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 pow(Matrix x, ll n)
{
	ll sz = x.size();
	Matrix res(sz, Array(sz));
	REP(i, sz) res[i][i] = 1;
	while (n > 0)
	{
		if (n & 1) res = res * x;
		x = x*x;
		n >>= 1;
	}
	return res;
}

Array gauss_jordan(const Matrix& A, const Array& b)
{
	int n = A.size();
	Matrix B(n, Array(n + 1));
	REP(i, n)REP(j, n) B[i][j] = A[i][j];
	REP(i, n) B[i][n] = b[i];
	REP(i, n)
	{
		int pivot = i;
		FOR(j, i, n)
		{
			if (abs(B[j][i]) > abs(B[pivot][i])) pivot = j;
		}
		swap(B[i], B[pivot]);

		if (abs(B[i][i]) < EPS) return Array();
		//FOR(j, i + 1, n + 1) B[i][j] /= B[i][i];
		REP(j, n)
		{
			if (i != j)
			{
				FOR(k, i + 1, n + 1) B[j][k] -= B[j][i] * B[i][k];
			}
		}
	}
	Array x(n);
	REP(i, n) x[i] = B[i][n];
	return x;
}

void output(int a)
{
	string ans;
	if (a == 0) ans = "ambiguous";
	if (a == 1) ans = "none";
	cout << ans << endl;
}

int main()
{
	cin.sync_with_stdio(false); cout << fixed << setprecision(10);
	int n;
	cin >> n;
	Matrix mat(n, Array(n));
	REP(i, n)REP(j, n)
	{
		int a;
		cin >> a;
		mat[i][j] = a;
	}
	Array b(n);
	REP(i, n)
	{
		int a; cin >> a;
		b[i] = a;
	}
	int t; cin >> t;
	Matrix exmat = mat;
	REP(i, n) exmat[i].push_back(b[i]);
	mat = pow(mat, t);
	if (rankMat(mat) != rankMat(exmat))
	{
		output(1);
		return 0;
	}
	if (rankMat(mat) != n)
	{
		output(0);
		return 0;
	}
	Array x = gauss_jordan(mat, b);
	REP(i, n) cout << x[i] << (i == n - 1 ? "\n" : " ");
	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)
      |   ^~~