Language: C++

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,k,n) for(int i = (int)(k); i < (int)(n); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) a.begin(), a.end()
#define MS(m,v) memset(m,v,sizeof(m))
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<string> vs;
typedef pair<int, int> pii;
const int MOD = 1000000007;
const int INF = MOD + 1;
const ld EPS = 1e-12;
template<class T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<class T> T &chmax(T &a, const T &b) { return a = max(a, b); }

/*--------------------template--------------------*/

template<int M>
class Cyclic {
	using ll = long long;
	int n;
	static ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p); }
public:
	Cyclic() : n(0) { ; }
	Cyclic(int m) : n(m) {
		if (n >= M) n %= M;
		else if (n < 0) n = (n % M + M) % M;
	}
	operator int() const { return n; }
	bool operator==(const Cyclic &a) const { return n == a.n; }
	Cyclic operator+=(const Cyclic &a) { n += a.n; if (n >= M) n -= M; return *this; }
	Cyclic operator-=(const Cyclic &a) { n -= a.n; if (n < 0) n += M; return *this; }
	Cyclic operator*=(const Cyclic &a) { n = (ll(n) * a.n) % M; return *this; }
	Cyclic operator+(const Cyclic &a) const { Cyclic res = *this; return res += a; }
	Cyclic operator-(const Cyclic &a) const { Cyclic res = *this; return res -= a; }
	Cyclic operator*(const Cyclic &a) const { Cyclic res = *this; return res *= a; }
	Cyclic operator/(const Cyclic &a) const { return *this * Cyclic<M>(inv(a, M)); }
	Cyclic operator^(int n) const {
		if (n == 0) return Cyclic(1);
		const Cyclic a = *this;
		Cyclic res = (a * a) ^ (n / 2);
		return n % 2 ? res * a : res;
	}
};

template<int M> Cyclic<M> fact(int n, bool sw = true) {
	static vector<Cyclic<M>> v1 = { 1 }, v2 = { 1 };
	if (n >= (int)v1.size()) {
		const int from = v1.size(), to = n + 1024;
		v1.reserve(to);
		v2.reserve(to);
		for (int i = from; i < to; ++i) {
			v1.push_back(v1.back() * Cyclic<M>(i));
			v2.push_back(v2.back() / Cyclic<M>(i));
		}
	}
	return sw ? v1[n] : v2[n];
}

template<int M> Cyclic<M> comb(int a, int b) {
	return fact<M>(a, true) * fact<M>(b, false) * fact<M>(a - b, false);
}

const int mod = 2;
using Mod = Cyclic<mod>;

typedef Mod Data;
typedef vector<Data> Array;
typedef vector<Array> Matrix;

bool is_zero(Data dat) { return (abs(dat) < EPS); }

Matrix operator-(Matrix mat) {
	REP(i, mat.size()) REP(j, mat[0].size()) mat[i][j] = -mat[i][j];
	return mat;
}

Matrix operator+(Matrix lhs, const Matrix &rhs) {
	REP(i, lhs.size()) REP(j, lhs[0].size()) lhs[i][j] = lhs[i][j] + rhs[i][j];
	return lhs;
}

Matrix operator-(Matrix lhs, const Matrix &rhs) {
	REP(i, lhs.size()) REP(j, lhs[0].size()) lhs[i][j] = lhs[i][j] - rhs[i][j];
	return lhs;
}

Matrix operator*(const Matrix &lhs, const Matrix &rhs) {
	Matrix res(lhs.size(), Array(rhs[0].size(), 0));
	REP(i, lhs.size()) REP(j, rhs[0].size()) REP(k, rhs.size())
		res[i][j] = fma(lhs[i][k], rhs[k][j], res[i][j]);
	return res;
}

Array operator+(const Array &lhs, const Array &rhs) {
	Array res = lhs;
	REP(i, rhs.size()) res[i] = res[i] + rhs[i];
	return res;
}

Array operator*(const Matrix &lhs, const Array &rhs) {
	Array res(lhs.size());
	REP(i, lhs.size())
		res[i] = inner_product(begin(lhs[i]), end(lhs[i]), begin(rhs), Data(0));
	return res;
}

Array operator*(Data scalar, const Array &rhs) {
	Array res(rhs.size());
	REP(i, rhs.size())
		res[i] = scalar * rhs[i];
	return res;
}

Matrix transpose(const Matrix &A) {
	const int n = A[0].size(), m = A.size();
	Matrix res(n, Array(m, 0));
	REP(i, n)REP(j, m) res[i][j] = A[j][i];
	return res;
}

Data inner_product_ex(const Array& a, const Array& b, const Matrix& m) {
	Array b_prime = m*b;
	return inner_product(begin(a), end(a), begin(b_prime), Data(0));
}

Data norm(const Array &a) {
	return inner_product(begin(a), end(a), begin(a), Data(0));
}

Data norm(const Array &a, const Matrix &M) {
	return inner_product_ex(a, a, M);
}

int rankMat(Matrix A) {
	const int n = A.size(), m = A[0].size();
	int r = 0;
	for (int i = 0; r < n && i < m; ++i) {
		int pivot = r;
		for (int j = r + 1; j < n; ++j)
			if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
		swap(A[pivot], A[r]);
		if (is_zero(A[r][i])) continue;
		for (int k = m - 1; k >= i; --k)
			A[r][k] = A[r][k] / A[r][i];
		for (int j = r + 1; j < n; ++j)
			for (int k = m - 1; k >= i; --k)
				A[j][k] = fma(-A[r][k], A[j][i], A[j][k]);
		++r;
	}
	return r;
}

Data det(Matrix A) {
	const int n = A.size();
	Data D = Data(1);
	for (int i = 0; i < n; ++i) {
		int pivot = i;
		for (int j = i + 1; j < n; ++j)
			if (abs(A[j][i]) > abs(A[pivot][i])) pivot = j;
		swap(A[pivot], A[i]);
		D = D * A[i][i] * Data(i != pivot ? -1 : 1);
		if (is_zero(A[i][i])) break;
		for (int j = i + 1; j < n; ++j)
			for (int k = n - 1; k >= i; --k)
				A[j][k] = A[j][k] - A[i][k] * A[j][i] / A[i][i];
	}
	return D;
}

Matrix E(int n)
{
	Matrix res(n, Array(n));
	REP(i, n) res[i][i] = 1;
	return res;
}

Matrix pow(Matrix x, int p)
{
	int n = x.size();
	Matrix res = E(n);
	while (p > 0)
	{
		if (p & 1) res = res * x;
		x = x*x;
		p >>= 1;
	}
	return res;
}

void out(int f)
{
	cout << (f ? "yes" : "no") << endl;
}

int main()
{
	cin.sync_with_stdio(false); cout << fixed << setprecision(10);
	int n, m, z;
	while (cin >> n >> m >> z, n)
	{
		Matrix g(n, Array(n));
		REP(i, m)
		{
			int a, b; cin >> a >> b;
			a--; b--;
			g[a][b] = g[b][a] = 1;
		}
		Matrix mat = E(n) * pow(g, 2);
		REP(i, n)
		{
			mat[i][i] = 0;
		}

		Matrix tmp(n, Array(n));
		tmp[0][0] = 1;
		if (z % 2 == 1)
		{
			tmp = tmp * g;
		}
		tmp = tmp * pow(mat, z / 2);
		out(int(tmp[0][n - 1]));
	}
	return 0;
}

Compiler output:
a.cc: In function 'Matrix operator*(const Matrix&, const Matrix&)':
a.cc:93:32: error: call of overloaded 'fma(const __gnu_cxx::__alloc_traits<std::allocator<Cyclic<2> >, Cyclic<2> >::value_type&, const __gnu_cxx::__alloc_traits<std::allocator<Cyclic<2> >, Cyclic<2> >::value_type&, __gnu_cxx::__alloc_traits<std::allocator<Cyclic<2> >, Cyclic<2> >::value_type&)' is ambiguous
   93 |                 res[i][j] = fma(lhs[i][k], rhs[k][j], res[i][j]);
      |                             ~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In file included from /usr/include/features.h:523,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/os_defines.h:39,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/c++config.h:683,
                 from /usr/include/c++/14/cassert:43,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:33,
                 from a.cc:1:
/usr/include/x86_64-linux-gnu/bits/mathcalls.h:373:1: note: candidate: 'double fma(double, double, double)'
  373 | __MATHCALL (fma,, (_Mdouble_ __x, _Mdouble_ __y, _Mdouble_ __z));
      | ^~~~~~~~~~
In file included from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:114:
/usr/include/c++/14/cmath:2403:3: note: candidate: 'constexpr long double std::fma(long double, long double, long double)'
 2403 |   fma(long double __x, long double __y, long double __z)
      |   ^~~
/usr/include/c++/14/cmath:2399:3: note: candidate: 'constexpr float std::fma(float, float, float)'
 2399 |   fma(float __x, float __y, float __z)
      |   ^~~
a.cc: In function 'int rankMat(Matrix)':
a.cc:150:46: error: call of overloaded 'fma(int, __gnu_cxx::__alloc_traits<std::allocator<Cyclic<2> >, Cyclic<2> >::value_type&, __gnu_cxx::__alloc_traits<std::allocator<Cyclic<2> >, Cyclic<2> >::value_type&)' is ambiguous
  150 |                                 A[j][k] = fma(-A[r][k], A[j][i], A[j][k]);
      |                                           ~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/x86_64-linux-gnu/bits/mathcalls.h:373:1: note: candidate: 'double fma(double, double, double)'
  373 | __MATHCALL (fma,, (_Mdouble_ __x, _Mdouble_ __y, _Mdouble_ __z));
      | ^~~~~~~~~~
/usr/include/c++/14/cmath:2403:3: note: candidate: 'constexpr long double std::fma(long double, long double, long double)'
 2403 |   fma(long double __x, long double __y, long double __z)
      |   ^~~
/usr/include/c++/14/cmath:2399:3: note: candidate: 'constexpr float std::fma(float, float, float)'
 2399 |   fma(float __x, float __y, float __z)
      |   ^~~