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 Rust (1.15.1) (judge verdict: Accepted)

//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

use std::io::Write;

fn root(parent: &[usize], mut x: usize) -> usize {
    while parent[x] != x {
        x = parent[x];
    }
    x
}

fn run() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    input! {
        n: usize,
        m: usize,
        e: [(usize1, usize1, u64); m],
        q: usize,
        p: [(usize1, usize1); q],
    }
    let mut parent = Vec::with_capacity(n);
    let mut size = Vec::with_capacity(n);
    let mut cost = Vec::with_capacity(n);
    for i in 0..n {
        parent.push(i);
        size.push(1);
        cost.push(1_000_000_000 + 1);
    }
    let mut e = e;
    e.sort_by_key(|e| e.2);
    let mut sum = 0;
    for (a, b, c) in e {
        let mut a = root(&parent, a);
        let mut b = root(&parent, b);
        if a == b {
            continue;
        }
        if size[a] < size[b] {
            std::mem::swap(&mut a, &mut b);
        }
        size[a] += size[b];
        parent[b] = a;
        cost[b] = c;
        sum += c;
    }
    for (mut a, mut b) in p {
        let mut ans = 0;
        while a != b {
            if cost[a] < cost[b] {
                ans = cost[a];
                a = parent[a];
            } else {
                ans = cost[b];
                b = parent[b];
            }
        }
        writeln!(out, "{}", sum - ans).ok();
    }
}

fn main() {
    run();
}