#define _USE_MATH_DEFINES #include #include using namespace std; #include using namespace atcoder; /* #include #include using bll = boost::multiprecision::cpp_int; using bdouble = boost::multiprecision::number>; using namespace boost::multiprecision; */ #if defined(LOCAL_TEST) || defined(LOCAL_DEV) #define BOOST_STACKTRACE_USE_ADDR2LINE #define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line #define _GNU_SOURCE 1 #include #endif #ifdef LOCAL_TEST namespace std { template class dvector : public std::vector { public: dvector() : std::vector() {} explicit dvector(size_t n, const T& value = T()) : std::vector(n, value) {} dvector(const std::vector& v) : std::vector(v) {} dvector(const std::initializer_list il) : std::vector(il) {} template dvector(const Itr first, const Itr last) : std::vector(first, last) {} template , std::nullptr_t> = nullptr> std::vector::reference operator[](size_t n) { if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n); } template , std::nullptr_t> = nullptr> const T_ operator[](size_t n) const { if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n); } template , std::nullptr_t> = nullptr> T_& operator[](size_t n) { if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n); } template , std::nullptr_t> = nullptr> const T_& operator[](size_t n) const { if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n); } }; template, typename Allocator = std::allocator> class dmultiset : public std::multiset { public: dmultiset() : std::multiset() {} dmultiset(const std::multiset& m) : std::multiset(m) {} dmultiset(const std::initializer_list il) : std::multiset(il) {} dmultiset(const Compare& comp) : std::multiset(comp) {} const typename std::multiset::iterator erase(const typename std::multiset::iterator it) { return std::multiset::erase(it); } size_t erase([[maybe_unused]] const T& x) { std::cerr << boost::stacktrace::stacktrace() << '\n'; assert(false); } size_t erase_all_elements(const T& x) { return std::multiset::erase(x); } }; } #define vector dvector #define multiset dmultiset class SIGFPE_exception : std::exception {}; class SIGSEGV_exception : std::exception {}; void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); } void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); } signed convertedmain(); signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); } #define main() convertedmain() #else #define erase_all_elements erase #endif #ifdef LOCAL_DEV template std::ostream& operator<<(std::ostream& s, const std::pair& p) { return s << "(" << p.first << ", " << p.second << ")"; } template std::ostream& operator<<(std::ostream& s, const std::array& a) { s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::set& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::multiset& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::map& m) { s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::deque& v) { for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::vector& v) { for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::vector>& vv) { s << "\\\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; } void debug_impl() { std::cerr << '\n'; } template void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); } #define debug(...) do { std::cerr << ":" << __LINE__ << " (" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false) constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return local; } #else #define debug(...) do {} while (false) constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return prod; } #endif //#define int long long using ll = long long; //INT_MAX = (1<<31)-1 = 2147483647, INT64_MAX = (1LL<<63)-1 = 9223372036854775807 constexpr ll INF = numeric_limits::max() == INT_MAX ? (ll)1e9 + 7 : (ll)1e18; //constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5 //constexpr ll MOD = 998244353; //primitive root = 3 constexpr double EPS = 1e-9; constexpr ll dx[4] = {1, 0, -1, 0}; constexpr ll dy[4] = {0, 1, 0, -1}; constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1}; #define rep(i, n) for(ll i=0, i##_length=(n); i< i##_length; ++i) #define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i) #define rrep(i, n) for(ll i=(n)-1; i>=0; --i) #define rrepeq(i, n) for(ll i=(n) ; i>=1; --i) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() void p() { std::cout << '\n'; } template void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); } template inline void pv(std::vector& v) { for(ll i=0, N=v.size(); i inline bool chmax(T& a, T b) { return a < b && (a = b, true); } template inline bool chmin(T& a, T b) { return a > b && (a = b, true); } template inline void uniq(std::vector& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); } template inline ll sz(T& v) { return v.size(); } template std::vector make_vector_impl(std::vector& sizes, typename std::enable_if<(N==1), T const&>::type x) { return std::vector(sizes.front(),x); } template auto make_vector_impl(std::vector& sizes, typename std::enable_if<(N>1), T const&>::type x) { ll size=sizes.back(); sizes.pop_back(); return std::vector(sizes,x))>(size,make_vector_impl(sizes,x)); } template auto make_vector(ll const (&sizes)[N], T const& x=T()) { std::vector s(N); for(size_t i=0; i(s,x); } /*-----8<-----template-----8<-----*/ constexpr ll MOD = 10; //primitive root = 5 //constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5 /* map inv_cache; struct Modint{ unsigned long long num = 0; constexpr Modint() noexcept {} //constexpr Modint(const Modint &x) noexcept : num(x.num){} inline constexpr operator ll() const noexcept { return num; } inline constexpr Modint& operator+=(Modint x) noexcept { num += x.num; if(num >= MOD) num -= MOD; return *this; } inline constexpr Modint& operator++() noexcept { if(num == MOD - 1) num = 0; else num++; return *this; } inline constexpr Modint operator++(int) noexcept { Modint ans(*this); operator++(); return ans; } inline constexpr Modint operator-() const noexcept { return Modint(0) -= *this; } inline constexpr Modint& operator-=(Modint x) noexcept { if(num < x.num) num += MOD; num -= x.num; return *this; } inline constexpr Modint& operator--() noexcept { if(num == 0) num = MOD - 1; else num--; return *this; } inline constexpr Modint operator--(int) noexcept { Modint ans(*this); operator--(); return ans; } inline constexpr Modint& operator*=(Modint x) noexcept { num = (unsigned long long)(num) * x.num % MOD; return *this; } inline Modint& operator/=(Modint x) noexcept { return operator*=(x.inv()); } template constexpr Modint(T x) noexcept { using U = typename conditional= 4, T, int>::type; U y = x; y %= U(MOD); if(y < 0) y += MOD; num = (unsigned long long)(y); } template inline constexpr Modint operator+(T x) const noexcept { return Modint(*this) += x; } template inline constexpr Modint& operator+=(T x) noexcept { return operator+=(Modint(x)); } template inline constexpr Modint operator-(T x) const noexcept { return Modint(*this) -= x; } template inline constexpr Modint& operator-=(T x) noexcept { return operator-=(Modint(x)); } template inline constexpr Modint operator*(T x) const noexcept { return Modint(*this) *= x; } template inline constexpr Modint& operator*=(T x) noexcept { return operator*=(Modint(x)); } template inline constexpr Modint operator/(T x) const noexcept { return Modint(*this) /= x; } template inline constexpr Modint& operator/=(T x) noexcept { return operator/=(Modint(x)); } inline Modint inv() const noexcept { return inv_cache.count(num) ? inv_cache[num] : inv_cache[num] = inv_calc(); } inline constexpr ll inv_calc() const noexcept { ll x = 0, y = 0; extgcd(num, MOD, x, y); return x; } static inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y) noexcept { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } inline constexpr Modint pow(ll x) const noexcept { Modint ans = 1, cnt = x>=0 ? *this : inv(); if(x<0) x = -x; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; } static inline constexpr ll get_mod() { return MOD; } }; std::istream& operator>>(std::istream& is, Modint& x){ ll a; is>>a; x = a; return is; } inline constexpr Modint operator""_M(unsigned long long x) noexcept { return Modint(x); } std::vector fac(1, 1), inv(1, 1); inline void reserve(size_t a){ if(fac.size() >= a) return; if(a < fac.size() * 2) a = fac.size() * 2; if(a >= MOD) a = MOD; fac.reserve(a); while(fac.size() < a) fac.push_back(fac.back() * Modint(fac.size())); inv.resize(fac.size()); inv.back() = fac.back().inv(); for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i; } inline Modint factorial(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; } inline Modint nPk(ll n, ll r){ if(r < 0 || n < r) return 0; if(n >> 24){ Modint ans = 1; for(ll i = 0; i < r; i++) ans *= n--; return ans; } reserve(n + 1); return fac[n] * inv[n - r]; } inline Modint nCk(ll n, ll r){ if(r < 0 || n < r) return 0; r = min(r, n - r); reserve(r + 1); return inv[r] * nPk(n, r); } inline Modint nHk(ll n, ll r){ return nCk(n + r - 1, n - 1); } //n種類のものから重複を許してr個選ぶ=玉r個と仕切りn-1個 inline Modint catalan(ll n){ reserve(n * 2 + 1); return fac[n * 2] * inv[n] * inv[n + 1]; } */ /* 計算量:和, 差: O(N^2)     積: O(N^3)     行列累乗(^=k): O(N^3logk)     行列式(determinant): O(N^3) */ /* https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1174464211 隣接行列Aについて、A^xの(i,j)成分は、i->jの長さxのパスの数に等しい。 A^xの(i,i)成分が0でないとき、頂点iを通る長さxのサイクルがある。 */ template< class T > struct Matrix { vector< vector< T > > A; static T &get_E() { static T eval = 1; return eval; } static void set_E(T e) { get_E() = e; } Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix E(size_t n) { T e = get_E(); Matrix mat(n); for(size_t i = 0; i < n; i++) mat[i][i] = e; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(size_t i = 0; i < n; i++) for(size_t j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(size_t i = 0; i < n; i++) for(size_t j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(size_t i = 0; i < n; i++) for(size_t j = 0; j < m; j++) for(size_t k = 0; k < p; k++){ C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); C[i][j] %= MOD; } A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::E(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } /* friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); os << '\n'; for (size_t i = 0; i < n; i++) { os << "["; for(size_t j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : "\t"); } } return (os); } */ T determinant() { assert(width() == height()); int N = width(); T ans = 1; Matrix m(*this); for(int i = 0; i < N; i++){ if(m[i][i] == T(0)){ for(int j = i + 1; j < N; j++) { if(m[j][i] != T(0)){ swap(m[i], m[j]); ans *= -1; break; } } if(m[i][i] == T(0)) return 0; } ans *= m[i][i]; T vv = m[i][i]; for (int j = 0; j < N; j++) { m[i][j] /= vv; } for (int j = i + 1; j < N; j++) { T a = m[j][i]; for (int k = 0; k < N; k++) { m[j][k] -= m[i][k] * a; } } } return ans; } }; /*-----8<-----library-----8<-----*/ void solve() { //using Modint = static_modint<10>; vector z(3); rep(i, 3) cin >> z[2-i]; ll N; cin >> N; /* Matrix v(3,3); rep(i,3)v[0][i] = 1; v[1][0] = v[1][2] = 1; v ^= (K - 3); */ ll K = 3; Matrix a(K, K); rep(i, K) a[0][i] = 1; rep(i, K - 1) a[i + 1][i] = 1; //行列累乗(^=k): O(N^3logk) a ^= (N - K); Matrix b(K); rep(i, K) b[i][0] = z[i]; Matrix c = a * b; //debug(c); auto ans = c[0][0]%MOD; p(ans); //1 2 3 4 5 6 7 //1 1 1 3 5 9 7 } signed main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); //ll Q; cin >> Q; while(Q--)solve(); solve(); return 0; }