#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using P = pair; #define rep(i, n) for (lint i = 0; i < (lint)(n); ++i) #define rep1(i, n) for (lint i = 1; i < (lint)(n); ++i) #define repn(i, a, b) for(lint i = (a); i < (lint)(b); ++i) #define rep_inv(i, n) for (lint i = (n); i >= 0; --i) #define all(vec) (vec).begin(), (vec).end() constexpr lint Mod = /**/ 1000'000'007LL /*/ 998244353LL /**/; constexpr lint Inf = 1'000'000'000'000'000'010LL; constexpr int IntInf = 1000'000'010; constexpr double Pi = 3.141592653589793238; constexpr double InvPi = 0.318309886183790671; const int di[4] = { 0,1,0,-1 }, dj[4] = { 1,0,-1,0 }; #if __has_include() #include using namespace atcoder; using mint = static_modint; inline istream& operator>>(istream & is, mint & rhs) { long long tmp; is >> tmp; rhs = tmp; return is; } inline ostream& operator<<(ostream & os, const mint & rhs) { return os << rhs.val(); } #endif template using prique = priority_queue; template using prique_inv = priority_queue, greater>; template inline istream& operator>>(istream& is, vector& v) { for (auto&& e : v) is >> e; return is; } template inline istream& operator>>(istream& is, complex& c) { double real, imag; is >> real >> imag; c.real(real); c.imag(imag); return is; } template inline ostream& operator<<(ostream& os, const vector& v) { size_t i = 0, n = v.size(); for (const auto& e : v) { os << e; if (++i < n) os << " "; } return os; } template inline bool chmin(T& a, const U b) { return a > b ? a = b, true : false; } template inline bool chmax(T& a, const U b) { return a < b ? a = b, true : false; } template inline istream& operator>>(istream& is, pair& rhs) { return is >> rhs.first >> rhs.second; } template inline ostream& operator<<(ostream& os, const pair& rhs) { return os << "{" << rhs.first << ", " << rhs.second << "}"; } template T gcd(const vector& vec) { T res = vec.front(); for (T e : vec) { res = gcd(res, e); if (res == 1) return 1; } return res; } template T gcd(initializer_list init) { auto first = init.begin(), last = init.end(); T res = *(first++); for (auto itr = first; itr != last; ++itr) { res = gcd(res, *itr); if (res == 1) return 1; } return res; } template T lcm(const vector& vec) { T res = vec.front(); for (T e : vec) res = lcm(res, e); return res; } template T lcm(initializer_list init) { auto first = init.begin(), last = init.end(); T res = *(first++); for (auto itr = first; itr != last; ++itr) { res = lcm(res, *itr); } return res; } template T pow(T x, lint n) { T res = 1; while (n > 0) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } void out() {} template void out(T x) { cout << x << endl; } template void out(T x, Args... xs) { cout << x << ", "; out(xs...); } bool is_prime(lint x) { for (lint i = 2; i * i <= x; ++i) { if (x % i == 0) return false; } return 1 < x; } vector fact, fact_inv; void fact_init(lint n, lint m = Mod) { fact.resize(n + 1); fact_inv.resize(n + 1); vector inv(n + 1); inv[1] = 1; fact[0] = fact[1] = 1; fact_inv[0] = 1; for (lint i = 2; i <= n; ++i) { fact[i] = i * fact[i - 1] % m; inv[i] = m - m / i * inv[m % i] % m; } for (lint i = 1; i <= n; ++i) { fact_inv[i] = fact_inv[i - 1] * inv[i] % m; } } lint modinv(lint a, lint m = Mod) { lint b = m, u = 1, v = 0; while (b != 0) { lint t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= m; if (u < 0) u += m; return u; } lint modpow(lint x, lint n, lint m = Mod) { lint res = 1; while (n > 0) { if (n & 1) res = res * x % m; x = x * x % m; n >>= 1; } return res; } lint intpow(lint x, lint n) { lint res = 1; while (n > 0) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } lint comb(lint n, lint r) { if (n < 0 || r < 0 || n < r) return 0; if (r == 0 || r == n) return 1; return fact[n] * fact_inv[n - r] % Mod * fact_inv[r] % Mod; } lint perm(lint n, lint r) { if (n < 0 || r < 0 || n < r) return 0; return fact[n] * fact_inv[n - r] % Mod; } template vector as_vector(const string& str) { const size_t n = str.size(); vector res(n); T* p_res = res.data(); const char* p_str = str.data(); for (size_t i = 0; i < n; ++i) { *p_res++ = T(*p_str++ - '0'); } return res; } template vector compressed(vector v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); return v; } class Factring { private: const lint max_n; vector sieve; public: explicit Factring(lint max_n) noexcept : max_n{ max_n } , sieve{ max_n } { iota(sieve.begin(), sieve.end(), 0); for (lint i = 2; i * i < max_n; ++i) { if (sieve[i] < i) continue; for (lint j = i * i; j < max_n; j += i) { if (sieve[j] == j) sieve[j] = i; } } } unordered_map calc(lint x) const noexcept { unordered_map res; while (x > 1) { ++res[sieve[x]]; x /= sieve[x]; } return res; } }; struct UnionFind { const int n; vector par, rank, siz, es; explicit UnionFind(int _n) noexcept : n(_n) , par(n) , rank(n) , siz(n, 1) , es(n) { iota(par.begin(), par.end(), 0); } int root(int x) noexcept { if (par[x] == x) return x; return par[x] = root(par[x]); } bool same(int x, int y) noexcept { return root(x) == root(y); } void unite(int x, int y) noexcept { x = root(x); y = root(y); if (x == y) ++es[x]; else if (rank[x] < rank[y]) { par[x] = y; siz[y] += siz[x]; es[y] += es[x] + 1; } else { par[y] = x; if (rank[x] == rank[y]) ++rank[x]; siz[x] += siz[y]; es[x] += es[y] + 1; } } int count(int x) noexcept { return siz[root(x)]; } vector> groups() noexcept { vector roots(n), group_size(n); for (int i = 0; i < n; ++i) { roots[i] = root(i); ++group_size[roots[i]]; } vector> res(n); for (int i = 0; i < n; ++i) { res.reserve(group_size[i]); } for (int i = 0; i < n; ++i) { res[roots[i]].push_back(i); } res.erase( remove_if(res.begin(), res.end(), [](const vector& v) { return v.empty(); }), res.end() ); return res; } }; template class CumulativeSum { private: const int n; vector dat; public: CumulativeSum() = default; explicit CumulativeSum(const int n) : n(n), dat(n + 1) {} CumulativeSum(const vector& vec) : n(vec.size()) , dat(n + 1) { for (int i = 0; i < n; ++i) dat[i + 1] = vec[i]; } void add(const int i, const T& x) { dat[i + 1] += x; } void build() { for (int i = 0; i < n; ++i) { dat[i + 1] += dat[i]; } } // [l, r) T sum(const int l, const int r) const { return dat[r] - dat[l]; } // [0, a) T sum(const int a) const { return dat[a]; } }; template class CumulativeSum2D { private: vector> dat; public: CumulativeSum2D() = default; explicit CumulativeSum2D(size_t n) : dat(n + 1, vector(n + 1)) {} CumulativeSum2D(size_t h, size_t w) : dat(h + 1, vector(w + 1)) {} CumulativeSum2D(const vector>& vec) noexcept { const size_t h = vec.size(), w = vec.front().size(); dat.resize(h + 1, vector(w + 1)); for (size_t i = 0; i < h; ++i) { for (size_t j = 0; j < w; ++j) { dat[i + 1][j + 1] = dat[i][j + 1] + dat[i + 1][j] - dat[i][j] + vec[i][j]; } } } void add(int h, int w, int v) noexcept { dat[h + 1][w + 1] += v; } void build() { const size_t h = dat.size(), w = dat.front().size(); for (size_t i = 0; i < h; ++i) { for (size_t j = 0; j < w; ++j) { dat[i + 1][j + 1] = dat[i][j + 1] + dat[i + 1][j] - dat[i][j]; } } } // [0, h) × [0, w) T sum(int h, int w) const noexcept { return sum(0, 0, h, w); } // [h1, h2) × [w1, w2) T sum(int h1, int w1, int h2, int w2) const noexcept { return dat[h2][w2] - dat[h1][w2] - dat[h2][w1] + dat[h1][w1]; } }; template class BinaryIndexedTree { private: const int size; vector dat; public: explicit BinaryIndexedTree(const int size) noexcept : size(size) , dat(size + 1) {} explicit BinaryIndexedTree(const vector& vec) noexcept : size(vec.size()) , dat(size + 1) { for (int i = 0; i < size; ++i) dat[i + 1] = vec[i]; for (int i = 0; i <= size; ++i) { const int j = i + (i & -i); if (j <= size) dat[j] += dat[i]; } } void add(const int a, const T w) noexcept { for (int x = a + 1; x <= size; x += (x & -x)) dat[x] += w; } void set(const int a, const T w) noexcept { add(a, w - dat[a]); } // [0, a) T sum(const int a) const noexcept { T res = 0; for (int x = a; x > 0; x -= x & -x) res += dat[x]; return res; } // [a, b) T sum(const int a, const int b) const noexcept { return sum(b) - sum(a); } const T& operator[](const size_t x) const noexcept { return dat[x + 1]; } }; template lint inversion_number(const vector vec) { vector v = vec; sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); const int n = vec.size(); lint res = 0; fenwick_tree b(n); for (int i = 0; i < n; ++i) { const int j = lower_bound(v.begin(), v.end(), vec[i]) - v.begin(); res += i - b.sum(0, j); b.add(j, 1); } return res; } template T nearest_value(const vector& v, const U& value) { auto itr = lower_bound(v.begin(), v.end(), value); if (itr == v.begin()) return *itr; if (itr == v.end()) return *prev(itr); return min(*itr - value, value - *prev(itr)) + value; } template struct matrix { size_t row, column; vector> mat; matrix() = default; explicit matrix(size_t size) : row(size) , column(size) , mat(size, vector(size)) {} matrix(size_t row, size_t column) : row(row) , column(column) , mat(row, vector(column)) {} matrix(size_t row, size_t column, const T& val) : row(row) , column(column) , mat(row, vector(column, val)) {} matrix(const vector& vec) : row(vec.size()) , column(1) { mat.resize(row, vector(1)); for (size_t i = 0; i < row; ++i) { mat[i][0] = vec[i]; } } matrix(const vector>& mat) : row(mat.size()) , column(mat.front().size()) , mat(mat) {} matrix& operator=(const matrix& rhs) { row = rhs.row, column = rhs.column, mat = rhs.mat; return (*this); } matrix operator*(const matrix& rhs) const { return matrix(*this) *= rhs; } matrix& operator*=(const matrix& rhs) { matrix res(row, rhs.column); for (size_t k = 0; k < column; ++k) { for (size_t i = 0; i < row; ++i) { for (size_t j = 0; j < rhs.column; ++j) { res[i][j] += mat[i][k] * rhs[k][j]; } } } return (*this) = res; } const vector& operator[](const size_t index) const { return mat[index]; } vector& operator[](const size_t index) { return mat[index]; } static matrix identity(size_t n) { matrix res(n); for (size_t i = 0; i < n; ++i) { res[i][i] = 1; } return res; } matrix pow(long long x) const { assert(row == column); matrix res = identity(row), base = (*this); while (x > 0) { if (x & 1) res *= base; base *= base; x >>= 1; } return res; } friend ostream& operator<<(ostream& os, const matrix& rhs) { for (size_t i = 0; i < rhs.row; ++i) { for (size_t j = 0; j < rhs.column; ++j) { os << rhs[i][j]; if (j + 1 < rhs.column) os << " "; else os << "\n"; } } return os; } }; int main() { using mint2 = static_modint; mint a, b, c; lint k; cin >> a >> b >> c >> k; matrix mat(3, 3); mat[0][0] = 0; mat[0][1] = 1; mat[0][2] = 1; mat[1][0] = 1; mat[1][1] = 0; mat[1][2] = 1; mat[2][0] = 1; mat[2][1] = 1; mat[2][2] = 0; mat = mat.pow(k); cout << a.pow((mat[0][0] + mat[1][0] + mat[2][0]).val()) * b.pow((mat[0][1] + mat[1][1] + mat[2][1]).val()) * c.pow((mat[0][2] + mat[1][2] + mat[2][2]).val()) << endl; }