//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; } int mypow(ll x,ll n){ ll res=1; while(n){ if(n&1) (res*=x)%=mod; (x*=x)%=mod; n>>=1; } return res; } int inv(int n){ return mypow(n,mod-2); } ll fact[200001],facinv[200001]; int comb(int n,int k){ return fact[n]*facinv[k]%mod*facinv[n-k]%mod; } typedef vectorvec; typedef vectormat; mat mul(mat a,mat b){ mat c(a.size(),vec(b[0].size())); for(int i=0;i>=1; } return b; } 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++) facinv[i]=inv(fact[i]); int n,k; ll m; cin>>n>>m>>k; int ans=0; for(ll i=1;i<=k;i++){ mat a,b,c; switch(n){ case 1: a.assign(1,vec(1)); b.assign(1,vec(1)); c.assign(1,vec(1)); a[0][0]=1; b[0][0]=i-1; c[0][0]=i; break; case 2: a.assign(1,vec(1)); b.assign(1,vec(1)); c.assign(1,vec(1)); a[0][0]=1; b[0][0]=(i*i-3*i+3)%mod; c[0][0]=(i*i-i)%mod; break; case 3: a.assign(1,vec(2)); b.assign(2,vec(2)); c.assign(2,vec(1)); a[0][0]=1; a[0][1]=1; b[0][0]=(i*i*i-i*i*6+i*14-13)%mod; b[0][1]=(i*i*i-i*i*6+i*13-10)%mod; b[1][0]=(i*i-i*4+5)%mod; b[1][1]=(i*i-i*3+3)%mod; c[0][0]=(i*i*i-i*i*3+i*2)%mod; c[1][0]=(i*i-i)%mod; break; } ll tmp=mul(a,mul(pow_mat(b,m-1),c))[0][0]; (tmp*=comb(k,i))%=mod; if((k-i)%2==1) tmp=(-tmp+mod)%mod; (ans+=tmp)%=mod; } cout<