#include using namespace std; #define rep(i,n) for(ll i=0;i=0;i--) #define perl(i,r,l) for(ll i=r-1;i>=l;i--) #define fi first #define se second #define pb push_back #define ins insert #define pqueue(x) priority_queue,greater> #define all(x) (x).begin(),(x).end() #define CST(x) cout<> #define rev(x) reverse(x); using ll=long long; using vl=vector; using vvl=vector>; using pl=pair; using vpl=vector; using vvpl=vector; const ll MOD=1000000007; const ll MOD9=998244353; const int inf=1e9+10; const ll INF=4e17; const ll dy[9]={0,1,-1,0,1,1,-1,-1,0}; const ll dx[9]={1,0,0,-1,1,-1,1,-1,0}; template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } const int mod = 1000000007; const int max_n = 200005; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } bool operator==(const mint &p) const { return x == p.x; } bool operator!=(const mint &p) const { return x != p.x; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} using vm=vector; using vvm=vector; struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } }comb(max_n); template vector matmul(vector &dp, vector> &mt){ int m=dp.size(); vector ret(m,0); for(int i=0;i vector> update(vector> &mt){ ll m=mt.size(); vector> ret(m,vector(m,0)); for(int i=0;i void matpow(vector &dp, vector> &mt, ll k){ ll m=dp.size(); while(k){ if(k&1)dp=matmul(dp,mt); mt=update(mt); k>>=1; } } mint calc1(ll n,ll k){ return mint(k)*mint(k-1).pow(n-1); } mint calc2(ll n,ll k){ mint p=(k-2)*(k-2)+k-1; return mint(k*(k-1))*p.pow(n-1); } mint calc(ll n,ll k,ll m){//縦nマスのグリッドをk色で塗り切る if(m==1)return calc1(n,k); if(m==2)return calc2(n,k); if(k<2)return 0; if(k==2)return 2; vvm mat(2,vm(2)); mat[0][0]=mint(k-1)+mint(k-2)*mint(k-2); mat[1][0]=mint(k-1)*mint(k-1)+mint(k-2)*mint(k-2)*mint(k-2); mat[1][0]-=mat[0][0]; mat[0][1]=mint(k-2)*2+mint(k-3)*mint(k-3); mat[1][1]=mint(k-2)*mint(k-1)*2+mint(k-3)*mint(k-2)*mint(k-2); mat[1][1]-=mat[0][1]; vm dp(2);dp[0]=k*(k-1);dp[1]=k*(k-1)*(k-2); matpow(dp,mat,n-1); return dp[0]+dp[1]; } int main(){ ll n,m,k;cin >> n >> m >> k; mint ans=0; for(int i=0;i<=k;i++){ mint ret=calc(m,i,n)*comb(k,i); if((k-i)&1)ans-=ret; else ans+=ret; } cout << ans << endl; }