#include "bits/stdc++.h" using namespace std; using ll=long long; using vll=vector< ll>; using vvll=vector< vll>; using vvvll=vector< vvll>; using vvvvll=vector; using dd=double; using vdd=vector< dd>; using vvdd=vector< vdd>; using pll=pair; using tll=tuple; using qll=tuple; using vpll=vector< pll>; constexpr ll INF = 1LL << 60; struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<::max_digits10); } } fast; #define REPS(i, S, E) for (ll i = (S); i <= (E); i++) #define REP(i, N) REPS(i, 0, (N)-1) #define DEPS(i, S, E) for (ll i = (E); i >= (S); i--) #define DEP(i, N) DEPS(i, 0, (N)-1) #define rep(i, S, E) for (ll i = (S); i <= (E); i++) #define dep(i, E, S) for (ll i = (E); i >= (S); i--) #define each(e, v) for (auto&& e : v) #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; } template inline T MaxE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; } template inline T MinE(vector&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; } template inline T MaxE(vector &v) { return MaxE(v,0,(ll)v.size()-1); } template inline T MinE(vector &v) { return MinE(v,0,(ll)v.size()-1); } template inline T Sum(vector &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; } template inline T Sum(vector &v) { return Sum(v,0,v.size()-1); } template inline ll sz(T &v){ return (ll)v.size(); } inline ll CEIL(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } inline ll FLOOR(ll a,ll b){ return -CEIL(-a,b); } template struct mll_{ ll val; mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; } mll_ operator - () const { return -val; } mll_ operator + (const mll_ &b) const { return val + b.val; } mll_ operator - (const mll_ &b) const { return val - b.val; } mll_ operator * (const mll_ &b) const { return val * b.val; } mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; } mll_ operator + (ll b) const { return *this + mll_(b); } mll_ operator - (ll b) const { return *this - mll_(b); } mll_ operator * (ll b) const { return *this * mll_(b); } friend mll_ operator + (ll a,const mll_ &b) { return b + a; } friend mll_ operator - (ll a,const mll_ &b) { return -b + a; } friend mll_ operator * (ll a,const mll_ &b) { return b * a; } friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; } mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; } mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; } mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; } mll_ &operator /= (const mll_ &b) { ll c=b.val,d=MOD,u=1,v=0; while (d){ ll t = c / d; c -= t * d; swap(c,d); u -= t * v; swap(u,v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } mll_ &operator += (ll b) { return *this += mll_(b); } mll_ &operator -= (ll b) { return *this -= mll_(b); } mll_ &operator *= (ll b) { return *this *= mll_(b); } mll_ &operator /= (ll b) { return *this /= mll_(b); } bool operator == (const mll_ &b) const { return val == b.val; } bool operator != (const mll_ &b) const { return val != b.val; } bool operator == (ll b) const { return *this == mll_(b); } bool operator != (ll b) const { return *this != mll_(b); } friend bool operator == (ll a,const mll_ &b) { return mll_(a) == b.val; } friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; } friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; } friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; } static mll_ Combination(ll a,ll b){ chmin(b,a-b); if (b<0) return mll_(0); mll_ c = 1; rep(i,0,b-1) c *= a-i; rep(i,0,b-1) c /= i+1; return c; } }; using mll = mll_<1000000007LL>; using vmll = std::vector; using vvmll = std::vector; using vvvmll = std::vector; using vvvvmll = std::vector; template struct MatG{ ll h=0, w=0; //h行w列 vector> mat; MatG(){} MatG(ll h_, ll w_, T x) { init(h_, w_, x); } MatG(ll h_, ll w_) { init(h_, w_); } MatG(ll h_, ll w_, string c) { init(h_, w_, c); } void init(ll h_, ll w_, T x){ h=h_; w=w_; mat.assign(h, vector(w,x)); } void init(ll h_, ll w_){ init(h_,w_,T()); } void init(ll h_, ll w_, string c){ init(h_, w_); if(c=="E")E(); } ll H() const { return h; } ll W() const { return w; } bool invalid() const { return mat.empty(); } vector &operator[](ll i) { return mat[i]; } const vector &operator[](ll i) const { return mat[i]; } MatG &operator+=(const MatG &B) {REP(i,h)REP(j,w) mat[i][j]+=B[i][j];return *this;} MatG operator+(const MatG &B) const {return MatG(*this) += B;} MatG operator*(const MatG &B) const { MatG ret(h, B.W()); REP(i, h) REP(j, B.W()) REP(k, w) ret[i][j] += mat[i][k] * B[k][j]; return move(ret); } vector operator*(const vector &v) const { vector ret(v.size()); REP(i, this->h) REP(j, this->w) ret[i] += this->mat[i][j] * v[j]; return move(ret); } MatG Pow(ll N) const { MatG ret(*this), a(*this); for (ll n=N-1; n>0; n>>=1, a=a*a){ if (n&1) ret=ret*a; } return move(ret); } MatG t() const { MatG ret(this->w, this->h); REP(i, this->w) REP(j, this->h) ret[i][j] = this->mat[j][i]; return move(ret); } void E(){ rep(i, 0, min(h,w)-1) mat[i][i]=1; } #if defined(_DEBUG) void dump() { ::dump(mat); } #endif MatG(MatG &&B){ *this=move(B); } //以下、ムーブ対応 MatG(MatG const &B){ *this=B; } MatG &operator=(MatG &&B){ h=B.h; w=B.w; mat.swap(B.mat); return *this; } MatG &operator=(MatG const &B){ h=B.h; w=B.w; mat=B.mat; return *this; } }; using Mat = MatG; #if 0 #include using namespace atcoder; #endif void solve() { ll a,b; cin >> a >> b; ll n; cin >> n; if (n==0){ cout << 2 << '\n'; return; } if (n==1){ cout << 2*a << '\n'; return; } if (n==2){ cout << 2*a*a+2*b << '\n'; return; } Mat m(2,2); m[0][0]=2*a; m[0][1]=b-a*a; m[1][0]=1; m[1][1]=0; Mat r=m.Pow(n-2); vmll v{mll(2*a*a+2*b),mll(2*a)}; v=r*v; cout << v[0] << '\n'; } int main(){ #if 1 solve(); #else ll t; cin >> t; rep(i, 0, t-1){ solve(); } #endif return 0; }