+1]; p0 = ps[i]
        c1 = cs[i+1]; c0 = cs[i]
        for v in xrange(n):
            p1[v] = -1 if p0[v] < 0 else p0[p0[v]]
            c1[v] = INF if p0[v] < 0 else max(c0[v], c0[p0[v]])
try:
    init(0)
except:
    exit(0)
def solve(u, v):
    res = 0
    if ds[u] > ds[v]:
        u,v = v,u
    for k in xrange(nl-1):
        if (ds[v] - ds[u]) >> k & 1:
            res = max(res, cs[k][v])
            v = ps[k][v]
    if u==v: return res
    for k in xrange(nl-1, -1, -1):
        pk = ps[k]
        if pk[u] != pk[v]:
            res = max(res, cs[k][u], cs[k][v])
            u = pk[u]; v = pk[v]
    res = max(res, cs[0][u], cs[0][v])
    return res

for i in xrange(input()):
    s, t = map(int, raw_input().split())
    print su - solve(s-1, t-1)