#include <bits/stdc++.h>
#include <atcoder/modint>
using namespace std;
using mint = atcoder::modint1000000007;
typedef long long ll;
template<class T>
struct matrix{
int n, m;
vector<vector<T>> data;
vector<T> &operator[](int i){
assert(0 <= i && i < n);
return data[i];
}
const vector<T> &operator[](int i) const{
assert(0 <= i && i < n);
return data[i];
}
matrix &inplace_slice(int il, int ir, int jl, int jr){
assert(0 <= il && il <= ir && ir <= n);
assert(0 <= jl && jl <= jr && jr <= m);
n = ir - il, m = jr - jl;
if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
data.resize(n);
for(auto &row: data){
row.erase(row.begin(), row.begin() + jl);
row.resize(m);
}
return *this;
}
matrix slice(int il, int ir, int jl, int jr) const{
return matrix(*this).inplace_slice(il, ir, jl, jr);
}
matrix &inplace_row_slice(int il, int ir){
assert(0 <= il && il <= ir && ir <= n);
n = ir - il;
if(il > 0) for(auto i = 0; i < n; ++ i) swap(data[i], data[il + i]);
data.resize(n);
return *this;
}
matrix row_slice(int il, int ir) const{
return matrix(*this).inplace_row_slice(il, ir);
}
matrix &inplace_column_slice(int jl, int jr){
assert(0 <= jl && jl <= jr && jr <= m);
m = jr - jl;
for(auto &row: data){
row.erase(row.begin(), row.begin() + jl);
row.resize(m);
}
return *this;
}
matrix column_slice(int jl, int jr) const{
return matrix(*this).inplace_column_slice(jl, jr);
}
bool operator==(const matrix &a) const{
assert(n == a.n && m == a.m);
return data == a.data;
}
bool operator!=(const matrix &a) const{
assert(n == a.n && m == a.m);
return data != a.data;
}
matrix &operator+=(const matrix &a){
assert(n == a.n && m == a.m);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] += a[i][j];
return *this;
}
matrix operator+(const matrix &a) const{
return matrix(*this) += a;
}
matrix &operator-=(const matrix &a){
assert(n == a.n && m == a.m);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] -= a[i][j];
return *this;
}
matrix operator-(const matrix &a) const{
return matrix(*this) -= a;
}
matrix operator*=(const matrix &a){
assert(m == a.n);
int l = a.m;
matrix res(n, l);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) for(auto k = 0; k < l; ++ k) res[i][k] += data[i][j] * a[j][k];
return *this = res;
}
matrix operator*(const matrix &a) const{
return matrix(*this) *= a;
}
matrix &operator*=(T c){
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] *= c;
return *this;
}
matrix operator*(T c) const{
return matrix(*this) *= c;
}
template<class U, typename enable_if<is_integral<U>::value>::type* = nullptr>
matrix &inplace_power(U e){
assert(n == m && e >= 0);
matrix res(n, n, T{1});
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class U>
matrix power(U e) const{
return matrix(*this).inplace_power(e);
}
matrix &inplace_transpose(){
assert(n == m);
for(auto i = 0; i < n; ++ i) for(auto j = i + 1; j < n; ++ j) swap(data[i][j], data[j][i]);
return *this;
}
matrix transpose() const{
if(n == m) return matrix(*this).inplace_transpose();
matrix res(m, n);
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[j][i] = data[i][j];
return res;
}
vector<T> operator*(const vector<T> &v) const{
assert(m == (int)v.size());
vector<T> res(n, T{0});
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) res[i] += data[i][j] * v[j];
return res;
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix, determinant, rank}
tuple<matrix &, T, int> inplace_REF(int up_to = -1){
if(n == 0) return {*this, T{1}, 0};
if(!~up_to) up_to = m;
T det = 1;
int rank = 0;
for(auto j = 0; j < up_to; ++ j){
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
int pivot = rank;
for(auto i = rank + 1; i < n; ++ i) if(abs(data[pivot][j]) < abs(data[i][j])) pivot = i;
if(rank != pivot){
swap(data[rank], data[pivot]);
det *= -1;
}
if(abs(data[rank][j]) <= eps) continue;
det *= data[rank][j];
T inv = 1 / data[rank][j];
for(auto i = rank + 1; i < n; ++ i) if(abs(data[i][j]) > eps){
T coef = data[i][j] * inv;
for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
}
++ rank;
}
else{
for(auto i = rank + 1; i < n; ++ i) while(data[i][j]!=0){
T q;
if constexpr(is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) q = data[rank][j] / data[i][j];
else q = data[rank][j].val() / data[i][j].val();
if(q!=0) for(auto k = j; k < m; ++ k) data[rank][k] -= q * data[i][k];
swap(data[rank], data[i]);
det *= -1;
}
if(rank == j) det *= data[rank][j];
else det = T{0};
if(data[rank][j]!=0) ++ rank;
}
if(rank == n) break;
}
return {*this, det, rank};
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Otherwise, O(n * up_to * log(size)) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix, determinant, rank}
tuple<matrix, T, int> REF(int up_to = -1) const{
return matrix(*this).inplace_REF(up_to);
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix, determinant, rank}
tuple<matrix &, T, int> inplace_REF_field(int up_to = -1){
if(n == 0) return {*this, T{1}, 0};
if(!~up_to) up_to = m;
T det = T{1};
int rank = 0;
for(auto j = 0; j < up_to; ++ j){
int pivot = -1;
for(auto i = rank; i < n; ++ i) if(data[i][j] != T{0}){
pivot = i;
break;
}
if(!~pivot){
det = T{0};
continue;
}
if(rank != pivot){
swap(data[rank], data[pivot]);
det *= -1;
}
det *= data[rank][j];
T inv = 1 / data[rank][j];
for(auto i = rank + 1; i < n; ++ i) if(data[i][j] != T{0}){
T coef = data[i][j] * inv;
for(auto k = j; k < m; ++ k) data[i][k] -= coef * data[rank][k];
}
++ rank;
if(rank == n) break;
}
return {*this, det, rank};
}
// Assumes T is a field.
// O(up_to) divisions with O(n * m * up_to) additions, subtractions, and multiplications.
// Returns {REF matrix, determinant, rank}
tuple<matrix, T, int> REF_field(int up_to = -1) const{
return matrix(*this).inplace_REF_field(up_to);
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
optional<matrix> inverse() const{
assert(n == m);
if(n == 0) return *this;
auto a = data;
auto res = multiplicative_identity();
for(auto j = 0; j < n; ++ j){
int rank = j, pivot = -1;
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
pivot = rank;
for(auto i = rank + 1; i < n; ++ i) if(abs(a[pivot][j]) < abs(a[i][j])) pivot = i;
if(abs(a[pivot][j]) <= eps) return {};
}
else{
for(auto i = rank; i < n; ++ i) if(a[i][j] != T{0}){
pivot = i;
break;
}
if(!~pivot) return {};
}
swap(a[rank], a[pivot]), swap(res[rank], res[pivot]);
T inv = 1 / a[rank][j];
for(auto k = 0; k < n; ++ k) a[rank][k] *= inv, res[rank][k] *= inv;
for(auto i = 0; i < n; ++ i){
if constexpr(is_floating_point_v<T>){
static const T eps = 1e-9;
if(i != rank && abs(a[i][j]) > eps){
T d = a[i][j];
for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
}
}
else if(i != rank && a[i][j] != T{0}){
T d = a[i][j];
for(auto k = 0; k < n; ++ k) a[i][k] -= d * a[rank][k], res[i][k] -= d * res[rank][k];
}
}
}
return res;
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
T determinant() const{
assert(n == m);
return get<1>(REF());
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
T determinant_field() const{
assert(n == m);
return get<1>(REF_field());
}
// Assumes T is either a floating, integral, or a modular type.
// If T is a floating type, O(n) divisions with O(n^3) additions, subtractions, and multiplications.
// Otherwise, O(n^2 * log(size)) divisions with O(n^3) additions, subtractions, and multiplications.
int rank() const{
return get<2>(REF());
}
// Assumes T is a field.
// O(n) divisions with O(n^3) additions, subtractions, and multiplications.
int rank_field() const{
return get<2>(REF_field());
}
// Regarding the matrix as a system of linear equations by separating first m-1 columns, find a solution of the linear equation.
// Assumes T is a field
// O(n * m^2)
optional<vector<T>> find_a_solution() const{
assert(m >= 1);
auto [ref, _, rank] = REF_field(m - 1);
for(auto i = rank; i < n; ++ i) if(ref[i][m - 1] != T{0}) return {};
vector<T> res(m - 1);
for(auto i = rank - 1; i >= 0; -- i){
int pivot = 0;
while(pivot < m - 1 && ref[i][pivot] == T{0}) ++ pivot;
assert(pivot < m - 1);
res[pivot] = ref[i][m - 1];
for(auto j = pivot + 1; j < m - 1; ++ j) res[pivot] -= ref[i][j] * res[j];
res[pivot] /= ref[i][pivot];
}
return res;
}
// O(n * 2^n)
T permanent() const{
assert(n <= 30 && n == m);
T perm = n ? 0 : 1;
vector<T> sum(n);
for(auto order = 1; order < 1 << n; ++ order){
int j = __lg(order ^ order >> 1 ^ order - 1 ^ order - 1 >> 1), sign = (order ^ order >> 1) & 1 << j ? 1 : -1;
T prod = order & 1 ? -1 : 1;
if((order ^ order >> 1) & 1 << j) for(auto i = 0; i < n; ++ i) prod *= sum[i] += data[i][j];
else for(auto i = 0; i < n; ++ i) prod *= sum[i] -= data[i][j];
perm += prod;
}
return perm * (n & 1 ? -1 : 1);
}
template<class output_stream>
friend output_stream &operator<<(output_stream &out, const matrix &a){
out << "\n";
for(auto i = 0; i < a.n; ++ i){
for(auto j = 0; j < a.m; ++ j) out << a[i][j].val() << " ";
out << "\n";
}
return out;
}
matrix(int n, int m, T init_diagonal = T{0}, T init_off_diagonal = T{0}): n(n), m(m){
assert(n >= 0 && m >= 0);
data.assign(n, vector<T>(m, T{0}));
for(auto i = 0; i < n; ++ i) for(auto j = 0; j < m; ++ j) data[i][j] = i == j ? init_diagonal : init_off_diagonal;
}
matrix(int n, int m, const vector<vector<T>> &a): n(n), m(m), data(a){ }
static matrix additive_identity(int n, int m){
return matrix(n, m, T{0}, T{0});
}
static matrix multiplicative_identity(int n, int m){
return matrix(n, m, T{1}, T{0});
}
};
template<class T>
matrix<T> operator*(T c, matrix<T> a){
for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) a[i][j] = c * a[i][j];
return a;
}
// Multiply a row vector v on the left
template<class T>
vector<T> operator*(const vector<T> &v, const matrix<T> &a){
assert(a.n == (int)size(v));
vector<T> res(a.m, T{0});
for(auto i = 0; i < a.n; ++ i) for(auto j = 0; j < a.m; ++ j) res[j] += v[i] * a[i][j];
return res;
}
mint calc(vector<vector<mint>> &G, int t){
int n = G.size();
vector<vector<mint>> fuck(n*t, vector<mint>(n*t, 0));
for (int z=0;z<t;z++){
for (int i=0;i<n;i++){
for (int j=0;j<n;j++){
fuck[z*n + i][z*n + j] = G[i][j];
}
}
for (int i=0;i<n;i++) if (z<t-1) fuck[z*n+i][(z+1)*n+i] = -1;
for (int i=0;i<n;i++) if (z<t-1) fuck[(z+1)*n+i][z*n+i] = -1;
}
fuck.pop_back();
for (auto &x:fuck) x.pop_back();
// cout << matrix<mint>(n*t-1, n*t-1, fuck);
return matrix<mint>(n*t-1, n*t-1, fuck).determinant();
}
mint guess(vector<vector<mint>> G, ll t){
int n = G.size();
vector<matrix<mint>> F(t+1, matrix<mint>(n, n));
F[0] = matrix<mint>(n, n, mint(1));
F[1] = matrix<mint>(n, n, G);
// cout << F[0];
for (int i=2;i<=t;i++) F[i] = F[i-1]*F[1] - F[i-2];
// return F[t].determinant();
for (auto &x:G) x.back() = 0;
for (auto &x:G.back()) x = 0;
G.back().back() = 1;
auto G2 = matrix<mint>(n, n, G);
auto I2 = matrix<mint>(n, n, mint(1));
I2[n-1][n-1] = 0;
// cout << "ok " << t << '\n';
// cout << F[t-1].n << F[t-1].m << G2.n << G2.m << F[t-2].n << F[t-2].m << I2.n << I2.m << '\n';
if (t==1) return G2.determinant();
if (t==2) return (F[t-1]*G2 - F[t-2]*I2).determinant();
auto FUCK = F[1];
for (int i=0;i<n;i++) FUCK[i][i] -= 1;
auto H1 = F[t-2]*FUCK - F[t-3];
auto H2 = F[t-3]*FUCK;
if (t>3) H2 -= F[t-4];
auto FUCK2 = FUCK;
for (int i=0;i<n;i++) FUCK2[i][n-1] = 0;
for (int j=0;j<n;j++) FUCK2[n-1][j] = 0;
FUCK2[n-1][n-1] = 1;
// cout << FUCK2 << "Hello\n";
// cout << FUCK2[n-1][n-1].val() << '\n';
return (H1*FUCK - H2*I2).determinant();
}
int main(){
int n, m;
ll t;
scanf("%d %d %lld", &n, &m, &t);
vector<vector<mint>> G(n, vector<mint>(n));
for (int i=1;i<=m;i++){
int x, y;
scanf("%d %d", &x, &y);
--x, --y;
G[x][y] -= 1;
G[y][x] -= 1;
G[x][x] += 1;
G[y][y] += 1;
}
for (int i=0;i<n;i++){
if (t==2) G[i][i] += 1;
else if (t>2) G[i][i] += 2;
}
cout << guess(G, t).val() << '\n';
}