結果

問題 No.1275 綺麗な式
ユーザー re_re0101re_re0101
提出日時 2021-06-10 00:29:10
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 30,718 bytes
コンパイル時間 2,299 ms
コンパイル使用メモリ 210,448 KB
実行使用メモリ 6,288 KB
最終ジャッジ日時 2023-08-19 10:37:28
合計ジャッジ時間 5,485 ms
ジャッジサーバーID
(参考情報)
judge11 / judge9
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 3 ms
6,140 KB
testcase_01 AC 3 ms
6,088 KB
testcase_02 AC 3 ms
6,024 KB
testcase_03 AC 3 ms
6,080 KB
testcase_04 AC 3 ms
6,208 KB
testcase_05 AC 3 ms
6,016 KB
testcase_06 AC 4 ms
5,980 KB
testcase_07 AC 3 ms
6,020 KB
testcase_08 AC 3 ms
6,080 KB
testcase_09 AC 4 ms
6,204 KB
testcase_10 AC 3 ms
6,140 KB
testcase_11 AC 2 ms
5,884 KB
testcase_12 AC 3 ms
6,260 KB
testcase_13 AC 3 ms
6,288 KB
testcase_14 AC 3 ms
6,200 KB
testcase_15 AC 3 ms
6,144 KB
testcase_16 AC 3 ms
6,140 KB
testcase_17 AC 3 ms
5,988 KB
testcase_18 AC 2 ms
6,012 KB
testcase_19 AC 3 ms
6,200 KB
testcase_20 AC 3 ms
6,076 KB
testcase_21 AC 3 ms
6,256 KB
testcase_22 AC 3 ms
6,264 KB
testcase_23 AC 3 ms
6,148 KB
testcase_24 AC 3 ms
6,204 KB
testcase_25 AC 4 ms
6,076 KB
testcase_26 AC 3 ms
5,916 KB
testcase_27 AC 3 ms
6,000 KB
testcase_28 AC 3 ms
6,144 KB
testcase_29 AC 3 ms
6,072 KB
testcase_30 AC 2 ms
6,080 KB
testcase_31 AC 3 ms
6,076 KB
testcase_32 AC 4 ms
6,204 KB
testcase_33 AC 2 ms
6,132 KB
testcase_34 AC 3 ms
6,260 KB
testcase_35 AC 3 ms
6,076 KB
testcase_36 AC 4 ms
5,964 KB
testcase_37 AC 3 ms
5,916 KB
testcase_38 AC 3 ms
5,980 KB
testcase_39 AC 2 ms
6,140 KB
testcase_40 AC 3 ms
6,148 KB
testcase_41 AC 2 ms
6,020 KB
testcase_42 AC 3 ms
6,260 KB
testcase_43 AC 3 ms
5,988 KB
testcase_44 AC 4 ms
6,144 KB
testcase_45 AC 3 ms
5,980 KB
testcase_46 AC 3 ms
6,144 KB
testcase_47 AC 3 ms
6,208 KB
testcase_48 AC 3 ms
5,976 KB
testcase_49 AC 3 ms
5,908 KB
testcase_50 AC 3 ms
6,080 KB
testcase_51 AC 3 ms
6,148 KB
testcase_52 AC 4 ms
6,148 KB
testcase_53 AC 4 ms
6,140 KB
testcase_54 AC 3 ms
6,024 KB
testcase_55 AC 3 ms
6,196 KB
testcase_56 AC 2 ms
6,012 KB
testcase_57 AC 3 ms
5,912 KB
testcase_58 AC 3 ms
5,960 KB
testcase_59 AC 3 ms
6,168 KB
testcase_60 AC 3 ms
6,200 KB
testcase_61 AC 3 ms
5,956 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

// #pragma GCC optimize ("O3")
// #pragma GCC target("avx512f")
// #pragma GCC optimize("unroll-loops")
// #ifndef ONLINE_JUDGE
// #define _GLIBCXX_DEBUG
// #endif
#include<bits/stdc++.h>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// #include <boost/rational.hpp>
// namespace mp = boost::multiprecision;
// using Bint=mp::cpp_int;
// using Real = mp::number<mp::cpp_dec_float<1024>>;
// #include<atcoder/all>
using namespace std;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define bit(n,k) (((ll)n>>(ll)k)&1) /*nのk bit目*/
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define eb emplace_back
#define endl '\n'
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define PI 3.14159265359
const double eps = 1e-12;
const long long INF= (long long)1e18+20;
const int inf= 1010101010;
typedef long double D;      // 座標値の型。doubleかlong doubleを想定
typedef complex<D> Point;  // Point
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl>vvl;
typedef vector<vvl>vvvl;
typedef vector<vvvl>vvvvl;
typedef vector<vvvvl>vvvvvl;
typedef vector<int>vi;
typedef vector<vi>vvi;
typedef vector<vvi>vvvi;
typedef vector<vvvi>vvvvi;
typedef vector<vvvvi>vvvvvi;
typedef pair<ll,ll> P;
// typedef double D;    
template<class T> using minpq=priority_queue<T,vector<T>,greater<T>>;
const ll MOD=1000000007LL;
// const ll MOD=998244353LL;
const ll mod=MOD;
vl dx={0,0,1,-1,1,1,-1,-1};
vl dy={1,-1,0,0,-1,1,-1,1};


template<class T> vector<T> make_vec(size_t a) { return vector<T>(a); }
template<class T, class... Ts> auto make_vec(size_t a, Ts... ts) {
  return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

//素因数分解O(√n)
map<ll,ll>prime_factor(ll n){
  map<ll,ll>res;
  for(ll i=2;i*i<=n;i++){
    while(n%i==0){
      res[i]++;
      n/=i;
    }
  }
  if(n!=1)res[n]=1;
  return res;
}

const ll MAX = 5000010;
long long fac[MAX], finv[MAX], inv[MAX];
//finvが階乗の逆元

// テーブルを作る前処理
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (ll i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}

// 二項係数計算
long long COM(ll n, ll k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

ll modpow(ll a, ll n,ll mod=MOD) {

    ll res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

/*Eratosthenes()
ll N=2000010;
vl arr(N);
void Eratosthenes(){
  for(ll i = 0; i < N; i++){
    arr[i] = 1;
  }
        arr[1]=0;
  for(ll i = 2; i < sqrt(N); i++){
    if(arr[i]){
      for(ll j = 0; i * (j + 2) < N; j++){
        arr[i *(j + 2)] = 0;
      }
    }
  }
}*/
//素数判定O(√n)
bool is_prime(ll n){
  for(ll i=2;i*i<=n;i++){
    if(n%i==0)return false;
  }
  return n!=1;
}

//約数の列挙O(√n)
vector<ll>divisor(ll n){
  vector<ll>res;
  for(ll i=1;i*i<=n;i++){
    if(n%i==0){
      res.push_back(i);
      if(i != n/i) res.push_back(n/i);
    }
  }
  return res;
}


/* Trie 木: 文字の種類(char_size)、int型で0に対応する文字(base)
    insert(word): 単語 word を Trie 木に挿入する
    search(word): 単語 word が Trie 木にあるか判定する
    start_with(prefix):  prefix が一致する単語が Trie 木にあるか判定する
    count(): 挿入した単語の数を返す
    size(): Trie 木の頂点数を返す
    計算量:insert, search ともに O(M)(Mは単語の長さ)
*/
template <int char_size, int base>
struct Trie {
    struct Node {            // 頂点を表す構造体
        vector<int> next;    // 子の頂点番号を格納。存在しなければ-1
        vector<int> accept;  // 末端がこの頂点になる単語の word_id を保存
        int c;               // base からの間隔をint型で表現したもの
        int common;          // いくつの単語がこの頂点を共有しているか
        Node(int c_) : c(c_), common(0) {
            next.assign(char_size, -1);
        }
    };
    vector<Node> nodes;  // trie 木本体
    int root;
    Trie() : root(0) {
        nodes.push_back(Node(root));
    }
    // 単語の挿入
    void insert(const string &word, int word_id) {
        int node_id = 0;
        for (int i = 0; i < (int)word.size(); i++) {
            int c = (int)(word[i] - base);
            int &next_id = nodes[node_id].next[c];
            if (next_id == -1) {  // 次の頂点が存在しなければ追加
                next_id = (int)nodes.size();
                nodes.push_back(Node(c));
            }
            ++nodes[node_id].common;
            node_id = next_id;
        }
        ++nodes[node_id].common;
        nodes[node_id].accept.push_back(word_id);
    }
    void insert(const string &word) {
        insert(word, nodes[0].common);
    }
    // 単語とprefixの検索
    bool search(const string &word, bool prefix = false) {
        int node_id = 0;
        for (int i = 0; i < (int)word.size(); i++) {
            int c = (int)(word[i] - base);
            int &next_id = nodes[node_id].next[c];
            if (next_id == -1) {  // 次の頂点が存在しなければ終了
                return false;
            }
            node_id = next_id;
        }
        return (prefix) ? true : nodes[node_id].accept.size() > 0;
    }
    // prefix を持つ単語が存在するかの検索
    bool start_with(const string &prefix) {
        return search(prefix, true);
    }
    // 挿入した単語の数
    int count() const {
        return (nodes[0].common);
    }
    // Trie木のノード数
    int size() const {
        return ((int)nodes.size());
    }
};

// //Lowest Common Ancestor
// struct Edge{
//     int to;
//     Edge(int to):to(to){}
// };
 
// using Graph = vector<vector<Edge>>;
// class lca {
// public:
//     const int n = 0;
//     const int log2_n = 0;
//     vector<vector<int>> parent;
//     vector<int> depth;
 
//     lca() {}
   
//     //g:グラフ root:根
//     lca(const Graph &g, int root)
//         : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, vector<int>(n)), depth(n) {
//         dfs(g, root, -1, 0);
//         for (int k = 0; k + 1 < log2_n; k++) {
//             for (int v = 0; v < (int)g.size(); v++) {
//                 if (parent[k][v] < 0)
//                     parent[k + 1][v] = -1;
//                 else
//                     parent[k + 1][v] = parent[k][parent[k][v]];
//             }
//         }
//     }
 
//     void dfs(const Graph &g, int v, int p, int d) {
//         parent[0][v] = p;
//         depth[v] = d;
//         for (auto &e : g[v]) {
//             if (e.to != p) dfs(g, e.to, v, d + 1);
//         }
//     }
//     //uとvのlcaを取得
//     int get(int u, int v) {
//         if (depth[u] > depth[v]) swap(u, v);
//         for (int k = 0; k < log2_n; k++) {
//             if ((depth[v] - depth[u]) >> k & 1) {
//                 v = parent[k][v];
//             }
//         }
//         if (u == v) return u;
//         for (int k = log2_n - 1; k >= 0; k--) {
//             if (parent[k][u] != parent[k][v]) {
//                 u = parent[k][u];
//                 v = parent[k][v];
//             }
//         }
//         return parent[0][u];
//     }
// 	int dep(int i) {
// 		return depth[i];
// 	}
//     int dist(int u,int v){
//         return depth[u]+depth[v]-depth[get(u,v)]*2;
//     }
// };

// union by size + path having
class UnionFind {
public:
    vector <ll> par; // 各元の親を表す配列
    vector <ll> siz; // 素集合のサイズを表す配列(1 で初期化)

    // Constructor
    UnionFind(ll sz_): par(sz_), siz(sz_, 1LL) {
        for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
    }
    void init(ll sz_) {
        par.resize(sz_);
        siz.assign(sz_, 1LL);  // resize だとなぜか初期化されなかった
        for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
    }

    // Member Function
    // Find
    ll root(ll x) { // 根の検索
        while (par[x] != x) {
            x = par[x] = par[par[x]]; // x の親の親を x の親とする
        }
        return x;
    }

    // Union(Unite, Merge)
    bool merge(ll x, ll y) {
        x = root(x);
        y = root(y);
        if (x == y) return false;
        // merge technique(データ構造をマージするテク.小を大にくっつける)
        if (siz[x] < siz[y]) swap(x, y);
        siz[x] += siz[y];
        par[y] = x;
        return true;
    }

    bool issame(ll x, ll y) { // 連結判定
        return root(x) == root(y);
    }

    ll size(ll x) { // 素集合のサイズ
        return siz[root(x)];
    }
};

// 0-indexed parmutation only
vvl cycle_partition(const vl &p){
    ll n=p.size();
    vvl ret;
    vector<bool> check(n,false);
    rep(i,n)if(!check[p[i]]){
        vl v;
        ll pos=p[i];
        v.pb(i);
        check[i]=true;
        while(pos!=i){
            v.pb(pos);
            check[pos]=true;
            pos=p[pos];
        }
        ret.pb(v);
    }
    return ret;
}

vl Z_algorithm(vl s){
    ll c=0,n=s.size();
    vl Z(n,0);
    for(ll i=1;i<n;i++){
        ll l=i-c;
        if(i+Z[l]<c+Z[c]){
            Z[i]=Z[l];
        }else{
            ll j=max(0LL,c+Z[c]-i);
            while(i+j<n && s[j]==s[i+j])j++;
            Z[i]=j;
            c=i;
        }
    }
    Z[0]=n;
    return Z;
}

//Manachar 修理中
// vl Manachar(string S){
//     ll c=0,n=S.size();
//     vl R(n,1);
//     for(ll i=0;i<n;i++){
//         ll l=c-(i-c);
//         if(i+R[l]<c+R[c]){
//             R[i]=R[l];
//         }else{
//             ll j=c+R[c]-i;
//             while(i-j>=0 && i+j<n && S[i-j] == S[i+j])j++;
//             R[i]=j;
//             c=i;
//         }
//     }
//     return R;
// }



template <typename T>
T pow(T a, long long n, T e = 1) {
    T ret = e;
    while (n) {
        if (n & 1) ret *= a;
        a *= a;
        n >>= 1;
    }
    return ret;
}
 
template <int mod>
struct ModInt {
    int x;
    ModInt() : x(0) {}
    ModInt(long long x_) {
        if ((x = x_ % mod + mod) >= mod) x -= mod;
    }
    ModInt& operator+=(ModInt rhs) {
        if ((x += rhs.x) >= mod) x -= mod;
        return *this;
    }
    ModInt& operator-=(ModInt rhs) {
        if ((x -= rhs.x) < 0) x += mod;
        return *this;
    }
    ModInt& operator*=(ModInt rhs) {
        x = (unsigned long long)x * rhs.x % mod;
        return *this;
    }
    ModInt& operator/=(ModInt rhs) {
        x = (unsigned long long)x * rhs.inv().x % mod;
        return *this;
    }
 
    ModInt operator-() const { return -x < 0 ? mod - x : -x; }
    ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; }
    ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; }
    ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; }
    ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; }
    bool operator==(ModInt rhs) const { return x == rhs.x; }
    bool operator!=(ModInt rhs) const { return x != rhs.x; }
    ModInt inv() const { return pow(*this, mod - 2); }
 
    friend ostream& operator<<(ostream& s, ModInt<mod> a) {
        s << a.x;
        return s;
    }
    friend istream& operator>>(istream& s, ModInt<mod>& a) {
        s >> a.x;
        return s;
    }
};
 
using mint = ModInt<MOD>;
typedef vector<mint> vm;
typedef vector<vector<mint> >vvm;
typedef vector<vector<vector<mint> > >vvvm;

template <typename T>
struct segment_tree_beats{
  int N;
  vector<T> max1, max2, min1, min2, add, sum;
  vector<int> maxc, minc, len;
  void update_max(int i, T x){
    sum[i] += (x - max1[i]) * maxc[i];
    if (max1[i] == min1[i]){
      min1[i] = x;
    } else if (max1[i] == min2[i]){
      min2[i] = x;
    }
    max1[i] = x;
  }
  void update_min(int i, T x){
    sum[i] += (x - min1[i]) * minc[i];
    if (min1[i] == max1[i]){
      max1[i] = x;
    } else if (min1[i] == max2[i]){
      max2[i] = x;
    }
    min1[i] = x;
  }
  void update_add(int i, T x){
    max1[i] += x;
    if (max2[i] != -INF){
      max2[i] += x;
    }
    min1[i] += x;
    if (min2[i] != INF){
      min2[i] += x;
    }
    sum[i] += x * len[i];
    add[i] += x;
  }
  void push(int i){
    if (i >= N - 1){
      return;
    }
    int l = i * 2 + 1;
    int r = i * 2 + 2;
    if (add[i] != 0){
      update_add(l, add[i]);
      update_add(r, add[i]);
      add[i] = 0;
    }
    if (max1[i] < max1[l]){
      update_max(l, max1[i]);
    }
    if (min1[i] > min1[l]){
      update_min(l, min1[i]);
    }
    if (max1[i] < max1[r]){
      update_max(r, max1[i]);
    }
    if (min1[i] > min1[r]){
      update_min(r, min1[i]);
    }
  }
  void update(int i){
    int l = i * 2 + 1;
    int r = i * 2 + 2;
    sum[i] = sum[l] + sum[r];
    if (max1[l] > max1[r]){
      max1[i] = max1[l];
      max2[i] = max(max2[l], max1[r]);
      maxc[i] = maxc[l];
    } else if (max1[l] < max1[r]){
      max1[i] = max1[r];
      max2[i] = max(max1[l], max2[r]);
      maxc[i] = maxc[r];
    } else {
      max1[i] = max1[l];
      max2[i] = max(max2[l], max2[r]);
      maxc[i] = maxc[l] + maxc[r];
    }
    if (min1[l] < min1[r]){
      min1[i] = min1[l];
      min2[i] = min(min2[l], min1[r]);
      minc[i] = minc[l];
    } else if (min1[l] > min1[r]){
      min1[i] = min1[r];
      min2[i] = min(min1[l], min2[r]);
      minc[i] = minc[r];
    } else {
      min1[i] = min1[l];
      min2[i] = min(min2[l], min2[r]);
      minc[i] = minc[l] + minc[r];
    }
  }
  segment_tree_beats(vector<T> A){
    int n = A.size();
    N = 1;
    while (N < n){
      N *= 2;
    }
    max1 = vector<T>(N * 2 - 1, -INF);
    max2 = vector<T>(N * 2 - 1, -INF);
    min1 = vector<T>(N * 2 - 1, INF);
    min2 = vector<T>(N * 2 - 1, INF);
    add = vector<T>(N * 2 - 1, 0);
    sum = vector<T>(N * 2 - 1, 0);
    maxc = vector<int>(N * 2 - 1, 1);
    minc = vector<int>(N * 2 - 1, 1);
    len = vector<int>(N * 2 - 1, 1);
    for (int i = 0; i < n; i++){
      max1[N - 1 + i] = A[i];
      min1[N - 1 + i] = A[i];
      sum[N - 1 + i] = A[i];
    }
    for (int i = N - 2; i >= 0; i--){
      len[i] = len[i * 2 + 1] + len[i * 2 + 2];
      update(i);
    }
  }
  void range_chmin(int L, int R, T x, int i, int l, int r){
    if (r <= L || R <= l || x >= max1[i]){
      return;
    } else if (L <= l && r <= R && x > max2[i]){
      update_max(i, x);
      return;
    }
    push(i);
    int m = (l + r) / 2;
    range_chmin(L, R, x, i * 2 + 1, l, m);
    range_chmin(L, R, x, i * 2 + 2, m, r);
    update(i);
  }
  void range_chmax(int L, int R, T x, int i, int l, int r){
    if (r <= L || R <= l || x <= min1[i]){
      return;
    } else if (L <= l && r <= R && x < min2[i]){
      update_min(i, x);
      return;
    }
    push(i);
    int m = (l + r) / 2;
    range_chmax(L, R, x, i * 2 + 1, l, m);
    range_chmax(L, R, x, i * 2 + 2, m, r);
    update(i);
  }
  void range_add(int L, int R, T x, int i, int l, int r){
    if (r <= L || R <= l){
      return;
    } else if (L <= l && r <= R){
      update_add(i, x);
      return;
    }
    push(i);
    int m = (l + r) / 2;
    range_add(L, R, x, i * 2 + 1, l, m);
    range_add(L, R, x, i * 2 + 2, m, r);
    update(i);
  }
  T range_sum(int L, int R, int i, int l, int r){
    if (r <= L || R <= l){
      return 0;
    } else if (L <= l && r <= R){
      return sum[i];
    }
    push(i);
    int m = (l + r) / 2;
    return range_sum(L, R, i * 2 + 1, l, m) +	range_sum(L, R, i * 2 + 2, m, r);
  }
  void range_chmin(int L, int R, T x){
    range_chmin(L, R, x, 0, 0, N);
  }
  void range_chmax(int L, int R, T x){
    range_chmax(L, R, x, 0, 0, N);
  }
  void range_add(int L, int R, T x){
    range_add(L, R, x, 0, 0, N);
  }
  T range_sum(int L, int R){
    return range_sum(L, R, 0, 0, N);
  }
};

struct PartiallyPersistentUnionFind {
    vector<ll> par, last;
    vector<vector<P> > history;
    
    PartiallyPersistentUnionFind(ll n) : par(n, -1), last(n, -1), history(n) {
        for (auto &vec : history) vec.emplace_back(-1, -1);
    }
    void init(ll n) {
        par.assign(n, -1); last.assign(n, -1); history.assign(n, vector<P>());
        for (auto &vec : history) vec.emplace_back(-1, -1);
    }
    
    ll root(ll t, ll x) {
        if (last[x] == -1 || t < last[x]) return x;
        return root(t, par[x]);
    }
    
    bool issame(ll t, ll x, ll y) {
        return root(t, x) == root(t, y);
    }
    
    bool merge(ll t, ll x, ll y) {
        x = root(t, x); y = root(t, y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        last[y] = t;
        history[x].emplace_back(t, par[x]);
        return true;
    }
    
    ll size(ll t, ll x) {
        x = root(t, x);
        return -prev(lower_bound(history[x].begin(), history[x].end(), make_pair(t, 0LL)))->second;
    }
};

// matrix
template<class T> struct Matrix {
    vector<vector<T> > val;
    Matrix(int n = 1, int m = 1, T v = 0) : val(n, vector<T>(m, v)) {}
    void init(int n, int m, T v = 0) {val.assign(n, vector<T>(m, v));}
    void resize(int n, int m) {
        val.resize(n);
        for (int i = 0; i < n; ++i) val[i].resize(m);
    }
    Matrix<T>& operator = (const Matrix<T> &A) {
        val = A.val;
        return *this;
    }
    size_t size() const {return val.size();}
    vector<T>& operator [] (int i) {return val[i];}
    const vector<T>& operator [] (int i) const {return val[i];}
    friend ostream& operator << (ostream& s, const Matrix<T>& M) {
        s << endl;
        for (int i = 0; i < (int)M.size(); ++i) s << M[i] << endl;
        return s;
    }
};

template<class T> Matrix<T> operator * (const Matrix<T> &A, const Matrix<T> &B) {
    Matrix<T> R(A.size(), B[0].size());
    for (int i = 0; i < A.size(); ++i)
        for (int j = 0; j < B[0].size(); ++j)
            for (int k = 0; k < B.size(); ++k)
                R[i][j] += A[i][k] * B[k][j];
    return R;
}

template<class T> Matrix<T> pow(const Matrix<T> &A, long long n) {
    Matrix<T> R(A.size(), A.size());
    auto B = A;
    for (int i = 0; i < A.size(); ++i) R[i][i] = 1;
    while (n > 0) {
        if (n & 1) R = R * B;
        B = B * B;
        n >>= 1;
    }
    return R;
}

template<class T> vector<T> operator * (const Matrix<T> &A, const vector<T> &B) {
    vector<T> v(A.size());
    for (int i = 0; i < A.size(); ++i)
        for (int k = 0; k < B.size(); ++k)
            v[i] += A[i][k] * B[k];
    return v;
}

template<class T> Matrix<T> operator + (const Matrix<T> &A, const Matrix<T> &B) {
    Matrix<T> R(A.size(), A[0].size());
    for (int i = 0; i < A.size(); ++i)
        for (int j = 0; j < A[0].size(); ++j)
            R[i][j] = A[i][j] + B[i][j];
    return R;
}

template<class T> Matrix<T> operator - (const Matrix<T> &A, const Matrix<T> &B) {
    Matrix<T> R(A.size(), A[0].size());
    for (int i = 0; i < A.size(); ++i)
        for (int j = 0; j < A[0].size(); ++j)
            R[i][j] = A[i][j] - B[i][j];
    return R;
}

const int MAX_ROW = 510; // to be set appropriately
const int MAX_COL = 510; // to be set appropriately
struct BitMatrix {
    int H, W;
    bitset<MAX_COL> val[MAX_ROW];
    BitMatrix(int m = 1, int n = 1) : H(m), W(n) {}
    inline bitset<MAX_COL>& operator [] (int i) {return val[i];}
};

int GaussJordan(BitMatrix &A, bool is_extended = false) {
    int rank = 0;
    for (int col = 0; col < A.W; ++col) {
        if (is_extended && col == A.W - 1) break;
        int pivot = -1;
        for (int row = rank; row < A.H; ++row) {
            if (A[row][col]) {
                pivot = row;
                break;
            }
        }
        if (pivot == -1) continue;
        swap(A[pivot], A[rank]);
        for (int row = 0; row < A.H; ++row) {
            if (row != rank && A[row][col]) A[row] ^= A[rank];
        }
        ++rank;
    }
    return rank;
}

int linear_equation(BitMatrix A, vector<int> b, vector<int> &res) {
    int m = A.H, n = A.W;
    BitMatrix M(m, n + 1);
    for (int i = 0; i < m; ++i) {
        for (int j = 0; j < n; ++j) M[i][j] = A[i][j];
        M[i][n] = b[i];
    }
    int rank = GaussJordan(M, true);

    // check if it has no solution
    for (int row = rank; row < m; ++row) if (M[row][n]) return -1;

    // answer
    res.assign(n, 0);
    for (int i = 0; i < rank; ++i) res[i] = M[i][n];
    return rank;
}


ll exp(ll n,ll r){
    if(r==0)return 1;
    return n*exp(n,r-1);
}

ll factorial(int n){
    if(n==0)return 1;
    return n*factorial(n-1);
}


void input_vvi(int n){
    vector<string>s(n);
    string ans;
    ans+="vector<vector<int>> dp={";
    rep(i,n){
        cin>>s[i];
        ans+="{";
        ans+=s[i];
        ans+="}";
        if(i!=n-1)ans+=",";
    }
    ans+="};";
    cout<<ans<<endl;
}

/**
 * @brief Rolling-Hash(ローリングハッシュ)
 * @see https://qiita.com/keymoon/items/11fac5627672a6d6a9f6
 * @docs docs/rolling-hash.md
 */
struct RollingHash {
  static const uint64_t mod = (1ull << 61ull) - 1;
  using uint128_t = __uint128_t;
  vector< uint64_t > power;
  const uint64_t base;

  static inline uint64_t add(uint64_t a, uint64_t b) {
    if((a += b) >= mod) a -= mod;
    return a;
  }

  static inline uint64_t mul(uint64_t a, uint64_t b) {
    uint128_t c = (uint128_t) a * b;
    return add(c >> 61, c & mod);
  }

  static inline uint64_t generate_base() {
    mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
    uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
    return rand(mt);
  }

  inline void expand(size_t sz) {
    if(power.size() < sz + 1) {
      int pre_sz = (int) power.size();
      power.resize(sz + 1);
      for(int i = pre_sz - 1; i < sz; i++) {
        power[i + 1] = mul(power[i], base);
      }
    }
  }

  explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}

  vector< uint64_t > build(const string &s) const {
    int sz = s.size();
    vector< uint64_t > hashed(sz + 1);
    for(int i = 0; i < sz; i++) {
      hashed[i + 1] = add(mul(hashed[i], base), s[i]);
    }
    return hashed;
  }

  template< typename T >
  vector< uint64_t > build(const vector< T > &s) const {
    int sz = s.size();
    vector< uint64_t > hashed(sz + 1);
    for(int i = 0; i < sz; i++) {
      hashed[i + 1] = add(mul(hashed[i], base), s[i]);
    }
    return hashed;
  }

  uint64_t query(const vector< uint64_t > &s, int l, int r) {
    expand(r - l);
    return add(s[r], mod - mul(s[l], power[r - l]));
  }

  uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
    expand(h2len);
    return add(mul(h1, power[h2len]), h2);
  }

  int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = 0, high = len + 1;
    while(high - low > 1) {
      int mid = (low + high) / 2;
      if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
      else high = mid;
    }
    return low;
  }
};

struct SuccinctIndexableDictionary {
  size_t length;
  size_t blocks;
  vector< unsigned > bit, sum;

  SuccinctIndexableDictionary() = default;

  SuccinctIndexableDictionary(size_t length) : length(length), blocks((length + 31) >> 5) {
    bit.assign(blocks, 0U);
    sum.assign(blocks, 0U);
  }

  void set(int k) {
    bit[k >> 5] |= 1U << (k & 31);
  }

  void build() {
    sum[0] = 0U;
    for(int i = 1; i < blocks; i++) {
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }

  bool operator[](int k) {
    return (bool((bit[k >> 5] >> (k & 31)) & 1));
  }

  int rank(int k) {
    return (sum[k >> 5] + __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
  }

  int rank(bool val, int k) {
    return (val ? rank(k) : k - rank(k));
  }
};

/*
 * @brief Wavelet-Matrix(ウェーブレット行列)
 * @docs docs/wavelet-matrix.md
 */
template< typename T, int MAXLOG >
struct WaveletMatrix {
  size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  int mid[MAXLOG];

  WaveletMatrix() = default;

  WaveletMatrix(vector< T > v) : length(v.size()) {
    vector< T > l(length), r(length);
    for(int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for(int i = 0; i < length; i++) {
        if(((v[i] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = v[i];
        } else {
          l[left++] = v[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      v.swap(l);
      for(int i = 0; i < right; i++) {
        v[left + i] = r[i];
      }
    }
  }

  pair< int, int > succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f, matrix[level].rank(f, r) + mid[level] * f};
  }

  // v[k]
  T access(int k) {
    T ret = 0;
    for(int level = MAXLOG - 1; level >= 0; level--) {
      bool f = matrix[level][k];
      if(f) ret |= T(1) << level;
      k = matrix[level].rank(f, k) + mid[level] * f;
    }
    return ret;
  }

  T operator[](const int &k) {
    return access(k);
  }

  // count i s.t. (0 <= i < r) && v[i] == x
  int rank(const T &x, int r) {
    int l = 0;
    for(int level = MAXLOG - 1; level >= 0; level--) {
      tie(l, r) = succ((x >> level) & 1, l, r, level);
    }
    return r - l;
  }

  // k-th(0-indexed) smallest number in v[l,r)
  T kth_smallest(int l, int r, int k) {
    assert(0 <= k && k < r - l);
    T ret = 0;
    for(int level = MAXLOG - 1; level >= 0; level--) {
      int cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);
      bool f = cnt <= k;
      if(f) {
        ret |= T(1) << level;
        k -= cnt;
      }
      tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  // k-th(0-indexed) largest number in v[l,r)
  T kth_largest(int l, int r, int k) {
    return kth_smallest(l, r, r - l - k - 1);
  }

  // count i s.t. (l <= i < r) && (v[i] < upper)
  int range_freq(int l, int r, T upper) {
    int ret = 0;
    for(int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((upper >> level) & 1);
      if(f) ret += matrix[level].rank(false, r) - matrix[level].rank(false, l);
      tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  // count i s.t. (l <= i < r) && (lower <= v[i] < upper)
  int range_freq(int l, int r, T lower, T upper) {
    return range_freq(l, r, upper) - range_freq(l, r, lower);
  }

  // max v[i] s.t. (l <= i < r) && (v[i] < upper)
  T prev_value(int l, int r, T upper) {
    int cnt = range_freq(l, r, upper);
    return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
  }

  // min v[i] s.t. (l <= i < r) && (lower <= v[i])
  T next_value(int l, int r, T lower) {
    int cnt = range_freq(l, r, lower);
    return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
  }
};

template< typename T, int MAXLOG >
struct CompressedWaveletMatrix {
  WaveletMatrix< int, MAXLOG > mat;
  vector< T > ys;

  CompressedWaveletMatrix(const vector< T > &v) : ys(v) {
    sort(begin(ys), end(ys));
    ys.erase(unique(begin(ys), end(ys)), end(ys));
    vector< int > t(v.size());
    for(int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletMatrix< int, MAXLOG >(t);
  }

  inline int get(const T& x) {
    return lower_bound(begin(ys), end(ys), x) - begin(ys);
  }

  T access(int k) {
    return ys[mat.access(k)];
  }

  T operator[](const int &k) {
    return access(k);
  }

  int rank(const T &x, int r) {
    auto pos = get(x);
    if(pos == ys.size() || ys[pos] != x) return 0;
    return mat.rank(pos, r);
  }

  T kth_smallest(int l, int r, int k) {
    return ys[mat.kth_smallest(l, r, k)];
  }

  T kth_largest(int l, int r, int k) {
    return ys[mat.kth_largest(l, r, k)];
  }

  int range_freq(int l, int r, T upper) {
    return mat.range_freq(l, r, get(upper));
  }

  int range_freq(int l, int r, T lower, T upper) {
    return mat.range_freq(l, r, get(lower), get(upper));
  }

  T prev_value(int l, int r, T upper) {
    auto ret = mat.prev_value(l, r, get(upper));
    return ret == -1 ? T(-1) : ys[ret];
  }

  T next_value(int l, int r, T lower) {
    auto ret = mat.next_value(l, r, get(lower));
    return ret == -1 ? T(-1) : ys[ret];
  }
};


pair<long long,long long>roop_search(vl next_index,ll first_point){
	ll idx=first_point;
	map<ll,ll>mp;
	mp[idx]=0;
	ll cur=1;
	ll roop_begin=-1;
	ll roop_size=-1;
	while(true){
		idx=next_index[idx];
		if(mp.count(idx)){
			roop_begin=mp[idx];
			roop_size=cur-roop_begin;
			break;
		}
		mp[idx]=cur++;
	}
	return {roop_begin,roop_size};
}

ll functional(ll x){
    if(x==0)return 1;
    else return x*functional(x-1);
}

struct edge{
    ll to;
    ll cost;
    ll q;
};
using graph = vector<vector<edge> >;
const ll MAX_V=100010;
graph G(MAX_V);
vl d(MAX_V);
void dijkstra(ll n,ll s,ll t) {
    minpq<P>q;
    rep(i,n)d[i]=INF;
    d[s]= t;
    q.push({t, s});

    while (!q.empty()) {
        auto p = q.top();
        q.pop();
        ll cur = p.second;
        //d[cur]が二度以上更新されている場合に、初期のものをskipする
        //これがないと一つの頂点につき高々一回更新されるという前提が破滅
        if(d[cur]<p.first)continue;
        for(auto e:G[cur]) {
            if (d[e.to] > d[cur]+e.cost+e.q/(p.first+1)) {
        
                d[e.to]=d[cur]+e.cost+e.q/(p.first+1);
                // cout<<e.to<<" "<<d[e.to]<<endl;
                q.push({d[e.to], e.to});
            }
        }
    }
}



int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << fixed << setprecision(13);
    //CDEは制約を読もう!
    //主客転倒!二重和のときは一番内側の物が何回使われるか
    //√Nで分けるテク
    //絶対値は外して2通りの式にした後、変数ごとにまとめる
    //組み合わせが少ないそうなものはdfsで実行してみる(典型25)
    /*--------------------------------*/

    ll a,b,n;cin>>a>>b>>n;
    Matrix<mint>A(2,2,0);
    A[1][0]=1;
    A[0][1]=(mint)-a*a+b;
    A[1][1]=(mint)2*a;
    auto res=pow(A,n);
    mint ans=res[0][0]*2+res[1][0]*2*a;
    cout<<ans<<endl;

}
0