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 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 97 ms / 1,000 ms |
| コード長 | 49,400 bytes |
| コンパイル時間 | 5,759 ms |
| コンパイル使用メモリ | 291,280 KB |
| 実行使用メモリ | 4,380 KB |
| 最終ジャッジ日時 | 2023-08-16 14:27:15 |
| 合計ジャッジ時間 | 8,121 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge12 |
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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 | 2 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,376 KB |
| testcase_02 | AC | 96 ms
4,376 KB |
| testcase_03 | AC | 97 ms
4,380 KB |
| testcase_04 | AC | 95 ms
4,380 KB |
| testcase_05 | AC | 2 ms
4,380 KB |
| testcase_06 | AC | 2 ms
4,380 KB |
| testcase_07 | AC | 2 ms
4,380 KB |
| testcase_08 | AC | 1 ms
4,380 KB |
| testcase_09 | AC | 1 ms
4,376 KB |
| testcase_10 | AC | 2 ms
4,376 KB |
| testcase_11 | AC | 2 ms
4,376 KB |
| testcase_12 | AC | 1 ms
4,376 KB |
| testcase_13 | AC | 1 ms
4,376 KB |
| testcase_14 | AC | 2 ms
4,380 KB |
| testcase_15 | AC | 1 ms
4,376 KB |
| testcase_16 | AC | 2 ms
4,376 KB |
| testcase_17 | AC | 1 ms
4,380 KB |
| testcase_18 | AC | 1 ms
4,376 KB |
| testcase_19 | AC | 1 ms
4,376 KB |
| testcase_20 | AC | 2 ms
4,376 KB |
| testcase_21 | AC | 1 ms
4,380 KB |
| testcase_22 | AC | 94 ms
4,380 KB |
| testcase_23 | AC | 95 ms
4,376 KB |
| testcase_24 | AC | 96 ms
4,376 KB |
| testcase_25 | AC | 93 ms
4,380 KB |
| testcase_26 | AC | 9 ms
4,380 KB |
| testcase_27 | AC | 95 ms
4,380 KB |
| testcase_28 | AC | 94 ms
4,380 KB |
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 second
void 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];
else
for(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>
#endif
namespace 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_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr 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 Lake
struct 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 m
unsigned 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 + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned 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/g
constexpr 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| <= b
long 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| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (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) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <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;
#else
template <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;
#endif
template <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 atcoder
namespace 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 internal
template <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 atcoder
namespace 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)) == 1
int 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) == 1
es[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)) == 1
int 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) == 1
es[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 internal
template <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; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static 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 = 4
long 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 atcoder
int 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";
}