#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, pair& p){return is >> p.first >> p.second;} template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const pair& p){return os << p.first << " " << p.second;} template ostream& operator << (ostream& os, const vector& vec){for(size_t i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(size_t i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; namespace Montgomery{ template constexpr long long PRE_COMP(long long r, long long res=0, long long t=0, long long i = 1){ return (r>1) ? ( PRE_COMP(r/2, res + (t%2==0?i:0), (t%2==0?(t+MOD):t) / 2, i*2) ):( res ); } template class Values{ public: static constexpr long long R = 1LL<<30; // R>MOD && gcd(R,MOD)==1 static constexpr long long mask = (1LL<<30)-1; static constexpr long long R2 = (R*R)%MOD; static constexpr long long Ninv = PRE_COMP(1<<30); // N*Ninv = R-1 mod R static long long Reduction(long long x){ long long s = ((x & mask) * Ninv) & mask; long long ret = (x + s*MOD ) >> 30; if(ret>=MOD) ret -= MOD; return ret; } }; template struct M_Int{ long long value; M_Int() : value(0) {} M_Int(long long val, bool convert=true) : value(convert ? Values::Reduction(val * Values::R2) : val){} //convert==true : int -> M_Int, false : M_Int::value -> M_Int M_Int(const M_Int& x) : value( x.value ){} //M_Int -> M_Int M_Int& operator = (const M_Int& x){ value = x.value; return *this; } M_Int& operator = (const long long& x){ value = Values::Reduction(x * Values::R2); return *this; } M_Int operator * (const M_Int& x) { return M_Int( Values::Reduction(value * x.value) , false ); } M_Int operator * (const long long& x){ return (*this) * M_Int(x); } template M_Int& operator *= (const T& x){ return (*this) = (*this)*x; } M_Int operator + (const M_Int& x) { long long tmp = value + x.value; if(tmp >= MOD) tmp -= MOD; return M_Int(tmp, false); } M_Int operator + (const long long& x){ return (*this)+M_Int(x); } template M_Int& operator += (const T& x) { return (*this) = (*this) + x; } M_Int operator - (const M_Int& x) { long long tmp = value - x.value; if(tmp < 0 ) tmp += MOD; return M_Int(tmp, false); } M_Int operator - (const long long& x){ return (*this)-M_Int(x); } template M_Int& operator -= (const T& x) { return (*this) = (*this) - x; } bool operator == (const M_Int& x){ return value == x.value; } bool operator == (const long long& x){ M_Int tmp(x); return (*this)==tmp; } long long to_i () { // M_int -> int return Values::Reduction(value); } operator long long () { // M_int -> int return Values::Reduction(value); } }; template istream& operator>>(istream& is, M_Int& v){ long long tmp; is >> tmp; v=tmp; return is; } template ostream& operator<<(ostream& os, M_Int v){ return os << v.to_i(); } template M_Int operator + (long long l, M_Int r){ return r+l; } template M_Int operator - (long long l, M_Int r){ return r-l; } template M_Int operator * (long long l, M_Int r){ return r*l; } } using mint = Montgomery::M_Int; array fact; //n! array fact_inv; // (n!)^-1 #include // nCk mod p, O(1) // precomputation O(size) template class combination_mod{ //const long long size; // vector fact; //n! // vector fact_inv; // (n!)^-1 void make_fact(){ fact[0] = 1; for(long long i=1; i c; int main(){ long long n,k,d; cin >> n,k,d; long long len = n; int t = 0; while( len >= k ){ len -= k-1; t++; } if( d == 1 ){ println(len); return 0; } if(len == 1){ println( my_pow_mod(d, t, mod) ); return 0; } mint ans = 0; mint dd(1); mint d_(d); for(int x=0; x<=t; x++){ int rem = t-x; //ans += dd * c(rem+len-2, rem) % mod * (len) % mod; ans += dd * c(rem+len-2, rem); dd *= d_; } println( ans.to_i() * len % mod ); return 0; }