#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (1000000007U) struct modint{ static unsigned md; unsigned val; modint(){ val=0; } modint(int a){ val = ord(a); } modint(unsigned a){ val = ord(a); } modint(long long a){ val = ord(a); } modint(unsigned long long a){ val = ord(a); } void setmod(unsigned m){ md = m; } unsigned ord(unsigned a){ return a%md; } unsigned ord(int a){ a %= (int)md; if(a < 0){ a += md; } return a; } unsigned ord(unsigned long long a){ return a%md; } unsigned ord(long long a){ a %= (int)md; if(a < 0){ a += md; } return a; } unsigned get(){ return val; } modint &operator+=(modint a){ val += a.val; if(val >= md){ val -= md; } return *this; } modint &operator-=(modint a){ if(val < a.val){ val = val + md - a.val; } else{ val -= a.val; } return *this; } modint &operator*=(modint a){ val = ((unsigned long long)val*a.val)%md; return *this; } modint &operator/=(modint a){ return *this *= a.inverse(); } modint operator+(modint a){ return modint(*this)+=a; } modint operator-(modint a){ return modint(*this)-=a; } modint operator*(modint a){ return modint(*this)*=a; } modint operator/(modint a){ return modint(*this)/=a; } modint operator+(int a){ return modint(*this)+=modint(a); } modint operator-(int a){ return modint(*this)-=modint(a); } modint operator*(int a){ return modint(*this)*=modint(a); } modint operator/(int a){ return modint(*this)/=modint(a); } modint operator+(long long a){ return modint(*this)+=modint(a); } modint operator-(long long a){ return modint(*this)-=modint(a); } modint operator*(long long a){ return modint(*this)*=modint(a); } modint operator/(long long a){ return modint(*this)/=modint(a); } modint operator-(void){ modint res; if(val){ res.val=md-val; } else{ res.val=0; } return res; } operator bool(void){ return val!=0; } operator int(void){ return get(); } operator long long(void){ return get(); } modint inverse(){ int a = val; int b = md; int u = 1; int v = 0; int t; modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += md; } res.val = u; return res; } modint pw(unsigned long long b){ modint a(*this); modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } bool operator==(int a){ return ord(a)==val; } bool operator!=(int a){ return ord(a)!=val; } } ; unsigned modint::md; modint operator+(int a, modint b){ return modint(a)+=b; } modint operator-(int a, modint b){ return modint(a)-=b; } modint operator*(int a, modint b){ return modint(a)*=b; } modint operator/(int a, modint b){ return modint(a)/=b; } modint operator+(long long a, modint b){ return modint(a)+=b; } modint operator-(long long a, modint b){ return modint(a)-=b; } modint operator*(long long a, modint b){ return modint(a)*=b; } modint operator/(long long a, modint b){ return modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(long long &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(modint x){ int i; i = (int)x; wt_L(i); } template inline T pow_L(T a, S b){ T res = 1; res = 1; for(;;){ if(b&1){ res *= a; } b >>= 1; if(b==0){ break; } a *= a; } return res; } inline double pow_L(double a, double b){ return pow(a,b); } long long a; long long b; long long c; modint r; int main(){ { modint x; x.setmod(MD); } rd(a); rd(b); rd(c); r.md=c; { int Lj4PdHRW; for(Lj4PdHRW=(1);Lj4PdHRW<((c) + 1);Lj4PdHRW++){ r+=a--/+c*(pow_L(modint(Lj4PdHRW),b)); } } wt_L(r); wt_L('\n'); return 0; } // cLay varsion 20200509-1 // --- original code --- // ll a,b,c;modint r;{rd(a,b,c);r.md=c;r+=a--/+c*modint(1..c)**b;wt(r);}