結果
| 問題 | No.3673 未来予知 |
| コンテスト | |
| ユーザー |
 Taiki0715
|
| 提出日時 | 2026-09-04 22:58:10 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 37 ms / 200 ms |
| + 433µs | |
| コード長 | 29,255 bytes |
| 記録 | |
| コンパイル時間 | 3,416 ms |
| コンパイル使用メモリ | 366,308 KB |
| 実行使用メモリ | 6,400 KB |
| 最終ジャッジ日時 | 2026-09-04 23:04:44 |
| 合計ジャッジ時間 | 6,399 ms |
|
ジャッジサーバーID （参考情報） |
judge3_1 / judge5_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 32 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
template<typename T1,typename T2>istream &operator>>(istream&,pair<T1,T2>&);
template<typename...Args>istream &operator>>(istream&,tuple<Args...>&a);
template<typename T>istream &operator>>(istream&is,vector<T>&a);
template<typename T,size_t N>istream &operator>>(istream&is,array<T,N>&a);
template<typename T1,typename T2>
istream &operator>>(istream&is,pair<T1,T2>&a){
is>>a.first>>a.second;
return is;
}
template<size_t pos,typename...Args>
void read_tuple(istream&is,tuple<Args...>&a){
if constexpr(pos<tuple_size<tuple<Args...>>::value){
is>>get<pos>(a);
read_tuple<pos+1>(is,a);
}
}
template<typename...Args>
istream &operator>>(istream&is,tuple<Args...>&a){
read_tuple<0>(is,a);
return is;
}
template<typename T>
istream &operator>>(istream&is,vector<T>&a){
for(T&x:a)is>>x;
return is;
}
template<typename T,size_t N>
istream &operator>>(istream&is,array<T,N>&a){
for(T&x:a)is>>x;
return is;
}
template<typename T1,typename T2>ostream &operator<<(ostream&os,const pair<T1,T2>&);
template<typename...Args>ostream &operator<<(ostream&os,const tuple<Args...>&);
template<typename T>ostream &operator<<(ostream&os,const vector<T>&);
template<typename T,typename Seq,typename Comp>ostream &operator<<(ostream&os,priority_queue<T,Seq,Comp>);
template<typename T>ostream &operator<<(ostream&os,queue<T>);
template<typename T>ostream &operator<<(ostream&os,deque<T>);
template<typename T>ostream &operator<<(ostream&os,stack<T>);
template<typename T,size_t N>ostream &operator<<(ostream&os,const array<T,N>&);
template<typename Key,typename Val,typename Comp>ostream &operator<<(ostream&os,const map<Key,Val,Comp>&);
template<typename Key,typename Val,typename Hash>ostream &operator<<(ostream&os,const unordered_map<Key,Val,Hash>&);
template<typename T,typename Comp>ostream &operator<<(ostream&os,const set<T,Comp>&);
template<typename T,typename Comp>ostream &operator<<(ostream&os,const multiset<T,Comp>&);
template<typename T,typename Hash>ostream &operator<<(ostream&os,const unordered_set<T,Hash>&);
template<typename T1,typename T2>
ostream &operator<<(ostream&os,const pair<T1,T2>&a){
os<<a.first<<' '<<a.second;
return os;
}
template<size_t pos,typename...Args>
void write_tuple(ostream&os,const tuple<Args...>&a){
if constexpr(pos<tuple_size<tuple<Args...>>::value){
if constexpr(pos>0)os<<' ';
os<<get<pos>(a);
write_tuple<pos+1>(os,a);
}
}
template<typename...Args>
ostream &operator<<(ostream&os,const tuple<Args...>&a){
write_tuple<0>(os,a);
return os;
}
template<typename T>
ostream &operator<<(ostream&os,const vector<T>&a){
os<<'{';
for(int i=0;i<(int)a.size();i++){
os<<a[i];
if(i+1!=a.size())os<<',';
}
os<<'}';
return os;
}
template<typename T,typename Seq,typename Comp>
ostream &operator<<(ostream&os,priority_queue<T,Seq,Comp>a){
os<<'{';
if(!a.empty()){
os<<a.top();a.pop();
while(!a.empty()){
os<<',';
os<<a.top();
a.pop();
}
}
os<<'}';
return os;
}
template<typename T>
ostream &operator<<(ostream&os,queue<T>a){
os<<'{';
if(!a.empty()){
os<<a.front();a.pop();
while(!a.empty()){
os<<',';
os<<a.front();
a.pop();
}
}
os<<'}';
return os;
}
template<typename T>
ostream &operator<<(ostream&os,deque<T>a){
os<<'{';
if(!a.empty()){
os<<a.front();a.pop_front();
while(!a.empty()){
os<<',';
os<<a.front();
a.pop_front();
}
}
os<<'}';
return os;
}
template<typename T>
ostream &operator<<(ostream&os,stack<T>a){
os<<'{';
if(!a.empty()){
os<<a.top();a.pop();
while(!a.empty()){
os<<',';
os<<a.top();
a.pop();
}
}
os<<'}';
return os;
}
template<typename T,size_t N>
ostream &operator<<(ostream&os,const array<T,N>&a){
os<<'{';
for(int i=0;i<(int)a.size();i++){
os<<a[i];
if(i+1!=a.size())os<<',';
}
os<<'}';
return os;
}
template<typename Key,typename Val,typename Comp>
ostream &operator<<(ostream&os,const map<Key,Val,Comp>&a){
if(a.empty()){
os<<"{}";
return os;
}
auto itr=a.begin();
os<<"{["<<itr->first<<","<<itr->second<<']';
while(++itr!=a.end())os<<",["<<itr->first<<','<<itr->second<<']';
os<<'}';
return os;
}
template<typename Key,typename Val,typename Hash>
ostream &operator<<(ostream&os,const unordered_map<Key,Val,Hash>&a){
if(a.empty()){
os<<"{}";
return os;
}
auto itr=a.begin();
os<<"{["<<itr->first<<","<<itr->second<<']';
while(++itr!=a.end())os<<",["<<itr->first<<','<<itr->second<<']';
os<<'}';
return os;
}
template<typename T,typename Comp>
ostream &operator<<(ostream&os,const set<T,Comp>&a){
if(a.empty()){
os<<"{}";
return os;
}
auto itr=a.begin();
os<<'{'<<*itr;
while(++itr!=a.end())os<<','<<*itr;
os<<'}';
return os;
}
template<typename T,typename Comp>
ostream &operator<<(ostream&os,const multiset<T,Comp>&a){
if(a.empty()){
os<<"{}";
return os;
}
auto itr=a.begin();
os<<'{'<<*itr;
while(++itr!=a.end())os<<','<<*itr;
os<<'}';
return os;
}
template<typename T,typename Hash>
ostream &operator<<(ostream&os,const unordered_set<T,Hash>&a){
if(a.empty()){
os<<"{}";
return os;
}
auto itr=a.begin();
os<<'{'<<*itr;
while(++itr!=a.end())os<<','<<*itr;
os<<'}';
return os;
}
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int){for(auto &i:a)i--;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
else return init;
}
#ifdef LOCAL
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
#endif
struct Timer{
clock_t start;
Timer(){
start=clock();
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout<<fixed<<setprecision(16);
}
inline double now(){return (double)(clock()-start)/1000;}
#ifdef LOCAL
~Timer(){
cerr<<"time:";
cerr<<now();
cerr<<"ms\n";
}
#endif
}timer;
void SOLVE();
int main(){
int testcase=1;
//cin>>testcase;
for(int i=0;i<testcase;i++){
SOLVE();
}
}
template<typename T>
std::vector<T> berlekamp_massey(const std::vector<T>&s){
const int n=s.size();
std::vector<T>b,c;
b.reserve(n+1),c.reserve(n+1);
b.emplace_back(1),c.emplace_back(1);
T y=1;
for(int i=1;i<=n;i++){
int l=c.size(),m=b.size();
T x=0;
for(int j=0;j<l;j++)x+=c[j]*s[i-l+j];
b.emplace_back(0);
++m;
if(x==0)continue;
T f=x/y;
if(l<m){
auto c2=c;
c.insert(c.begin(),m-l,0);
for(int j=0;j<m;j++)c[m-1-j]-=f*b[m-1-j];
b=c2;
y=x;
}
else{
for(int j=0;j<m;j++)c[l-1-j]-=f*b[m-1-j];
}
}
std::reverse(c.begin(),c.end());
return c;
}
template<typename T>
std::vector<T>reeds_sloane(const std::vector<T>a,std::pair<int,int>pe){
int n=a.size();
std::vector<std::vector<T>>Q(pe.second),B(pe.second);
std::vector<int>nb(pe.second,-1);
std::vector<T>tb(pe.second);
T powp=1;
for(int j=0;j<pe.second;j++){
Q[j]={powp};
powp*=pe.first;
}
for(int i=0;i<n;i++){
std::vector<std::pair<T,int>>tu(pe.second);
for(int j=0;j<pe.second;j++){
T x=0;
for(int k=0;k<(int)Q[j].size();k++){
x+=Q[j][k]*a[i-k];
}
if(x.val()==0)tu[j]=std::make_pair(1,pe.second);
else{
auto x2=x.val();
int ne=tu[j].second;
while(x2%pe.first==0)x2/=pe.first,ne++;
tu[j]=std::make_pair(x2,ne);
}
}
std::vector<std::vector<T>>nQ(Q);
for(int j=0;j<pe.second;j++){
if(tu[j].second==pe.second)continue;
int k=pe.second-1-tu[j].second;
if(nb[k]==-1)nQ[j].resize(i+2);
else{
T c=tu[j].first/tb[k];
if(i+B[k].size()-nb[k]>nQ[j].size())nQ[j].resize(i+B[k].size()-nb[k]);
for(int l=0;l<(int)B[k].size();l++)nQ[j][i+l-nb[k]]-=c*B[k][l];
}
}
for(int j=0;j<pe.second;j++){
if(Q[j].size()<nQ[j].size()){
int k=pe.second-1-tu[j].second;
B[j]=Q[k];
nb[j]=i;
tb[j]=tu[k].first;
}
}
Q=std::move(nQ);
}
return Q[0];
}
#include<type_traits>
#include<concepts>
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}
template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}
template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}
template<std::integral T>
constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);}
template<std::integral T>
constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);}
constexpr unsigned long long binary_gcd(unsigned long long a,unsigned long long b){
if(a==0||b==0||a==b)return a<b?b:a;
int n=lsb(a),m=lsb(b);
while(a!=b){
if(a>b)a=(a-b)>>lsb(a-b);
else b=(b-a)>>lsb(b-a);
}
return a<<(n<m?n:m);
}
#include<initializer_list>
bool isprime(unsigned long long n){
using u64=unsigned long long;
if(n<=1)return false;
if(n%2==0)return n==2;
u64 d=n-1;
int s=0;
while(!(d&1))d>>=1,s++;
int q=63;
while(!(d>>q))q--;
u64 r=n;
for(int i=0;i<5;i++)r*=2-r*n;
auto redc=[&r,&n](__uint128_t x)->u64 {
x=(x+__uint128_t(u64(x)*-r)*n)>>64;
return x>=n?x-n:x;
};
__uint128_t r2=-__uint128_t(n)%n;
u64 one=redc(r2);
for(u64 base:{2,325,9375,28178,450775,9780504,1795265022}){
if(base%n==0)continue;
u64 a=base=redc((base%n)*r2);
for(int i=q-1;i>=0;i--){
a=redc(__uint128_t(a)*a);
if(d>>i&1)a=redc(__uint128_t(a)*base);
}
if(a==one)continue;
for(int i=1;a!=n-one;i++){
if(i>=s)return false;
a=redc(__uint128_t(a)*a);
}
}
return true;
}
template<std::integral T>
std::vector<std::pair<T,int>>factorize(T n)noexcept{
std::vector<unsigned long long>fs;
auto div=[](unsigned long long x)noexcept->unsigned long long {
unsigned long long r=x;
for(int i=0;i<5;i++)r*=2-r*x;
unsigned long long r2=-__uint128_t(x)%x;
auto redc=[&r,&x](__uint128_t t)->unsigned long long {
t=(t+__uint128_t((unsigned long long)t*-r)*x)>>64;
return t>=x?t-x:t;
};
unsigned long long a=0,b=0;
const unsigned long long one=redc(r2);
unsigned long long e=one;
int m=1ll<<((63-__builtin_clzll(x))>>3);
while(true){
unsigned long long ca=a,cb=b;
unsigned long long sk=one;
for(int i=0;i<m;i++){
a=redc(__uint128_t(a)*a+e);
b=redc(__uint128_t(b)*b+e);
b=redc(__uint128_t(b)*b+e);
unsigned long long c=redc(a),d=redc(b);
sk=redc(__uint128_t(sk)*(c>d?c-d:d-c));
}
unsigned long long g=binary_gcd(redc(sk),x);
if(g>1){
if(g<x)return g;
for(int i=0;i<m;i++){
ca=redc(__uint128_t(ca)*ca+e);
cb=redc(__uint128_t(cb)*cb+e);
cb=redc(__uint128_t(cb)*cb+e);
unsigned long long c=redc(ca),d=redc(cb);
unsigned long long cg=binary_gcd(c>d?c-d:d-c,x);
if(cg>1){
if(cg<x)return cg;
else{
e+=one;
a=b=0;
break;
}
}
}
}
}
};
static unsigned long long st[64];
int p=0;
while(!(n&1)){
n>>=1;
fs.push_back(2);
}
if(n>1)st[p++]=n;
while(p){
unsigned long long now=st[--p];
if(isprime(now)){
fs.push_back(now);
continue;
}
unsigned long long d=div(now);
st[p++]=d;
now/=d;
if(now!=1)st[p++]=now;
}
std::sort(fs.begin(),fs.end());
std::vector<std::pair<T,int>>res;
for(int i=0;i<(int)fs.size();){
int j=i;
while(j<(int)fs.size()&&fs[i]==fs[j])j++;
res.emplace_back(fs[i],j-i);
i=j;
}
return res;
}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits<=32),T>pow_mod(T a,T n,T mod){
using u64=unsigned long long;
u64 res=1;
while(n>0){
if(n&1)res=((u64)res*a)%mod;
a=((u64)a*a)%mod;
n>>=1;
}
return T(res);
}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),T>pow_mod(T a,T n,T mod){
using u128=__uint128_t;
u128 res=1;
while(n>0){
if(n&1)res=((u128)res*a)%mod;
a=((u128)a*a)%mod;
n>>=1;
}
return T(res);
}
template<typename Ts>
struct CRT{
using T=std::make_signed_t<Ts>;
std::vector<std::pair<T,int>>f;
std::vector<T>pe;
std::vector<T>invs;
using T2=std::conditional_t<(std::numeric_limits<T>::digits<=32),int64_t,__int128_t>;
CRT(){}
CRT(T n):f(factorize(n)){
pe.resize(f.size());
for(int i=0;i<(int)f.size();i++){
pe[i]=1;
for(int j=0;j<f[i].second;j++)pe[i]*=f[i].first;
}
invs.resize(f.size());
T prod=1;
for(int i=0;i<(int)f.size();i++){
invs[i]=pow_mod(prod%pe[i],pe[i]/f[i].first*(f[i].first-1)-1,pe[i]);
prod*=pe[i];
}
}
Ts operator()(std::vector<Ts>v){
assert(v.size()==pe.size());
T res=0,prod=1;
for(int i=0;i<(int)pe.size();i++){
v[i]%=pe[i];
if constexpr(std::is_signed_v<Ts>){
if(v[i]<0)v[i]+=pe[i];
}
T x=T2(T(v[i])-res)*T2(invs[i])%pe[i];
res+=x*prod;
prod*=pe[i];
if(res<0)res+=prod;
}
return res;
}
};
#include<optional>
#include<variant>
struct BarrettReduction{
private:
using i64=long long;
using u64=unsigned long long;
using u32=unsigned int;
using u128=__uint128_t;
u32 m;
u64 im;
public:
BarrettReduction():m(0),im(0){}
BarrettReduction(u32 n):m(n),im(u64(-1)/n+1){}
inline i64 quo(u64 x)const{
if(m==1)return x;
u64 y=u64((u128(x)*im)>>64);
u32 r=x-y*m;
return m<=r?y-1:y;
}
inline u32 rem(u64 x)const{
if(m==1)return 0;
u64 y=u64((u128(x)*im)>>64);
u32 r=x-y*m;
return m<=r?r+m:r;
}
inline std::pair<u64,u32>quo_rem(u64 x)const{
if(m==0)return std::make_pair(x,0);
u64 y=u64((u128(x)*im)>>64);
u32 r=x-y*m;
return m<=r?std::make_pair(y-1,r+m):std::make_pair(y,r);
}
inline u32 pow(u32 a,u64 p)const{
u32 res=m!=1;
while(p){
if(p&1)res=rem(u64(res)*a);
a=rem(u64(a)*a);
p>>=1;
}
return res;
}
};
constexpr std::pair<long long,long long>ext_gcd(long long a,long long b){
if(b==0)return std::make_pair(1,0);
auto [x,y]=ext_gcd(b,a%b);
std::swap(x,y);
return std::make_pair(x,y-a/b*x);
}
template<std::signed_integral T>
constexpr std::pair<T,T> inv_mod(T a,T b){
a%=b;
if(a<0)a+=b;
if(a==0)return std::make_pair(b,0);
T s=b,t=a;
T m0=0,m1=1;
while(t){
T u=s/t;
s-=t*u;
m0-=m1*u;
std::swap(s,t);
std::swap(m0,m1);
}
if(m0<0)m0+=b/s;
return std::make_pair(s,m0);
}
template<typename T,int id>
struct arbitrary_modint{
using value_type=std::make_unsigned_t<T>;
using mul_type=std::conditional_t<(std::numeric_limits<T>::digits<=32),uint64_t,__uint128_t>;
private:
using mint=arbitrary_modint;
value_type v;
static value_type umod;
static std::conditional_t<(std::numeric_limits<T>::digits<=32),BarrettReduction,std::monostate>br;
mint sqrt_impl()const{
if(this->val()<=1)return *this;
if(umod%8==1){
mint b=2;
while(b.pow((umod-1)/2).val()==1)b++;
value_type m2=umod-1;
int e=0;
while(m2%2==0)m2>>=1,e++;
mint x=this->pow((m2-1)/2);
mint y=(*this)*x*x;
x*=*this;
mint z=b.pow(m2);
while(y.val()!=1){
int j=0;
mint t=y;
while(t.val()!=1)t*=t,j++;
z=z.pow((value_type(1))<<(e-j-1));
x*=z;
z*=z;
y*=z;
e=j;
}
return x;
}
else if(umod%8==5){
mint res=this->pow((umod+3)/8);
if((res*res).val()==this->val())return res;
else return res*mint(2).pow((umod-1)/4);
}
else return this->pow((umod+1)/4);
}
public:
arbitrary_modint():v(0){}
template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
arbitrary_modint(U x){
x%=std::make_signed_t<value_type>(umod);
v=x>=0?x:x+umod;
}
template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
arbitrary_modint(U x):v(x%umod){}
static void set_mod(T m){
assert(1<=m);
umod=m;
if constexpr(std::numeric_limits<T>::digits<=32)br=BarrettReduction(umod);
}
static T mod(){return umod;}
static mint raw(T x){
mint res;
res.v=x;
return res;
}
inline T val()const{return v;}
inline mint &operator+=(const mint&b){
this->v+=b.v;
if(this->v>=umod)this->v-=umod;
return *this;
}
inline mint &operator-=(const mint&b){
this->v-=b.v;
if(this->v>=umod)this->v+=umod;
return *this;
}
inline mint &operator*=(const mint&b){
mul_type v=mul_type(this->v)*mul_type(b.v);
if constexpr(std::numeric_limits<T>::digits<=32)this->v=br.rem(v);
else this->v=v%umod;
return *this;
}
inline mint &operator/=(const mint&b){return *this*=b.inv();}
inline mint operator+()const{return *this;}
inline mint operator-()const{return mint()-*this;}
friend inline mint operator+(const mint&a,const mint&b){return mint(a)+=b;}
friend inline mint operator-(const mint&a,const mint&b){return mint(a)-=b;}
friend inline mint operator*(const mint&a,const mint&b){return mint(a)*=b;}
friend inline mint operator/(const mint&a,const mint&b){return mint(a)/=b;}
auto operator<=>(const mint&)const=default;
inline mint operator++(int){
mint res=*this;
this->v++;
if(this->v==umod)this->v=0;
return res;
}
inline mint operator--(int){
mint res=*this;
if(this->v==0)this->v=umod;
this->v--;
return res;
}
template<std::integral U>
mint pow(U k)const{
if constexpr(std::is_signed_v<U>){
assert(0<=k);
}
mint res=1,a(*this);
while(k){
if(k&1)res*=a;
a*=a;
k>>=1;
}
return res;
}
mint inv()const{
mint res;
auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
assert(g==1);
res.v=x;
return res;
}
std::optional<mint>sqrt()const{
if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
else return std::nullopt;
}
friend std::istream &operator>>(std::istream&is,mint&b){
long long a;
is>>a;
b=mint(a);
return is;
}
friend std::ostream &operator<<(std::ostream&os,const mint&b){
os<<b.val();
return os;
}
};
template<typename T,int id>typename arbitrary_modint<T,id>::value_type arbitrary_modint<T,id>::umod=2;
template<typename T,int id>std::conditional_t<(std::numeric_limits<T>::digits<=32),BarrettReduction,std::monostate>arbitrary_modint<T,id>::br;
template<typename T,int id>
struct std::hash<arbitrary_modint<T,id>>{
std::size_t operator()(arbitrary_modint<T,id>x)const{
return std::hash<unsigned int>()(x.val());
}
};
struct is_modint_impl{
template<typename T>
static auto check(T&&x)->decltype(x.mod(),std::true_type{});
template<typename T>
static auto check(...)->std::false_type;
};
template<typename T>
struct is_modint:public decltype(is_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_modint_v=is_modint<T>::value;
struct is_dynamic_modint_impl{
template<typename T>
static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{});
template<typename T>
static auto check(...)->std::false_type;
};
template<typename T>
struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_dynamic_modint_v=is_dynamic_modint<T>::value;
template<typename T>
inline constexpr bool is_static_modint_v=is_modint_v<T>&&!is_dynamic_modint_v<T>;
struct is_uso_modint_impl{
template<typename T>
static auto check(T&&x)->decltype(x.uso(),std::true_type{});
template<typename T>
static auto check(...)->std::false_type;
};
template<typename T>
struct is_uso_modint:public decltype(is_uso_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_uso_modint_v=is_uso_modint<T>::value;
template<typename T>
std::vector<T>find_linear_recurrence(std::vector<T>a){
static_assert(is_modint_v<T>);
if(T::mod()==1)return {0};
using mint=arbitrary_modint<typename T::value_type,20260702>;
CRT<typename T::value_type>crt(T::mod());
std::vector<std::vector<typename T::value_type>>f(crt.f.size());
int l=0;
for(int i=0;i<(int)crt.f.size();i++){
mint::set_mod(crt.pe[i]);
std::vector<mint>b(a.size());
for(int j=0;j<(int)a.size();j++)b[j]=a[j].val();
if(crt.f[i].second==1)b=berlekamp_massey(b);
else b=reeds_sloane(b,crt.f[i]);
f[i].resize(b.size());
for(int j=0;j<(int)b.size();j++)f[i][j]=b[j].val();
if(l<(int)f[i].size())l=f[i].size();
}
std::vector<T>res(l);
for(int i=0;i<l;i++){
std::vector<typename T::value_type>now(f.size());
for(int j=0;j<(int)f.size();j++){
now[j]=i<(int)f[j].size()?f[j][i]:0;
}
res[i]=crt(now);
}
return res;
}
constexpr bool isprime_constexpr(unsigned long long n){
if(n==998244353)return true;
if(n==1000000007)return true;
if(n<64)return 2891462833508853932ll>>n&1;
if(n%2==0)return false;
unsigned long long d=n-1;
int s=0;
while(!(d&1))d>>=1,s++;
int q=63;
while(!(d>>q))q--;
unsigned long long r=n;
for(int i=0;i<5;i++)r*=2-r*n;
auto redc=[&r,&n](__uint128_t x)->unsigned long long {
x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;
return x>=n?x-n:x;
};
__uint128_t r2=-__uint128_t(n)%n;
unsigned long long one=redc(r2);
for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){
if(base%n==0)continue;
unsigned long long a=base=redc((base%n)*r2);
for(int i=q-1;i>=0;i--){
a=redc(__uint128_t(a)*a);
if(d>>i&1)a=redc(__uint128_t(a)*base);
}
if(a==one)continue;
for(int i=1;a!=n-one;i++){
if(i>=s)return false;
a=redc(__uint128_t(a)*a);
}
}
return true;
}
template<auto m>
struct modint{
static_assert(1<=m&&m<(1ull<<63));
using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
private:
value_type v;
static constexpr value_type umod=m;
constexpr modint sqrt_impl()const{
if(this->val()<=1)return *this;
if(umod%8==1){
modint b=2;
while(b.pow((umod-1)/2).val()==1)b++;
value_type m2=umod-1;
int e=0;
while(m2%2==0)m2>>=1,e++;
modint x=this->pow((m2-1)/2);
modint y=(*this)*x*x;
x*=*this;
modint z=b.pow(m2);
while(y.val()!=1){
int j=0;
modint t=y;
while(t.val()!=1)t*=t,j++;
z=z.pow((value_type(1))<<(e-j-1));
x*=z;
z*=z;
y*=z;
e=j;
}
return x;
}
else if(umod%8==5){
modint res=this->pow((umod+3)/8);
if((res*res).val()==this->val())return res;
else return res*modint(2).pow((umod-1)/4);
}
else return this->pow((umod+1)/4);
}
template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
static constexpr value_type take_mod(U x){
if constexpr(std::numeric_limits<U>::max()<umod)return x;
if constexpr(umod==(1ull<<61)-1){
value_type res=(x>>61)+(x&umod);
if(res>=umod)res-=umod;
return res;
}
if constexpr(umod==(1ull<<61)-(1ull<<24)+1){
value_type high=x>>61,low=x&((1ull<<61)-1);
mul_type t=low+(mul_type(high)<<24)-high;
high=t>>61,low=t&((1ull<<61)-1);
low=low+(mul_type(high)<<24)-high;
if(low>=umod)low-=umod;
return low;
}
return x%umod;
}
public:
constexpr modint():v(0){}
template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
constexpr modint(U x){
x%=std::make_signed_t<value_type>(umod);
v=x>=0?x:x+umod;
}
template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
constexpr modint(U x):v(take_mod<U>(x)){}
static constexpr value_type mod(){return umod;}
template<typename U>
static constexpr modint raw(U x){
modint res;
res.v=x;
return res;
}
constexpr std::make_signed_t<value_type> val()const{return v;}
constexpr modint &operator+=(const modint&b){
this->v+=b.v;
if(this->v>=umod)this->v-=umod;
return *this;
}
constexpr modint &operator-=(const modint&b){
this->v-=b.v;
if(this->v>=umod)this->v+=umod;
return *this;
}
constexpr modint &operator*=(const modint&b){
this->v=take_mod(mul_type(this->v)*mul_type(b.v));
return *this;
}
constexpr modint &operator/=(const modint&b){return *this*=b.inv();}
constexpr modint operator+()const{return *this;}
constexpr modint operator-()const{return modint()-*this;}
friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;}
friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;}
friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;}
friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;}
constexpr auto operator<=>(const modint&)const=default;
constexpr modint operator++(int){
modint res=*this;
this->v++;
if(this->v==umod)this->v=0;
return res;
}
constexpr modint operator--(int){
modint res=*this;
if(this->v==0)this->v=umod;
this->v--;
return res;
}
template<std::integral U>
constexpr modint pow(U k)const{
if constexpr(std::is_signed_v<U>){
assert(0<=k);
}
modint res=1,a(*this);
while(k){
if(k&1)res*=a;
a*=a;
k>>=1;
}
return res;
}
constexpr modint inv()const{
if constexpr(isprime_constexpr(umod)){
if(std::is_constant_evaluated()){
if(v==0){
throw "no inverse";
}
}
else assert(v!=0);
return pow(umod-2);
}
else{
modint res;
auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
if(std::is_constant_evaluated()){
if(g!=1){
throw "no inverse";
}
}
else assert(g==1);
res.v=x;
return res;
}
}
std::optional<modint>sqrt()const{
if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
else return std::nullopt;
}
friend std::istream &operator>>(std::istream&is,modint&b){
long long a;
is>>a;
b=modint(a);
return is;
}
friend std::ostream &operator<<(std::ostream&os,const modint&b){
os<<b.val();
return os;
}
};
template<auto m>
struct std::hash<modint<m>>{
std::size_t operator()(modint<m>x)const{
return std::hash<typename modint<m>::value_type>(x.val());
}
};
using mint998=modint<998244353>;
using mint107=modint<1000000007>;
using mint61=modint<2305843009213693951>;
using mint6124=modint<2305843009196916737>;
using mint=modint<2>;
void SOLVE(){
string t;
int n;
cin>>t>>n;
vector<mint>pre(t.size()*2);
string a="RSPX";
string win="XRSP";
rep(i,t.size()){
int p=a.find(t[i]);
pre[i*2]=p&1;
pre[i*2+1]=p>>1;
}
auto coef=find_linear_recurrence(pre);
pre.resize((t.size()+n)*2);
rep(i,t.size()*2,pre.size()){
mint now=0;
rep(j,1,coef.size())if(i-j>=0)now+=coef[j]*pre[i-j];
pre[i]=now;
}
string ans;
rep(i,n){
int id=(pre[t.size()*2+i*2].val())+(pre[t.size()*2+i*2+1].val())*2;
ans+=win[id];
}
cout<<ans<<endl;
}