#include using namespace std; //using namespace atcoder; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin);i<(end);i++) #define REP(i, n) FOR(i,0,n) #define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--) #define IREP(i, n) IFOR(i,0,n) #define Sort(v) sort(v.begin(), v.end()) #define Reverse(v) reverse(v.begin(), v.end()) #define all(v) v.begin(),v.end() #define SZ(v) ((int)v.size()) #define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x)) #define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x)) #define chmax(a, b) a = max(a, b) #define chmin(a, b) a = min(a, b) #define bit(n) (1LL<<(n)) #define debug(x) cout << #x << "=" << x << endl; #define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl; } #define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} } #define pb push_back #define fi first #define se second #define int long long #define INF 1000000000000000000 template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, vector &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; } template ostream &operator<<(ostream &os, pair p){ cout << '(' << p.first << ',' << p.second << ')'; return os; } template void Out(T x) { cout << x << endl; } template void chOut(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); } using vec = vector; using mat = vector; using Pii = pair; using v_bool = vector; using v_Pii = vector; //int dx[4] = {1,0,-1,0}; //int dy[4] = {0,1,0,-1}; //char d[4] = {'D','R','U','L'}; //const int mod = 1000000007; const int mod = 998244353; template struct ModInt{ using ll = long long; ll val; void setval(ll v) { val = v % MOD; }; ModInt(): val(0) {} ModInt(ll v) { setval(v); }; ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); } ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); } ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); } ModInt operator/(const ModInt &x) const { return *this * x.inv(); } ModInt operator-() const { return ModInt(MOD - val); } ModInt operator+=(const ModInt &x) { return *this = *this + x; } ModInt operator-=(const ModInt &x) { return *this = *this - x; } ModInt operator*=(const ModInt &x) { return *this = *this * x; } ModInt operator/=(const ModInt &x) { return *this = *this / x; } bool operator==(const ModInt &x) const { return (*this).val == x.val; } friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; } friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; } ModInt pow(ll n) const { ModInt a = 1; if(n == 0) return a; int i0 = 64 - __builtin_clzll(n); for(int i = i0 - 1; i >= 0; i--){ a = a * a; if((n >> i) & 1) a *= (*this); } return a; } ModInt inv() const { return this->pow(MOD - 2); } }; using mint = ModInt; mint pow(mint x, long long n) { return x.pow(n); } //using mint = double; //for debug using mvec = vector; using mmat = vector; struct Combination{ vector fact, invfact; Combination(int N){ fact = vector({mint(1)}); invfact = vector({mint(1)}); fact_initialize(N); } void fact_initialize(int N){ int i0 = fact.size(); if(i0 >= N + 1) return; fact.resize(N + 1); invfact.resize(N + 1); for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i; invfact[N] = (mint)1 / fact[N]; for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); } mint nCr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if(fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[r] * invfact[n - r]; } mint nPr(int n, int r){ if(n < 0 || r < 0 || r > n) return mint(0); if(fact.size() < n + 1) fact_initialize(n); return fact[n] * invfact[n - r]; } mint Catalan(int n){ if(n < 0) return 0; else if(n == 0) return 1; if(fact.size() < 2 * n + 1) fact_initialize(2 * n); return fact[2 * n] * invfact[n + 1] * invfact[n]; } }; template class NTT { private: vector> f, f_tmp; void init(){ n = 31 - __builtin_clz((signed)N); assert(N == (1 << n)); assert((e.pow(N)).val == 1); pow_e.resize(N + 1); pow_e[0] = 1; bool e_valid = true; FOR(i, 1, N){ pow_e[i] = pow_e[i - 1] * e; if(pow_e[i].val == 1) e_valid = false; } pow_e[N] = 1; assert(e_valid); inv_N = ((ModInt)N).inv(); f.resize(N); f_tmp.resize(N); } void forward_exec(int l, int r, int t){ if(t == n) return; int sz = (r - l) >> 1; REP(i, sz){ f_tmp[l + i] = f[l + 2 * i]; f_tmp[l + sz + i] = f[l + 2 * i + 1]; } FOR(i, l, r) f[i] = f_tmp[i]; forward_exec(l, l + sz, t + 1); forward_exec(l + sz, r, t + 1); REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[i << t]; REP(i, sz) f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[(sz + i) << t]; FOR(i, l, r) f[i] = f_tmp[i]; } void inverse_exec(int l, int r, int t){ if(t == n) return; int sz = (r - l) / 2; REP(i, sz){ f_tmp[l + i] = f[l + 2 * i]; f_tmp[l + sz + i] = f[l + 2 * i + 1]; } FOR(i, l, r) f[i] = f_tmp[i]; inverse_exec(l, l + sz, t + 1); inverse_exec(l + sz, r, t + 1); REP(i, sz) f_tmp[l + i] = f[l + i] + f[l + sz + i] * pow_e[N - (i << t)]; REP(i, sz) f_tmp[l + sz + i] = f[l + i] + f[l + sz + i] * pow_e[N - ((sz + i) << t)]; FOR(i, l, r) f[i] = f_tmp[i]; } public: int N, n; ModInt e, inv_N; vector> pow_e; //array size M is converted to N = 2^n (>=M) //only for MOD = 924844033, 998244353, 1012924417 NTT(int M){ N = 1; while(M > N) N <<= 1; ModInt x; if(MOD == 924844033) x = 5; else if(MOD == 998244353) x = 3; else if(MOD == 1012924417) x = 5; assert((MOD - 1) % N == 0); e = x.pow((MOD - 1) / N); init(); } //N=2^n, e^N=1, e^k!=1 (k e): N(N), e(e){ init(); } void exec(vector> &F, bool inverse = false){ assert(F.size() == N); f.swap(F); if(!inverse) forward_exec(0, N, 0); else inverse_exec(0, N, 0); F.swap(f); if(inverse){ REP(i, N) F[i] *= inv_N; } } //if resize_result is true, the array size of the result becomes A.size() + B.size() - 1 //array size must be equal to N if negetive indices are included vector> convolution(vector> A, vector> B, bool resize_result = false){ int sA = A.size(), sB = B.size(); assert(sA <= N && sB <= N); A.resize(N); B.resize(N); exec(A); exec(B); vector> C(N); REP(i, N) C[i] = A[i] * B[i]; exec(C, true); if(resize_result) C.resize(sA + sB - 1); return C; } }; void ntt2d(mmat &F, bool inverse = false){ int n = F.size(), m = F[0].size(); NTT ntt1(m), ntt2(n); REP(i, n) ntt1.exec(F[i], inverse); REP(j, m){ mvec tmp(n); REP(i, n) tmp[i] = F[i][j]; ntt2.exec(tmp, inverse); REP(i, n) F[i][j] = tmp[i]; } } signed main(){ int X, Y, T, a, b, c, d; cin >> X >> Y >> T >> a >> b >> c >> d; a--; b--; c--; d--; mmat A(bit(X + 1), mvec(bit(Y + 1))), F(bit(X + 1), mvec(bit(Y + 1))); A[a][b] = 1; A[bit(X + 1) - 2 - a][b] = mod - 1; A[a][bit(Y + 1) - 2 - b] = mod - 1; A[bit(X + 1) - 2 - a][bit(Y + 1) - 2 - b] = 1; FOR(i, -1, 2) FOR(j, -1, 2) if(abs(i) + abs(j) <= 1) F[(i + bit(X + 1)) % bit(X + 1)][(j + bit(Y + 1)) % bit(Y + 1)] = 1; ntt2d(A); ntt2d(F); REP(i, bit(X + 1)) REP(j, bit(Y + 1)) A[i][j] *= F[i][j].pow(T); ntt2d(A, true); Out(A[c][d]); return 0; }