#include using namespace std; #define rep(i, a) for (int i = 0; i < (int)(a); i++) #define sz(x) (int)(x).size() #define pcnt __builtin_popcountll typedef long long ll; templateistream& operator>>(istream&i,vector&v){rep(j,sz(v))i>>v[j];return i;} templatestring join(const vector&v){stringstream s;rep(i,sz(v))s<<' '<ostream& operator<<(ostream&o,const vector&v){if(sz(v))o<istream& operator>>(istream&i,pair&v){return i>>v.first>>v.second;} templateostream& operator<<(ostream&o,const pair&v){return o<bool mins(T& x,const T&y){if(x>y){x=y;return true;}else return false;} templatebool maxs(T& x,const T&y){if(xT dup(T x, T y){return (x+y-1)/y;} templatell suma(const vector&a){ll res(0);for(auto&&x:a)res+=x;return res;} int keta(ll n) { int ret = 0; while (n>0) { n/=10; ret++; } return ret; } #ifdef _DEBUG inline void dump() { cerr << endl; } template void dump(Head &&head) { cerr << head; dump(); } template void dump(Head &&head, Tail &&... tail) { cerr << head << ", "; dump(forward(tail)...); } #define debug(...) do { cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false) #else #define dump(...) #define debug(...) #endif template struct edge { int src, to; T cost; edge(int to, T cost) : src(-1), to(to), cost(cost) {} edge(int src, int to, T cost) : src(src), to(to), cost(cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template using Edges = vector>; template using WeightedGraph = vector>; using UnWeightedGraph = vector>; const ll LINF = 1LL << 60; const int INF = 1001001001; ///////////////////////////////////////////////////////////////////// template struct Matrix { int h, w; vector> d; Matrix() {} Matrix(int h, int w, T val=0): h(h), w(w), d(h, vector(w, val)) {} Matrix& unit() { assert(h == w); rep(i, h) d[i][i] = 1; return *this; } const vector& operator[](int i) const { return d[i]; } vector& operator[](int i) { return d[i]; } Matrix& operator+=(const Matrix& a) { assert(h == a.h && w == a.w); rep(i, h) rep(j, w) d[i][j] += a[i][j]; return *this; } Matrix& operator-=(const Matrix& a) { assert(h == a.h && w == a.w); rep(i, h) rep(j, w) d[i][j] -= a[i][j]; return *this; } Matrix& operator*=(const Matrix& a) { assert(w == a.h); Matrix r(h, a.w); rep(i, h) rep(k, w) rep(j, a.w) { r[i][j] += d[i][k] * a[k][j]; } rep(i, h) rep(j, w) d[i][j] = r[i][j]; return *this; } Matrix& operator/=(const Matrix& a) { assert(h == a.h && w == a.w); return *this *= a.inv(); } Matrix operator+(const Matrix& a) const { return Matrix(*this) += a; } Matrix operator-(const Matrix& a) const { return Matrix(*this) -= a; } Matrix operator*(const Matrix& a) const { return Matrix(*this) *= a; } Matrix operator/(const Matrix& a) const { return Matrix(*this) /= a; } bool operator==(const Matrix& a) { assert(h == a.h && w == a.w); rep(i, h) rep(j, w) if (d[i][j] != a[i][j]) return false; return true; } Matrix& operator+=(const T& a) { rep(i, h) rep(j, w) d[i][j] += a; return *this; } Matrix& operator-=(const T& a) { rep(i, h) rep(j, w) d[i][j] -= a; return *this; } Matrix& operator*=(const T& a) { rep(i, h) rep(j, w) d[i][j] *= a; return *this; } Matrix& operator/=(const T& a) { rep(i, h) rep(j, w) d[i][j] /= a; return *this; } Matrix operator+(const T& a) const { return Matrix(*this) += a; } Matrix operator-(const T& a) const { return Matrix(*this) -= a; } Matrix operator*(const T& a) const { return Matrix(*this) *= a; } Matrix operator/(const T& a) const { return Matrix(*this) /= a; } Matrix pow(ll t) const { assert(h == w); if (!t) return Matrix(h, h).unit(); if (t == 1) return *this; Matrix r = pow(t>>1); r = r*r; if (t&1) r = r*(*this); return r; } T det() { assert(h == w); Matrix b(*this); T ret = 1; for (int i=0; i 0) cout << " "; cout << d[i][j]; } cout << "\n"; } } }; template struct ModInt { ll x; ModInt(ll x=0):x((x%mod+mod)%mod){} ModInt operator-() const { return ModInt(-x); } ModInt& operator+=(const ModInt a) { if ((x += a.x) >= mod) x -= mod; return *this; } ModInt& operator-=(const ModInt a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } ModInt& operator*=(const ModInt a) { (x *= a.x) %= mod; return *this; } ModInt operator+(const ModInt a) const { return ModInt(*this)+=a; } ModInt operator-(const ModInt a) const { return ModInt(*this)-=a; } ModInt operator*(const ModInt a) const { return ModInt(*this)*=a; } ModInt pow(ll t) const { if (!t) return 1; ModInt a = *this, r = 1; while (t) { if (t & 1) r *= a; a *= a; t >>= 1; } return r; } ModInt inv() const { ll a = x; ll b = mod; ll c = 1, d = 0; while (b) { ll t = a/b; a -= t*b; swap(a, b); c -= t*d; swap(c, d); } c %= mod; if (c < 0) c += mod; return c; } ModInt& operator/=(const ModInt a) { return (*this) *= a.inv(); } ModInt operator/(const ModInt a) const { return ModInt(*this)/=a; } bool operator==(const ModInt a) const { return x == a.x; } bool operator!=(const ModInt a) const { return x != a.x; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { ll t; is >> t; a = ModInt(t); return (is); } }; using mint = ModInt<10>; void solve() { ll p,q,r,k; cin>>p>>q>>r>>k; Matrix mat(3, 3); Matrix a(3, 1); a[0][0] = r; a[1][0] = q; a[2][0] = p; mat[0][0] = 1; mat[0][1] = 1; mat[0][2] = 1; mat[1][0] = 1; mat[1][1] = 0; mat[1][2] = 0; mat[2][0] = 0; mat[2][1] = 1; mat[2][2] = 0; Matrix ans = mat.pow(k-3) * a; rep(i, 3) debug(ans[i][0]); cout << ans[0][0] << "\n"; } int main() { int t; t = 1; // cin>>t; while (t--) solve(); return 0; }