#include using namespace std; using LL = long long int; #define incID(i, l, r) for(int i = (l) ; i < (r); i++) #define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--) #define incII(i, l, r) for(int i = (l) ; i <= (r); i++) #define decII(i, l, r) for(int i = (r) ; i >= (l); i--) #define inc(i, n) incID(i, 0, n) #define dec(i, n) decID(i, 0, n) #define inc1(i, n) incII(i, 1, n) #define dec1(i, n) decII(i, 1, n) #define inID(v, l, r) ((l) <= (v) && (v) < (r)) #define inII(v, l, r) ((l) <= (v) && (v) <= (r)) #define PB push_back #define EB emplace_back #define MP make_pair #define MT make_tuple #define FI first #define SE second #define FR front() #define BA back() #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() auto setmin = [](auto & a, auto b) { return (b < a ? a = b, true : false); }; auto setmax = [](auto & a, auto b) { return (b > a ? a = b, true : false); }; auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); }; auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); }; #define SI(v) static_cast(v.size()) #define RF(e, v) for(auto & e: v) #define until(e) while(! (e)) #define if_not(e) if(! (e)) #define ef else if #define UR assert(false) // 以下、入出力関係のテンプレ案のテスト auto * IS = & cin; // input elements (as a tuple) template void in_(U & t) { } template void in_(U & t) { (* IS) >> get(t); in_(t); } template auto in() { tuple t; in_, 0, T ...>(t); return t; } // input a array template auto ain() { array a; inc(i, N) { (* IS) >> a[i]; } return a; } // input a (multi-dimensional) vector template T vin() { return * istream_iterator(* IS); } template auto vin(N n, M ... m) { vector(m ...))> v(n); inc(i, n) { v[i] = vin(m ...); } return v; } // input multi-column (as a tuple of vector) template void colin_(U & t) { } template void colin_(U & t) { get(t).emplace_back(* istream_iterator(* IS)); colin_(t); } template auto colin(int n) { tuple ...> t; inc(i, n) { colin_ ...>, 0, T ...>(t); } return t; } auto * OS = & cout; string SP = " ", LN = "\n"; // output elements void out() { (* OS) << LN << flush; } template void out(A && a ) { (* OS) << a ; out( ); } template void out(A && a, B && ... b) { (* OS) << a << SP; out(b ...); } // output a (multi-dimensional) vector template ostream & operator<<(ostream & os, vector const & v) { inc(i, v.size()) { os << (i == 0 ? "" : SP) << v[i]; } return os << flush; } template void vout_(T && v) { (* OS) << v; } template void vout_(T && v, A a, B ... b) { for(auto && w: v) { vout_(w, b ...); (* OS) << a; } } template void vout(T && v, A ... a) { vout_(v, a ...); out(); } // ---- ---- template class DynModInt { private: static LL M; LL v; pair ext_gcd(LL a, LL b) { if(b == 0) { assert(a == 1); return { 1, 0 }; } auto p = ext_gcd(b, a % b); return { p.SE, p.FI - (a / b) * p.SE }; } public: DynModInt() { v = 0; } DynModInt(LL vv) { assert(M > 0); v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } } static void set_M(LL m) { M = m; } static LL get_M() { return M; } LL get_v() { return v; } DynModInt inv() { return ext_gcd(M, v).SE; } DynModInt exp(LL b) { DynModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; } while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; } return p; } friend bool operator< (DynModInt a, DynModInt b) { return (a.v < b.v); } friend bool operator> (DynModInt a, DynModInt b) { return (a.v > b.v); } friend bool operator<=(DynModInt a, DynModInt b) { return (a.v <= b.v); } friend bool operator>=(DynModInt a, DynModInt b) { return (a.v >= b.v); } friend bool operator==(DynModInt a, DynModInt b) { return (a.v == b.v); } friend bool operator!=(DynModInt a, DynModInt b) { return (a.v != b.v); } friend DynModInt operator+ (DynModInt a ) { return DynModInt(+a.v); } friend DynModInt operator- (DynModInt a ) { return DynModInt(-a.v); } friend DynModInt operator+ (DynModInt a, DynModInt b) { return DynModInt(a.v + b.v); } friend DynModInt operator- (DynModInt a, DynModInt b) { return DynModInt(a.v - b.v); } friend DynModInt operator* (DynModInt a, DynModInt b) { return DynModInt(a.v * b.v); } friend DynModInt operator/ (DynModInt a, DynModInt b) { return a * b.inv(); } friend DynModInt operator^ (DynModInt a, LL b) { return a.exp(b); } friend DynModInt & operator+=(DynModInt & a, DynModInt b) { return (a = a + b); } friend DynModInt & operator-=(DynModInt & a, DynModInt b) { return (a = a - b); } friend DynModInt & operator*=(DynModInt & a, DynModInt b) { return (a = a * b); } friend DynModInt & operator/=(DynModInt & a, DynModInt b) { return (a = a / b); } friend DynModInt & operator^=(DynModInt & a, LL b) { return (a = a ^ b); } friend istream & operator>>(istream & s, DynModInt & b) { s >> b.v; b = DynModInt(b.v); return s; } friend ostream & operator<<(ostream & s, DynModInt b) { return (s << b.v); } }; template LL DynModInt::M = 0; // ---- using DMI = DynModInt<>; auto fl = [](auto a, auto b) { assert(b != 0); return a / b - (a % b != 0 && ((a >= 0) != (b >= 0)) ? 1 : 0); }; auto ce = [](auto a, auto b) { assert(b != 0); return a / b + (a % b != 0 && ((a >= 0) == (b >= 0)) ? 1 : 0); }; auto mo = [](auto a, auto b) { assert(b != 0); a %= b; if(a < 0) { a += abs(b); } return a; }; // { x in (l, r] | x mod m = a } の要素数 LL cmCI(LL l, LL r, LL m, LL a) { assert(m > 0); return max(0LL, fl(r - a, m) - fl(l - a, m)); } LL cmCD(LL l, LL r, LL m, LL a) { return cmCI(l , r - 1, m, a); } LL cmII(LL l, LL r, LL m, LL a) { return cmCI(l - 1, r , m, a); } LL cmID(LL l, LL r, LL m, LL a) { return cmCI(l - 1, r - 1, m, a); } int main() { auto [a, b, c] = ain(); DMI::set_M(c); DMI ans = 0; inc(i, c) { ans += cmII(1, a, c, i) * (DMI(i) ^ b); } out(ans); }