結果
| 問題 | No.167 N^M mod 10 |
| ユーザー |
 soraie_
|
| 提出日時 | 2021-03-23 12:07:45 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 203 ms / 1,000 ms |
| コード長 | 49,400 bytes |
| コンパイル時間 | 9,014 ms |
| コンパイル使用メモリ | 292,968 KB |
| 最終ジャッジ日時 | 2025-01-19 21:11:10 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 27 |
ソースコード
#ifdef _DEBUG#define _GLIBCXX_DEBUG#endif#include <bits/stdc++.h>#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")using namespace std;//--------------------------------------------------------------------#define all(a) (a).begin(),(a).end()#define rall(a) (a).rbegin(),(a).rend()#define overload4(_1,_2,_3,_4,name,...) name#define rep1(n) for(ll _=0;_<(ll)n;++_)#define rep2(i,n) for(ll i=0;i<(ll)n;++i)#define rep3(i,a,b) for(ll i=(ll)a;i<(ll)b;++i)#define rep4(i,a,b,c) for(ll i=(ll)a;i<(ll)b;i+=(ll)c)#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)#ifdef _DEBUG#define pass(...) __VA_ARGS__ ;#define debug1(a) cerr<<#a<<": "<<a<<"\n"#define debug2(a,b) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"#define debug3(a,b,c) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"#define debug4(a,b,c,d) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"/*#define debug1(a) cout<<#a<<": "<<a<<"\n"#define debug2(a,b) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"#define debug3(a,b,c) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"#define debug4(a,b,c,d) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"*/#define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__)#define koko cerr << "koko\n";#else#define debug(...) void(0)#define pass(...) void(0);#define koko void(0);#endif#define mp make_pair//#define fi first//#define se secondvoid myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}void doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}using ll = long long;using ld = long double;using dou = double;template<class First,class Second>ostream& operator<<(ostream& os,const pair<First,Second>& pp){return os << "{" << pp.first << "," << pp.second << "}";}template<class T>ostream& operator<<(ostream& os,const vector<T>& VV){if(VV.empty())return os<<"[]";os<<"[";rep(i,VV.size())os<<VV[i]<<(i==int(VV.size()-1)?"]":",");return os;}template<class T>ostream& operator<<(ostream& os,const set<T>& SS){if(SS.empty())return os<<"[]";os<<"[";auto ii=SS.begin();for(;ii!=SS.end();ii++)os<<*ii<<(ii==prev(SS.end())?"]":",");return os;}template<class Key,class Tp>ostream& operator<<(ostream& os,const map<Key,Tp>& MM){if(MM.empty())return os<<"[]";os<<"[";auto ii=MM.begin();for(;ii!=MM.end();ii++)os<<"{"<<ii->first<<":"<<ii->second<<"}"<<(ii==prev(MM.end())?"]":",");return os;}const int inf = 1 << 30;const ll INF = 1LL << 61;const ld pi = 3.14159265358;const ll mod1 = 1000000007LL;const ll mod2 = 998244353LL;typedef pair<ll,ll> P;template<class T, class U> inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }template<class T, class U> inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }ll modpow(ll n,ll m,ll MOD){if(m == 0)return 1;if(m < 0)return 0;ll res = 1;n %= MOD;while(m){if(m & 1)res = (res * n) % MOD;m >>= 1;n *= n;n %= MOD;}return res;}ll mypow(ll n,ll m){if(m == 0)return 1;if(m < 0)return -1;ll res = 1;while(m){if(m & 1)res = (res * n);m >>= 1;n *= n;}return res;}inline bool isp(ll n){bool res = true;if(n == 1 || n == 0)return false;else{for(ll i = 2;i * i <= n;i++){if(n % i == 0){res = false;break;}}return res;}}inline bool Yes(bool b = 1){cout << (b ? "Yes\n":"No\n");return b;}inline bool YES(bool b = 1){cout << (b ? "YES\n":"NO\n");return b;}map<ll,ll> primefactor(ll n){map<ll,ll> ma;if(n <= 1)return ma;ll m = n;for(ll i = 2;i * i <= n;i++){while(m % i == 0){ma[i]++;m /= i;}}if(m != 1)ma[m]++;return ma;}vector<ll> divisor(ll n,bool sorted = true,bool samein = false){vector<ll> res;for(ll i = 1;i * i <= n;i++){if(n % i == 0){res.push_back(i);if(i * i != n || samein)res.push_back(n / i);}}if(sorted)sort(all(res));return res;}ll __lcm(ll a,ll b){return a / __gcd(a,b) * b;}template<class T>T sum(const vector<T> &V){T r=0;for(auto x:V)r+=x;return r;}template<class T>T sum(const initializer_list<T> &V){T r=0;for(auto x:V)r+=x;return r;}//#include <atcoder/all>//#include "atcoder/lazysegtree.hpp"//using namespace atcoder;//--------------------------------------------------------------------long long extgcd(long long a,long long b,long long &x,long long &y){if(b == 0){x = 1;y = 0;return a;}long long d = extgcd(b,a % b,y,x);y -= a / b * x;return d;}long long modinv(long long a,long long p){long long b = p, u = 1, v = 0;while(b){long long t = a / b;a -= t * b;std::swap(a, b);u -= t * v;std::swap(u, v);}u %= p;if(u < 0)u += p;return u;}/*** @brief garner precalc* @return long long*/long long pregarner(std::vector<long long> &rems,std::vector<long long> &mods,long long MOD){assert(rems.size() == mods.size());for(int i = 0;i < int(rems.size());i++){for(int j = 0;j < i;j++){long long g = std::gcd(mods[i],mods[j]);if((rems[i] - rems[j]) % g != 0)return -1;mods[i] /= g;mods[j] /= g;long long gi = std::gcd(g,mods[i]),gj = g / gi;do{g = std::gcd(gi,gj);gi *= g;gj /= g;}while(g != 1);mods[i] *= gi;mods[j] *= gj;rems[i] %= mods[i];rems[j] %= mods[j];}}long long res = 1;for(long long &a : mods)res = res * a % MOD;return res;}/*** @brief returns a integer where rems[i](mod.mods[i]).* @return long long*/long long garner(std::vector<long long> rems,std::vector<long long> mods,long long MOD){assert(rems.size() == mods.size());mods.push_back(MOD);int sz = mods.size();std::vector<long long> cof(sz,1LL),con(sz,0LL);for(int i = 0;i < sz - 1;i++){long long cur = (rems[i] - con[i]) * modinv(cof[i],mods[i]) % mods[i];if(cur < 0)cur += mods[i];for(int j = i + 1;j < sz;j++){con[j] = (con[j] + cur * cof[j]) % mods[j];cof[j] = cof[j] * mods[i] % mods[j];}}return con.back();}template<long long MOD = 1000000007>struct modint {using mint = modint<MOD>;long long x;modint(long long a = 0):x((a % MOD + MOD) % MOD){}inline constexpr modint operator-()const noexcept{return modint(-x);}inline constexpr modint &operator+=(const modint &a)noexcept{if ((x += a.x) >= MOD) x -= MOD;return *this;}inline constexpr modint &operator-=(const modint &a)noexcept{if ((x -= a.x) < 0) x += MOD;return *this;}inline constexpr modint &operator*=(const modint &a)noexcept{(x *= a.x) %= MOD;return *this;}inline constexpr modint &operator++()noexcept{x++;if(x == MOD)x = 0;return *this;}inline constexpr modint operator++(int)noexcept{modint res(*this);operator++();return res;}inline constexpr modint &operator--()noexcept{x--;if(x == -1)x = MOD - 1;return *this;}inline constexpr modint operator--(int)noexcept{modint res(*this);operator--();return res;}inline constexpr modint operator+(const modint &a)const noexcept{modint res(*this);return res += a;}inline constexpr modint operator-(const modint &a)const noexcept{modint res(*this);return res -= a;}inline constexpr modint operator*(const modint &a)const noexcept{modint res(*this);return res *= a;}inline constexpr modint inv()const{long long a = x,b = MOD,u = 1,v = 0;while(b){long long t = a / b;a -= t * b;std::swap(a,b);u -= t * v;std::swap(u,v);}return u;}inline constexpr modint &operator/=(const modint &a)noexcept{return (*this) *= a.inv();}inline constexpr modint operator/(const modint &a)const noexcept{modint res(*this);return res /= a;}inline constexpr bool operator==(const modint &a)const noexcept{return x == a.x;}friend std::istream &operator>>(std::istream &is,modint &a) {is >> a.x;a.x = (a.x % MOD + MOD) % MOD;return is;}friend std::ostream &operator<<(std::ostream &os,const modint &a){os << a.x;return os;}long long getmod(){return MOD;}friend mint modpow(mint a,long long b)noexcept{mint res(1);while(b){if(b & 1)res *= a;a *= a;b >>= 1;}return res;}};//using mint = modint<1'000'000'007>::mint;//ex. (2013265921,137,27),(998244353,31,23),(469762049,30,26)template<long long MOD,int base,int max_exp>struct NTT_primitive{using mint = modint<MOD>;std::vector<mint> bases,invs;NTT_primitive(){bases.resize(max_exp + 1);invs.resize(max_exp + 1);bases[max_exp] = base;invs[max_exp] = mint(base).inv();for(int i = max_exp - 1;i >= 0;i--){bases[i] = bases[i + 1] * bases[i + 1];invs[i] = invs[i + 1] * invs[i + 1];}}void dft(std::vector<mint>& vec,int t){int sz = vec.size();if(sz == 1)return;std::vector<mint> veca,vecb;for(int i = 0;i < sz / 2;i++){veca.push_back(vec[i * 2]);vecb.push_back(vec[i * 2 + 1]);}dft(veca,t);dft(vecb,t);int e = __builtin_ffsll(sz) - 1;mint now = 1,zeta = (t == 1 ? bases[e]:invs[e]);for(int i = 0;i < sz;i++){vec[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];now *= zeta;}}std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){// assert(A.size() == B.size());int sz = 1;while(sz < int(A.size() + B.size()))sz <<= 1;std::vector<mint> f(sz),g(sz);for(int i = 0;i < int(A.size());i++)f[i] = A[i];for(int i = 0;i < int(B.size());i++)g[i] = B[i];dft(f,1);dft(g,1);for(int i = 0;i < sz;i++)f[i] = f[i] * g[i];dft(f,-1);mint inv = mint(sz).inv();for(int i = 0;i < sz;i++)f[i] *= inv;return f;}void dft(std::vector<long long>& vec,int t){int sz = vec.size();if(sz == 1)return;std::vector<long long> veca,vecb;for(int i = 0;i < sz / 2;i++){veca.push_back(vec[i * 2]);vecb.push_back(vec[i * 2 + 1]);}dft(veca,t);dft(vecb,t);int e = __builtin_ffsll(sz) - 1;long long now = 1,zeta = (t == 1 ? bases[e].x:invs[e].x);for(int i = 0;i < sz;i++){vec[i] = (veca[i % (sz / 2)] + now * vecb[i % (sz / 2)] % MOD) % MOD;now = now * zeta % MOD;}}std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){// assert(A.size() == B.size());int sz = 1;while(sz < int(A.size() + B.size()))sz <<= 1;std::vector<long long> f(sz),g(sz);for(int i = 0;i < int(A.size());i++)f[i] = A[i] % MOD;for(int i = 0;i < int(B.size());i++)g[i] = B[i] % MOD;dft(f,1);dft(g,1);for(int i = 0;i < sz;i++)f[i] = f[i] * g[i] % MOD;dft(f,-1);long long inv = modinv(sz,MOD);for(int i = 0;i < sz;i++)f[i] = f[i] * inv % MOD;return f;}};template<long long MOD>struct NTT_all{NTT_primitive<2013265921,137,27> ntt1;NTT_primitive<998244353,31,23> ntt2;NTT_primitive<469762049,30,26> ntt3;using mint = modint<MOD>;using mint1 = modint<2013265921>;using mint2 = modint<998244353>;using mint3 = modint<469762049>;NTT_all(){}std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){int sza = A.size(),szb = B.size();std::vector<mint1> A1(sza),B1(szb);std::vector<mint2> A2(sza),B2(szb);std::vector<mint3> A3(sza),B3(szb);for(int i = 0;i < sza;i++){A1[i] = A[i].x;A2[i] = A[i].x;A3[i] = A[i].x;}for(int i = 0;i < szb;i++){B1[i] = B[i].x;B2[i] = B[i].x;B3[i] = B[i].x;}auto C1 = ntt1.convolution(A1,B1);auto C2 = ntt2.convolution(A2,B2);auto C3 = ntt3.convolution(A3,B3);int rs = C1.size();std::vector<mint> res(rs);for(int i = 0;i < rs;i++){std::vector<long long> r = {C1[i].x,C2[i].x,C3[i].x},m = {2013265921,998244353,469762049};res[i] = garner(r,m,MOD);}return res;}std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){int sza = A.size(),szb = B.size();std::vector<long long> A1(sza),B1(szb),A2(sza),B2(szb),A3(sza),B3(szb);for(int i = 0;i < sza;i++){A1[i] = A[i] % 2013265921;A2[i] = A[i] % 998244353;A3[i] = A[i] % 469762049;}for(int i = 0;i < szb;i++){B1[i] = B[i] % 2013265921;B2[i] = B[i] % 998244353;B3[i] = B[i] % 469762049;}auto C1 = ntt1.convolution(A1,B1);auto C2 = ntt2.convolution(A2,B2);auto C3 = ntt3.convolution(A3,B3);int rs = C1.size();std::vector<long long> res(rs);for(int i = 0;i < rs;i++){std::vector<long long> r = {C1[i],C2[i],C3[i]},m = {2013265921,998244353,469762049};res[i] = garner(r,m,MOD) % MOD;}return res;}};namespace bigint_convolution{bool is_set = false;std::function<std::vector<long long>(std::vector<long long>,std::vector<long long>)> f;void set(const std::function<std::vector<long long>(std::vector<long long>,std::vector<long long>)>& _f){is_set = true;f = _f;}std::vector<long long> convolution(const std::vector<long long>& a,const std::vector<long long>& b){assert(is_set);return f(a,b);}std::vector<long long> naive(const std::vector<long long>& a,const std::vector<long long>& b){int n = int(a.size()),m = int(b.size());std::vector<long long> res(n + m - 1);if(n < m)for(int j = 0;j < m;j++)for(int i = 0;i < n;i++)res[i + j] += a[i] * b[j];elsefor(int i = 0;i < n;i++)for(int j = 0;j < m;j++)res[i + j] += a[i] * b[j];return res;};};template<int d,int base>struct bigint{using bint = bigint<d,base>;bigint(const std::string& _s){sign = 1;dat.clear();if(_s.empty())return;if(_s[0] == '-')sign = -1;std::string s = sign == 1 ? _s : _s.substr(1);int i;for(i = int(s.size()) - d;i >= 0;i -= d){assert('0' <= s[i] && s[i] <= '9');dat.push_back(std::stoll(s.substr(i,d)));}if(i + d)dat.push_back(std::stoll(s.substr(0,i + d)));while(!dat.empty() && dat.back() == 0)dat.pop_back();}bigint(long long n = 0){sign = 1;dat.clear();if(n < 0)sign = -1,n = -n;while(n){dat.push_back(n % base);n /= base;}}int size()const{return int(dat.size());}int number_len()const{if(size() == 0)return 0;int res = (int(dat.size()) - 1) * d;int b = 1,p = 0;while(b <= dat.back())p++,b *= 10;return res + p;}std::string to_string()const{if(size() == 0)return "0";std::string res = "";if(sign == -1)res = "-";auto to_string_pad = [](long long m,int _d){std::string r = std::to_string(m);std::string ap(_d - int(r.size()),'0');return ap + r;};for(int i = size() - 1;i >= 0;i--){if(i != size() - 1)res += to_string_pad(dat[i],d);else res += std::to_string(dat[i]);}return res;}long long to_ll()const{long long res = 0;for(int i = size() - 1;i >= 0;i--)res = res * base + dat[i];return sign * res;}void norm(){if(dat.empty())return;for(int i = 0;i < size() - 1;i++){long long nex = dat[i] / base;if(nex * base > dat[i])nex--;dat[i] -= nex * base;dat[i + 1] += nex;}while(dat.back() >= base){long long nex = dat.back() / base;dat.back() -= nex * base;dat.push_back(nex);}while(!dat.empty() && dat.back() == 0)dat.pop_back();}inline constexpr bool operator<(const bint& a)const noexcept{if(a.dat.empty())return false;else if(sign != a.sign)return sign < a.sign;else if(sign == -1)return (-a) < (-bint(*this));else if(number_len() != a.number_len())return number_len() < a.number_len();else{for(int i = size() - 1;i >= 0;i--)if(dat[i] != a.dat[i])return dat[i] < a.dat[i];return false;}}inline constexpr bool operator>(const bint& a)const noexcept{return a < bint(*this);}inline constexpr bool operator<=(const bint& a)const noexcept{return !(a < bint(*this));}inline constexpr bool operator>=(const bint& a)const noexcept{return !(bint(*this) < a);}inline constexpr bool operator==(const bint& a)const noexcept{return dat == a.dat;}inline constexpr bool operator!=(const bint& a)const noexcept{return dat != a.dat;}inline constexpr bint operator-()const noexcept{bint res(*this);res.sign = -res.sign;return res;}friend bint abs(const bint& a){return a.sign == -1 ? -a : a;}inline constexpr bint &operator+=(const bint& a)noexcept{if(sign != a.sign)return *this -= (-a);else{if(size() < a.size())dat.resize(a.size());for(int i = 0;i < a.size();i++)dat[i] += a.dat[i];norm();return *this;}}inline constexpr bint &operator-=(const bint& a)noexcept{if(sign != a.sign)return *this += (-a);else if(abs(bint(*this)) < abs(a)){*this = a - *this;sign = -sign;return *this;}else{for(int i = 0;i < a.size();i++)dat[i] -= a.dat[i];norm();return *this;}}inline constexpr bint &operator++()noexcept{return *this += bint(1);}inline constexpr bint operator++(int)noexcept{operator++();return bint(*this);}inline constexpr bint &operator--()noexcept{return *this -= bint(1);}inline constexpr bint operator--(int)noexcept{operator--();return bint(*this);}inline constexpr bint &operator*=(const bint& a)noexcept{if(size() == 0 || a.size() == 0)return *this = bint(0);if(std::min(size(),a.size()) <= 60)dat = bigint_convolution::naive(dat,a.dat);else dat = bigint_convolution::convolution(dat,a.dat);norm();sign *= a.sign;return *this;}inline constexpr bint mul2()const noexcept{bint res(*this);for(auto& x : res.dat)x *= 2;res.norm();return res;}inline constexpr bint div2()const noexcept{bint res(*this);int nex = 0;for(int i = res.size() - 1;i >= 0;i--){long long cur = (res.dat[i] + nex * base);res.dat[i] = cur >> 1;nex = cur & 1;}while(!res.dat.empty() && res.dat.back() == 0)res.dat.pop_back();return res;}inline constexpr int rem2()const noexcept{if(dat.empty())return 0;else return dat[0] & 1;}inline constexpr bint &operator>>=(int k)noexcept{dat = std::vector<long long>(dat.begin() + std::min(k,int(size())),dat.end());return *this;}inline constexpr bint &operator<<=(int k)noexcept{if(!dat.empty()){std::vector<long long> add(k,0);dat.insert(dat.begin(),add.begin(),add.end());}return *this;}inline constexpr bint &operator/=(long long v)noexcept{if(v < 0)sign = -sign,v = -v;for(int i = size() - 1,rem = 0;i >= 0;i--){long long cur = dat[i] + rem * (long long)(base);dat[i] = (long long)(cur / v);rem = (long long)(cur % v);}norm();return *this;}friend std::pair<bint,bint> divmod_naive(const bint& _a,const bint& _b){bint zero,s,t;bint a = abs(_a),b = abs(_b);if(a < b)return std::make_pair(zero,a);bint ar = b;s.dat.resize(a.size()),t.dat.resize(b.size());int tx = a.size() - 1;for(;tx >= 0;--tx)if(a.dat[tx] > 0)break;for(int i = tx; i >= 0; --i){t <<= 1;t += a.dat[i];long long lo = 0,hi = base;if(t >= ar){while(hi - lo > 1){int mid = (hi + lo) / 2;if(ar * mid > t)hi = mid;else lo = mid;}t -= ar * lo;}s.dat[i] = lo;}if(_a.sign == _b.sign)s.sign = 1,t.sign = 1;else s.sign = -1,t.sign = 1;s.norm();t.norm();return std::make_pair(s,t);}inline constexpr bint &operator/=(const bint& a)noexcept{if(size() - a.size() <= 10)return *this = divmod_naive(bint(*this),a).first;else return *this = this->div_fast(a);}inline constexpr bint &operator%=(const bint& a)noexcept{if(size() - a.size() <= 10)return *this = divmod_naive(bint(*this),a).second;else return *this = bint(*this) - this->div_fast(a) * a;}inline constexpr bint operator+(const bint& a)const noexcept{return bint(*this) += a;}inline constexpr bint operator-(const bint& a)const noexcept{return bint(*this) -= a;}inline constexpr bint operator*(const bint& a)const noexcept{return bint(*this) *= a;}inline constexpr bint operator>>(int k)const noexcept{return bint(*this) >>= k;}inline constexpr bint operator<<(int k)const noexcept{return bint(*this) <<= k;}inline constexpr bint operator/(long long v)const noexcept{return bint(*this) /= v;}inline constexpr bint operator/(const bint& a)const noexcept{return bint(*this) /= a;}inline constexpr bint operator%(const bint& a)const noexcept{return bint(*this) %= a;}friend std::ostream &operator<<(std::ostream& os,const bint& a){return os << a.to_string();}friend std::istream &operator>>(std::istream& is,bint& a){std::string s;is >> s;a = bint(s);return is;}explicit operator bool()const noexcept{return !dat.empty();}explicit operator int()const noexcept{return to_ll();}using long_long = long long;explicit operator long_long()const noexcept{return to_ll();}int sign;std::vector<long long> dat;bint div_fast(const bint& _a)const noexcept{bint a = abs(*this),b = abs(_a);if(a < b)return bint();int tar = a.size() - b.size() + 1,m = 1;while(b.dat.back() * m * 10 < base)m *= 10;bint inv(m * base),pre(0);const bint two(2);while(inv != pre){pre = inv;inv *= (two << 2) - inv * b.dat.back();inv >>= 2;}int cur = 2,bcur = 1;pre = bint(0);while(inv != pre){bint c;c.dat = std::vector<long long>(b.dat.end() - bcur,b.dat.end());pre = inv;inv *= (two << (cur + bcur - 1)) - inv * c;int nex = std::min(cur << 1,tar);inv.dat = std::vector<long long>(inv.dat.end() - nex,inv.dat.end());cur = nex;bcur = std::min(bcur << 1,b.size());}inv.dat = std::vector<long long>(inv.dat.end() - tar,inv.dat.end());bint res = a * inv;res.dat = std::vector<long long>(res.dat.begin() + a.size(),res.dat.end());bint mul = res * b;while(mul + b <= a){res++;mul += b;}res.sign = sign * _a.sign;return res;}};using bint = bigint<4,10000>;#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param n `0 <= n`// @return minimum non-negative `x` s.t. `n <= 2**x`int ceil_pow2(int n) {int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;}// @param n `1 <= n`// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace atcoder#ifdef _MSC_VER#include <intrin.h>#endif#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}// Fast modular multiplication by barrett reduction// Reference: https://en.wikipedia.org/wiki/Barrett_reduction// NOTE: reconsider after Ice Lakestruct barrett {unsigned int _m;unsigned long long im;// @param m `1 <= m < 2^31`explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}// @return munsigned int umod() const { return _m; }// @param a `0 <= a < m`// @param b `0 <= b < m`// @return `a * b % m`unsigned int mul(unsigned int a, unsigned int b) const {// [1] m = 1// a = b = im = 0, so okay// [2] m >= 2// im = ceil(2^64 / m)// -> im * m = 2^64 + r (0 <= r < m)// let z = a*b = c*m + d (0 <= c, d < m)// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2// ((ab * im) >> 64) == c or c + 1unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x =(unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};// @param n `0 <= n`// @param m `1 <= m`// @return `(x ** n) % m`constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}// Reference:// M. Forisek and J. Jancina,// Fast Primality Testing for Integers That Fit into a Machine Word// @param n `0 <= n`constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime = is_prime_constexpr(n);// @param b `1 <= b`// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/gconstexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};// Contracts:// [1] s - m0 * a = 0 (mod b)// [2] t - m1 * a = 0 (mod b)// [3] s * |m1| + t * |m0| <= blong long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b// [3]:// (s - t * u) * |m1| + t * |m0 - m1 * u|// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)// = s * |m1| + t * |m0| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (m0 < 0) m0 += b / s;return {s, m0};}// Compile time primitive root// @param m must be prime// @return primitive root (and minimum in now)constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root = primitive_root_constexpr(m);// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = internal::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcodernamespace atcoder {namespace internal {template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i <= cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>void butterfly_inv(std::vector<mint>& a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for (int i = 0; i <= cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mint::mod() + l.val() - r.val()) *inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_naive(const std::vector<mint>& a, const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());std::vector<mint> ans(n + m - 1);if (n < m) {for (int j = 0; j < m; j++) {for (int i = 0; i < n; i++) {ans[i + j] += a[i] * b[j];}}} else {for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {ans[i + j] += a[i] * b[j];}}}return ans;}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for (int i = 0; i < z; i++) {a[i] *= b[i];}internal::butterfly_inv(a);a.resize(n + m - 1);mint iz = mint(z).inv();for (int i = 0; i < n + m - 1; i++) a[i] *= iz;return std::move(a);}} // namespace internaltemplate <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <class mint, internal::is_static_modint_t<mint>* = nullptr>std::vector<mint> convolution(const std::vector<mint>& a, const std::vector<mint>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (std::min(n, m) <= 60) return convolution_naive(a, b);return internal::convolution_fft(a, b);}template <unsigned int mod = 998244353,class T,std::enable_if_t<internal::is_integral<T>::value>* = nullptr>std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};using mint = static_modint<mod>;std::vector<mint> a2(n), b2(m);for (int i = 0; i < n; i++) {a2[i] = mint(a[i]);}for (int i = 0; i < m; i++) {b2[i] = mint(b[i]);}auto c2 = convolution(move(a2), move(b2));std::vector<T> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {c[i] = c2[i].val();}return c;}std::vector<long long> convolution_ll(const std::vector<long long>& a,const std::vector<long long>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};static constexpr unsigned long long MOD1 = 754974721; // 2^24static constexpr unsigned long long MOD2 = 167772161; // 2^25static constexpr unsigned long long MOD3 = 469762049; // 2^26static constexpr unsigned long long M2M3 = MOD2 * MOD3;static constexpr unsigned long long M1M3 = MOD1 * MOD3;static constexpr unsigned long long M1M2 = MOD1 * MOD2;static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;static constexpr unsigned long long i1 =internal::inv_gcd(MOD2 * MOD3, MOD1).second;static constexpr unsigned long long i2 =internal::inv_gcd(MOD1 * MOD3, MOD2).second;static constexpr unsigned long long i3 =internal::inv_gcd(MOD1 * MOD2, MOD3).second;auto c1 = convolution<MOD1>(a, b);auto c2 = convolution<MOD2>(a, b);auto c3 = convolution<MOD3>(a, b);std::vector<long long> c(n + m - 1);for (int i = 0; i < n + m - 1; i++) {unsigned long long x = 0;x += (c1[i] * i1) % MOD1 * M2M3;x += (c2[i] * i2) % MOD2 * M1M3;x += (c3[i] * i3) % MOD3 * M1M2;// B = 2^63, -B <= x, r(real value) < B// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)// r = c1[i] (mod MOD1)// focus on MOD1// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)// r = x,// x - M' + (0 or 2B),// x - 2M' + (0, 2B or 4B),// x - 3M' + (0, 2B, 4B or 6B) (without mod!)// (r - x) = 0, (0)// - M' + (0 or 2B), (1)// -2M' + (0 or 2B or 4B), (2)// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)// we checked that// ((1) mod MOD1) mod 5 = 2// ((2) mod MOD1) mod 5 = 3// ((3) mod MOD1) mod 5 = 4long long diff =c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));if (diff < 0) diff += MOD1;static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};x -= offset[diff % 5];c[i] = x;}return c;}} // namespace atcoderint main(){myset();bigint_convolution::set(atcoder::convolution_ll);bint _n,m;cin >> _n >> m;ll n = (_n % 10).to_ll(),ans = 1;debug(n,ans);while(m){if(m.rem2())ans = ans * n % 10;n = (n * n) % 10;m = m.div2();}cout << ans << "\n";}