Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Connected Components

Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.

Input

In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0, 1, ..., n-1$.

In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).

In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.

Output

For each query, print "yes" if $t$ is reachable from $s$ through the social network, "no" otherwise.

Constraints

$2 \leq n \leq 100,000$

$0 \leq m \leq 100,000$

$1 \leq q \leq 10,000$

Sample Input

10 9
0 1
0 2
3 4
5 7
5 6
6 7
6 8
7 8
8 9
3
0 1
5 9
1 3

Sample Output

yes
yes
no

Solution in JavaScript (judge verdict: Accepted)

function main(_stdin) {
    const stdin = _stdin.split('\n');
    const [user, relation] = stdin.shift().split(' ');
    const relations = stdin.filter((e, i) => i < relation).map(e => e.split(' ').map(e => parseInt(e, 10)));
    const qblock = stdin.slice(relation);
    const qnum = parseInt(qblock.shift(), 10);
    const questions = qblock.filter((e, i) => i < qnum).map(e => e.split(' ').map(e => parseInt(e, 10)));

    const nodes = createNodes(relations);
    const color = [...new Array(parseInt(user, 10)).keys()].fill(null);

    assignColor(nodes, color);


    for(const q of questions){
        if(color[q[0]] && color[q[1]] && color[q[0]] === color[q[1]]) {
            console.log('yes');
        } else {
            console.log('no');
        }
    }
}

function createNodes(relations) {
    const nodes = [];
    for (let i = 0, l = relations.length; i < l; i++) {
        const [from, to] = relations[i];
        if (!nodes[from]) {
            nodes[from] = [from, 1, to];
        } else {
            nodes[from][1]++;
            nodes[from].push(to);
        }
        if (!nodes[to]) {
            nodes[to] = [to, 1, from];
        } else {
            nodes[to][1]++;
            nodes[to].push(from);
        }
    }
    return nodes;
}

function dfs(nodes, color, r, c) {
    const stack = [];
    stack.push(r);
    color[r] = c;

    while (stack.length !== 0) {
        const u = stack.pop();
        const children = nodes[u].slice(2);
        for (let i = 0, l = children.length; i < l; i++) {
            const v = children[i];
            if (color[v] === null) {
                color[v] = c;
                stack.push(v);
            }
        }
    }
}

function assignColor(nodes, color) {
    let id = 1;
    let max = color.length - 1;
    for (let i = 0; i < max; i++) {
        if (color[i] === null && nodes[i] !== undefined) {
            dfs(nodes, color, i, id++);
        }
    }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));