/* -*- coding: utf-8 -*- * * 673.cc: No.673 カブトムシ - yukicoder */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; /* constant */ const long long MOD = 1000000007; /* typedef */ typedef long long ll; /* global variables */ /* subroutines */ inline ll powmod(ll a, ll b) { ll p = 1; while (b > 0LL) { if ((b & 1LL) != 0LL) p = p * a % MOD; a = a * a % MOD; b >>= 1; } return p; } /* main */ int main() { ll b, c, d; scanf("%lld%lld%lld", &b, &c, &d); b %= MOD, c %= MOD; if (c == 1) { printf("%lld\n", b * (d % MOD) % MOD); return 0; } // x[i+1]=(x[i]+b)*c // y[i]=x[i]+a,y[i+1]=y[i]*c -> y[i] = y[0]*c^i // x[i+1]+a=(x[i]+a)*c // -> x[i+1]=(x[i]+a)*c-a=(x[i]+a-a/c)*c // -> a-a/c=b -> a*(c-1)/c=b -> a=b*c/(c-1) // x[i]=y[i]-a=y[0]*c^i-a=(X[0]+a)*c^i-a ll a = b * c % MOD * powmod(c - 1, MOD - 2) % MOD; ll r = (a * powmod(c, d) % MOD + MOD - a) % MOD; printf("%lld\n", r); return 0; }