// Copyright (C) 2017 __debug.

// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; version 3

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; If not, see <http://www.gnu.org/licenses/>.


#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/priority_queue.hpp>

#define x first
#define y second
#define MP std::make_pair
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(), (x).end()
#define DEBUG(...) fprintf(stderr, __VA_ARGS__)
#ifdef __linux__
#define getchar getchar_unlocked
#define putchar putchar_unlocked
#endif

using std::pair;
using std::vector;
using std::string;

typedef long long LL;
typedef pair<int, int> Pii;

const int oo = 0x3f3f3f3f;

template<typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, true : false; }
template<typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, true : false; }
string procStatus()
{
    std::ifstream t("/proc/self/status");
    return string(std::istreambuf_iterator<char>(t), std::istreambuf_iterator<char>());
}
template<typename T> T read(T &x)
{
    int f = 1;
    char ch = getchar();
    for (; !isdigit(ch); ch = getchar())
        f = (ch == '-' ? -1 : 1);
    for (x = 0; isdigit(ch); ch = getchar())
        x = 10 * x + ch - '0';
    return x *= f;
}
template<typename T> void write(T x)
{
    if (x == 0) {
        putchar('0');
        return;
    }
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    static char s[20];
    int top = 0;
    for (; x; x /= 10)
        s[++top] = x % 10 + '0';
    while (top)
        putchar(s[top--]);
}
// EOT

const int MAXN = 55, MAXM = 205;
const int MOD = 1e9 + 7;

int N, M, K;
vector<int> G[MAXN];

void input()
{
    read(N); read(M); read(K);
    for (int i = 1; i <= M; ++i) {
        int u, v;
        read(u); read(v);
        G[u].push_back(v);
        G[v].push_back(u);
    }
}

int dfsclock, dfn[MAXN], low[MAXN];
int totbcc, bccid[MAXN];
Pii st[MAXM];
int top;
LL ans;

LL fpm(LL base, LL exp)
{
    LL ret = 1;
    for (; exp; exp >>= 1) {
        if (exp & 1)
            (ret *= base) %= MOD;
        (base *= base) %= MOD;
    }
    return ret;
}

LL polya(int n)
{
    LL ret = 0;
    for (int i = 0; i < n; ++i) {
        (ret += fpm(K, std::__gcd(n, i))) %= MOD;
    }
    (ret *= fpm(n, MOD - 2)) %= MOD;
    return ret;
}

LL C(int n, int k)
{
    assert(0 <= k && k <= n);
    LL ret = 1;
    for (int i = 0; i < k; ++i) {
        (ret *= n - i) %= MOD;
        (ret *= fpm(i + 1, MOD - 2)) %= MOD;
    }
    return ret;
}

void calc(int u, int f)
{
    dfn[u] = low[u] = ++dfsclock;
    for (int i = 0; i < SZ(G[u]); ++i) {
        int v = G[u][i];
        if (v == f)
            continue;
        Pii e = MP(u, v);
        if (!dfn[v]) {
            st[++top] = e;
            calc(v, u);
            chkmin(low[u], low[v]);
            if (low[v] >= dfn[u]) {
                int top0 = top, cntv = 0;
                ++totbcc;
                do {
                    cntv += chkmax(bccid[st[top].x], totbcc);
                    cntv += chkmax(bccid[st[top].y], totbcc);
                } while (st[top--] != e);
                int cnte = top0 - top;
                if (cnte == 1)
                    (ans *= K) %= MOD;
                else if (cnte == cntv)
                    (ans *= polya(cnte)) %= MOD;
                else
                    (ans *= C(cnte + K - 1, K - 1)) %= MOD;
            }
        } else if (dfn[v] < dfn[u]) {
            st[++top] = e;
            chkmin(low[u], dfn[v]);
        }
    }
}

void solve()
{
    ans = 1;
    for (int i = 1; i <= N; ++i) {
        if (!dfn[i])
            calc(i, 0);
    }

    printf("%lld\n", ans);
}

int main()
{
#ifdef __DEBUG
    freopen("F.in", "r", stdin);
    freopen("F.out", "w", stdout);
#endif

    input();
    solve();
}

// 此生谁料，心在天山，身老沧洲。
//     -- 陆游《诉衷情·当年万里觅封侯》


Measured memory_bytes: 256