Calculating pre-xors in a Tree (DSU application)

This is related to a problem I came across in OJ 4 (DSA) and the following is the solution:

int n, m, k;
map<int, int> parent, val;
int net = 0, ans = INF;

int power(int x, int N)
{
    int y = 1;
    while (N > 0)
    {
        if (N & 1)
            y = (y * x) % MOD;
        N /= 2;
        x = (x * x) % MOD;
    }

    return y;
}

int Get(int i)
{
    if (!parent.count(i)) parent[i] = i, val[i] = 0;
    return parent[i];
}

int Find(int x)
{
    int p = Get(x);
    if (p == x) return x;

    int r = (parent[x] = Find(p));
    val[x] ^= val[p];
    return r;
}

void Union(int i, int j, int x)
{
    int a = Find(i), b = Find(j);
    x ^= val[i] ^ val[j];

    if (a != b)
    {
        parent[a] = b;
        val[a] = x;

        net--;

    } else
    {
        if (x == 0) return;
        else
            ans = 0;
    }
}

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> n >> m >> k;
    net = n + m - 1;

    while (k--)
    {
        int i, j, x;
        cin >> i >> j >> x;
        j = 1005 + j;

        if (ans != 0)
            Union(i, j, x);
    }

    if (ans == 0)
        cout << 0 << endl;
    else
    {
        ans = power(2, 30);
        ans = power(ans, net);
        cout << ans << endl;
    }
    return 0;
}