#include #include #include // 想定解(式をeditorialと一致させた) template struct ModInt { using lint = long long; static int get_mod() { return mod; } static int get_primitive_root() { assert(mod == 998244353); return 3; } int val; constexpr ModInt() : val(0) {} constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; } constexpr ModInt(lint v) { _setval(v % mod + mod); } explicit operator bool() const { return val != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } constexpr ModInt operator-() const { return ModInt()._setval(mod - val); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } constexpr bool operator==(const ModInt &x) const { return val == x.val; } constexpr bool operator!=(const ModInt &x) const { return val != x.val; } friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } constexpr lint power(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod; n /= 2; } return ans; } constexpr lint inv() const { return this->power(mod - 2); } }; template void ntt(std::vector &a, bool is_inverse = false) { int n = a.size(); if (n == 1) return; static const int mod = MODINT::get_mod(); static const MODINT root = MODINT::get_primitive_root(); assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0); static std::vector w{1}, iw{1}; for (int m = w.size(); m < n / 2; m *= 2) { MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw; w.resize(m * 2), iw.resize(m * 2); for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } if (!is_inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m] * w[k]; a[i] = x + y, a[i + m] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m]; a[i] = x + y, a[i + m] = (x - y) * iw[k]; } } } int n_inv = MODINT(n).inv(); for (auto &v : a) v *= n_inv; } } template void ntt2d(std::vector> &mat) { for (auto &vec : mat) ntt(vec, false); int h = mat.size(), w = mat[0].size(); for (int j = 0; j < w; j++) { std::vector v(h); for (int i = 0; i < h; i++) v[i] = mat[i][j]; ntt(v, false); for (int i = 0; i < h; i++) mat[i][j] = v[i]; } } template void ntt2dinv(std::vector> &mat) { int h = mat.size(), w = mat[0].size(); for (int j = 0; j < w; j++) { std::vector v(h); for (int i = 0; i < h; i++) v[i] = mat[i][j]; ntt(v, true); for (int i = 0; i < h; i++) mat[i][j] = v[i]; } for (auto &vec : mat) ntt(vec, true); } using namespace std; using mint = ModInt<998244353>; int main() { int X, Y; long long T; int a, b, c, d; cin >> X >> Y >> T >> a >> b >> c >> d; assert(X >= 1 and Y >= 1); assert(X + Y <= 18); assert(T >= 1 and T <= 1'000'000'000'000'000'000LL); assert(a >= 1 and a < (1 << X)); assert(b >= 1 and b < (1 << Y)); assert(c >= 1 and c < (1 << X)); assert(d >= 1 and d < (1 << Y)); vector dp(1 << (X + 1), vector(1 << (Y + 1))); dp[a][b] = 1; dp[(1 << (X + 1)) - a][(1 << (Y + 1)) - b] = 1; dp[(1 << (X + 1)) - a][b] = -1; dp[a][(1 << (Y + 1)) - b] = -1; vector trans(1 << (X + 1), vector(1 << (Y + 1))); trans[0][0] = trans[0][1] = trans[0][(1 << (Y + 1)) - 1] = trans[1][0] = trans[(1 << (X + 1)) - 1][0] = 1; ntt2d(dp); ntt2d(trans); for (size_t i = 0; i < dp.size(); i++) { for (size_t j = 0; j < dp[i].size(); j++) { dp[i][j] *= trans[i][j].power(T); } } ntt2dinv(dp); cout << dp[c][d] << '\n'; }