#include using namespace std; #include using namespace atcoder; //高速化 struct ponjuice{ponjuice(){cin.tie(0);ios::sync_with_stdio(0);cout<using vc = vector; templateusing vvc = vc>; templateusing vvvc = vvc>; using vi = vc; using vvi = vvc; using vvvi = vvvc; using vl = vc; using vvl = vvc; using vvvl = vvvc; using pi = pair; using pl = pair; using ull = unsigned ll; templateusing priq = priority_queue; templateusing priqg = priority_queue, greater>; // for文 #define overload4(a, b, c, d, e, ...) e #define rep1(n) for(ll i = 0; i < n; i++) #define rep2(i, n) for(ll i = 0; i < n; i++) #define rep3(i, a, b) for(ll i = a; i < b; i++) #define rep4(i, a, b, step) for(ll i = a; i < b; i+= step) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define per1(n) for(ll i = n-1; i >= 0; i--) #define per2(i, n) for(ll i = n-1; i >= 0; i--) #define per3(i, a, b) for(ll i = b-1; i >= a; i--) #define per4(i, a, b, step) for(ll i = b-1; i >= a; i-= step) #define per(...) overload4(__VA_ARGS__, per4, per3, per2, per1)(__VA_ARGS__) #define fore1(a) for(auto&& i : a) #define fore2(i,a) for(auto&& i : a) #define fore3(x,y,a) for(auto&& [x, y] : a) #define fore4(x,y,z,a) for(auto&& [x, y, z] : a) #define fore(...) overload4(__VA_ARGS__, fore4, fore3, fore2, fore1)(__VA_ARGS__) //関数 #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define si(x) (ll)(x).size() templateinline bool chmax(S& a, T b){return a < b && ( a = b , true);} templateinline bool chmin(S& a, T b){return a > b && ( a = b , true);} templatevoid uniq(vc&a){sort(all(a));a.erase(unique(all(a)),a.end());} templatevc operator++(vc&v,signed){auto res = v;fore(e,v)e++;return res;} templatevc operator--(vc&v,signed){auto res = v;fore(e,v)e--;return res;} templatevc operator++(vc&v){fore(e,v)e++;return v;} templatevc operator--(vc&v){fore(e,v)e--;return v;} //入出力(operator) templateistream&operator>>(istream&is,static_modint&a){ll v;is>>v;a=v;return is;} istream&operator>>(istream&is,modint&a){ll v;cin>>v;a=v;return is;} templateistream&operator>>(istream&is,pair&a){is>>a.a>>a.b;return is;} templateistream&operator>>(istream&is,vc&a){fore(e,a)is>>e;return is;} templateostream&operator<<(ostream&os,static_modinta){return os<ostream&operator<<(ostream&os,pair&a){return os<ostream&operator<<(ostream&os,set&a){fore(it,a){os<ostream&operator<<(ostream&os,multiset&a){fore(it,a){os<ostream&operator<<(ostream&os,map&a){fore(x,y,a){os<ostream&operator<<(ostream&os,unordered_set&a){fore(it,a){os<ostream&operator<<(ostream&os,unordered_map&a){fore(x,y,a){os<ostream&operator<<(ostream&os,vc&a){fore(e,a)os<ostream&operator<<(ostream&os,vvc&a){fore(e,a)os<>a;return a;} vl readvl(ll n){vl a(n);cin>>a;return a;} vvi readg(ll n,ll m,bool bidirected=true){vvi g(n);rep(i,m){ll a,b;cin>>a>>b;a--;b--;g[a].emplace_back(b);if(bidirected)g[b].emplace_back(a);}return g;} vvcreadgc(ll n,ll m,bool bidirected=true){vvc g(n);rep(i,m){ll a,b,c;cin>>a>>b>>c;a--;b--;g[a].emplace_back(b,c);if(bidirected)g[b].emplace_back(a,c);}return g;} vvi readt(ll n,bool bidirected=true){return readg(n,n-1,bidirected);} vvc readtc(ll n,bool bidirected=true){return readgc(n,n-1,bidirected);} inline void yes(){cout << "Yes\n";} inline void no(){cout << "No\n";} inline void yesno(bool y = true){if(y)yes();else no();} inline void print(){cout<inline void print(T a){cout<inline void print(T a,Ts ...b){cout<>t; while(t--)solve(); } const int MAX = 5100000; ll fac[MAX], finv[MAX], inv[MAX]; void cominit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i %mod; inv[i] = mod - inv[mod%i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } ll com(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } void solve(){ cominit(); ll h,w,m; cin >> h >> w >> m; if(m < h+w-1){ print(0); return; } mint ans = com(h+w-2, h-1); ans *= mint(m).pow(h*w-h-w+1); ll k = m - h - w + 2; rep(i, h+w-1){ ans *= mint(k+i); ans /= mint(i+1); } print(ans); }