//Source.cpp //いつもの #ifdef LOCAL #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #else #include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #ifdef ONLINE_JUDGE #include using namespace atcoder; #else #define gcd __gcd #define lcm __detail::__lcm #endif #endif using namespace std; typedef long long ll; typedef unsigned long long ull; #ifdef LOCAL /* #include using namespace atcoder; //*/ unsigned popcount(unsigned x){ return __popcnt(x); } unsigned popcountll(ull x){ return __popcnt64(x); } unsigned parity(unsigned x){ return popcount(x)%2; } unsigned parityll(ull x){ return popcountll(x)%2; } unsigned clz(unsigned x){ if(x==0) throw; unsigned cnt=__lzcnt(x); return cnt; } unsigned clzll(ull x){ if(x==0) throw; unsigned cnt=__lzcnt64(x); return cnt; } unsigned ctz(unsigned x){ if(x==0) throw; x&=~x+1; unsigned cnt=0; if(x&0xffff0000) cnt|=16; if(x&0xff00ff00) cnt|=8; if(x&0xf0f0f0f0) cnt|=4; if(x&0xcccccccc) cnt|=2; if(x&0xaaaaaaaa) cnt|=1; return cnt; } unsigned ctzll(ull x){ if(x==0) throw; x&=~x+1; unsigned cnt=0; if(x&0xffffffff00000000) cnt|=32; if(x&0xffff0000ffff0000) cnt|=16; if(x&0xff00ff00ff00ff00) cnt|=8; if(x&0xf0f0f0f0f0f0f0f0) cnt|=4; if(x&0xcccccccccccccccc) cnt|=2; if(x&0xaaaaaaaaaaaaaaaa) cnt|=1; return cnt; } unsigned ffs(unsigned x){ if(x==0) return 0; return ctz(x)+1; } unsigned ffsll(ull x){ if(x==0) return 0; return ctzll(x)+1; } #define __builtin_popcount popcount #define __builtin_popcountll popcountll #define __builtin_parity parity #define __builtin_parityll parityll #define __builtin_clz clz #define __builtin_clzll clzll #define __builtin_ctz ctz #define __builtin_ctzll ctzll #define __builtin_ffs ffs #define __builtin_ffsll ffsll #endif constexpr int mod=1e9+7; constexpr int Mod=998244353; constexpr int inf=mod; constexpr ll linf=(ll)mod*mod; struct fastio{ fastio(){ cin.tie(0); ios::sync_with_stdio(0); cout< bool chmax(T&a,const T&b){ if(a bool chmin(T&a,const T&b){ if(a>b){ a=b; return 1; } return 0; } ll fact[200001],invfact[200001]; int main(){ fact[0]=1; for(int i=1;i<=200000;i++) fact[i]=fact[i-1]*i%mod; for(int i=0;i<=200000;i++){ ll a=fact[i]; ll mm=mod-2; ll b=1; while(mm){ if(mm&1) (b*=a)%=mod; (a*=a)%=mod; mm>>=1; } invfact[i]=b; } int n,k; ll m; cin>>n>>m>>k; int ans=0; for(ll i=1;i<=k;i++){ ll tmp=0; if(n==1){ ll a=i-1; ll x=i; ll mm=m-1; ll b=1; while(mm){ if(mm&1) (b*=a)%=mod; (a*=a)%=mod; mm>>=1; } tmp=b*x%mod; } if(n==2){ ll a=(i*i-3*i+3)%mod; ll x=(i*i-i)%mod; ll mm=m-1; ll b=1; while(mm){ if(mm&1) (b*=a)%=mod; (a*=a)%=mod; mm>>=1; } tmp=b*x%mod; } if(n==3){ ll a00=(i*i*i-i*i*6+i*14-13)%mod; ll a01=(i*i*i-i*i*6+i*13-10)%mod; ll a10=(i*i-i*4+5)%mod; ll a11=(i*i-i*3+3)%mod; ll x=(i*i*i-i*i*3+i*2)%mod; ll y=(i*i-i)%mod; ll mm=m-1; ll b00=1,b01=0,b10=0,b11=1; while(mm){ if(mm&1){ ll bb00=(b00*a00+b01*a10)%mod; ll bb01=(b00*a01+b01*a11)%mod; ll bb10=(b10*a00+b11*a10)%mod; ll bb11=(b10*a01+b11*a11)%mod; b00=bb00; b01=bb01; b10=bb10; b11=bb11; } ll aa00=(a00*a00+a01*a10)%mod; ll aa01=(a00*a01+a01*a11)%mod; ll aa10=(a10*a00+a11*a10)%mod; ll aa11=(a10*a01+a11*a11)%mod; a00=aa00; a01=aa01; a10=aa10; a11=aa11; mm>>=1; } tmp=(b00*x+b01*y+b10*x+b11*y)%mod; } (tmp*=fact[k]*invfact[i]%mod*invfact[k-i]%mod)%=mod; if((k-i)%2==1) tmp=(-tmp+mod)%mod; (ans+=tmp)%=mod; } cout<