#pragma GCC optimize("O3") #include #include #define ll long long #define rep(i,n) for(ll i=0;i<(n);i++) #define pll pair #define pii pair #define pq priority_queue #define pb push_back #define eb emplace_back #define fi first #define se second #define endl '\n' #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance(c.begin(),lower_bound(all(c),x)) #define ub(c,x) distance(c.begin(),upper_bound(all(c),x)) using namespace std; template inline bool chmax(T& a,T b){if(a inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} const int INF=1e9; using vv=vector>; const ll MOD=1e9+7; vv E(int n) //行列の初期化(単位行列) { vv res(n, vector(n)); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) res[i][j] = (i == j); //対角成分を1に、それ以外を0にする。 return res; } vv matprod(vv A, vv B) //行列の掛け算 { int l = A.size(), m = B.size(), n = B[0].size(); vv res(l, vector(n, 0)); for (int i = 0; i < l; i++) for (int j = 0; j < n; j++) for (int k = 0; k < m; k++) res[i][j] = (res[i][j] + A[i][k] * B[k][j]) % MOD; return res; } vv matpow(vv A, ll n) //行列累乗 { vv p = A, res = E(A.size()); while (n > 0) { if (n & 1) res = matprod(res, p); p = matprod(p, p); n >>= 1; } return res; } int main(){ ll a,b,n; cin >> a >> b >> n; if(n==0){ cout << 2 << endl; return 0; } n-=1; vv c(2,vector(1)); c[0][0]=2*a; c[0][0]%=MOD; c[1][0]=2; vv tran(2,vector(2)); tran[0][0]=2*a; tran[0][0]%=MOD; tran[0][1]=b-a*a; if(b-a*a<0){ ll s=abs(b-a*a); ll num=s/MOD+1; tran[0][1]+=num*MOD; } tran[0][1]%=MOD; tran[1][0]=1; tran[1][1]=0; tran=matpow(tran,n); c=matprod(tran,c); cout << c[0][0] << endl; return 0; }