#line 2 "/home/sakflat/CP/_library/cpp/template/template.cpp" //yukicoder@cpp17 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using P = pair; const ll MOD = 1000000007; const ll MOD2 = 1000000006; const int INF = (1<<30)-1; const ll LINF = (1LL<<62LL)-1; const double EPS = (1e-10); P ar4[4] = {{0,1},{0,-1},{1,0},{-1,0}}; P ar8[8] = {{-1,-1},{-1,0},{-1,1},{0,-1},{0,1},{1,-1},{1,0},{1,1}}; template vector make_vector(size_t a, T b) { return vector(a, b); } template auto make_vector(size_t a, Ts... ts) { return vector(a, make_vector(ts...)); } /* 確認ポイント cout << fixed << setprecision(n) << 小数計算//n桁の小数表記になる 計算量は変わらないが楽できるシリーズ min(max)_element(iter,iter)で一番小さい(大きい)値のポインタが帰ってくる count(iter,iter,int)でintがiterからiterの間にいくつあったかを取得できる */ /* function corner below */ /* Function corner above */ /* comment outed because can cause bugs __attribute__((constructor)) void initial() { cin.tie(0); ios::sync_with_stdio(false); } */ template struct ModInt{ int n; ModInt():n(0){} ModInt(int n_):n(n_ >= 0 ? n_%mod : mod - ((-n_)%mod) ){} ModInt &operator+=(const ModInt &p){ if((n+=p.n) >= mod)n-=mod; return *this; } ModInt &operator-=(const ModInt &p){ n+=mod-p.n; if(n >= mod)n-=mod; return *this; } ModInt &operator*=(const ModInt &p){ n = (int) ((1LL*n*p.n)%mod); return *this; } ModInt &operator/=(const ModInt &p){ *this *= p.inverse(); return *this; } ModInt operator-() const {return ModInt(-n);} ModInt operator+(const ModInt &p) const {return ModInt(*this) += p;} ModInt operator-(const ModInt &p) const {return ModInt(*this) -= p;} ModInt operator*(const ModInt &p) const {return ModInt(*this) *= p;} ModInt operator/(const ModInt &p) const {return ModInt(*this) /= p;} bool operator==(const ModInt &p) const {return n==p.n;} bool operator<(const ModInt &p) const {return n(const ModInt &p) const {return n>p.n;} bool operator>=(const ModInt &p) const {return n>=p.n;} bool operator<=(const ModInt &p) const {return n<=p.n;} bool operator!=(const ModInt &p) const {return n!=p.n;} ModInt inverse() const { int a = n,b = mod,u = 1,v = 0; while(b){ int t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } return ModInt(u); } ModInt pow(int64_t z) const { ModInt ret(1),mul(n); while(z > 0){ if(z & 1) ret *= mul; mul *= mul; z >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p){ return os << p.n; } friend istream &operator>>(istream &is, ModInt &a){ int64_t t; is >> t; a = ModInt (t); return (is); } }; template T uPow(T z,T n, T mod){ T ans = 1; while(n != 0){ if(n%2){ ans*=z; if(mod)ans%=mod; } n >>= 1; z*=z; if(mod)z%=mod; } return ans; } int main(){ long long a,b,n;cin>>a>>b>>n; vector> ret(b+1); for(int i = b; 1 <= i; i--){ ModInt tmp = uPow(b/i - (a-1)/i, n, MOD); for(int j = i+i; b >= j; j+=i){ tmp -= ret[j]; } ret[i] = tmp; } ModInt ans = 1; for(int i = 1; b >= i; i++){ ans *= uPow((long long)i, (long long)ret[i].n, MOD); } cout << ans << endl; return 0; }