#include #include using namespace std; using ll = long long; using mint = atcoder::modint; struct dsu { public: int csz; dsu() : _n(0) {} dsu(int n) : _n(n), csz(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); csz--; parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } int _n; // root node: -1 * component size // otherwise: parent std::vector parent_or_size; }; int main(){ ios::sync_with_stdio(false); cin.tie(0); int h, w; ll k; int m; cin >> h >> w >> k >> m; mint::set_mod(m); vector fact(26); vector comb(26, vector(26)); comb[0][0] = 1; fact[0] = 1; for(int i = 1; i <= 25; i++){ fact[i] = i * fact[i - 1]; comb[i][0] = 1; for(int j = 1; j <= i; j++){ comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j]; } } vector tb(26), div(26); for(int i = 1; i <= 25; i++){ tb[i] = mint(i).pow(k); div[i] = mint(i).inv(); } mint den; for(int i = 1; i <= h * w; i++) den += div[i]; dsu uf(h * w); auto f = [&](int S){ auto &&tmp = uf.parent_or_size; fill(tmp.begin(), tmp.end(), -1); for(int y = 0; y + 1 < h; y++){ for(int x = 0; x < w; x++){ int u = y * w + x; int v = (y + 1) * w + x; if((S >> u & 1) && (S >> v & 1)) uf.merge(u, v); } } for(int y = 0; y < h; y++){ for(int x = 0; x + 1 < w; x++){ int u = y * w + x; int v = y * w + x + 1; if((S >> u & 1) && (S >> v & 1)) uf.merge(u, v); } } mint res; for(int i = 0; i < h * w; i++){ if((S >> i & 1) && uf.leader(i) == i) res += tb[uf.size(i)]; } return res; }; mint ans; for(int S = 1; S < (1 << (h * w)); S++){ ans += f(S); } ans *= den; ans /= 1 << h * w; cout << ans.val() << '\n'; }