#include <bits/stdc++.h>
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>istream &operator>>(istream &is,pair<T1,T2>&p){is>>p.first>>p.second;return is;}
template<typename T1,typename T2,typename T3>istream &operator>>(istream &is,tuple<T1,T2,T3>&a){is>>std::get<0>(a)>>std::get<1>(a)>>std::get<2>(a);return is;}
template<typename T,size_t n>istream &operator>>(istream &is,array<T,n>&a){for(auto&i:a)is>>i;return is;}
template<typename T>istream &operator>>(istream &is,vector<T> &a){for(auto &i:a)is>>i;return is;}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int n){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int n){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int n){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int n){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
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
template<typename T1,typename T2>ostream &operator<<(ostream &os,const pair<T1,T2>&p){os<<p.first<<' '<<p.second;return os;}
#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();
  }
}
#include<type_traits>
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);
}
constexpr int primitive_root_constexpr(int x){
  if(x==167772161)return 3;
  if(x==469762049)return 3;
  if(x==754974721)return 11;
  if(x==880803841)return 26;
  if(x==998244353)return 3;
  if(x==2)return 1;
  int x2=x;
  int p[20]={};
  int c=0;
  x--;
  for(int i=2;i*i<=x;i++){
    if(x%i==0){
      p[c++]=i;
      while(x%i==0)x/=i;
    }
  }
  if(x!=1)p[c++]=x;
  x=x2;
  for(int g=2;;g++){
    bool ok=true;
    for(int i=0;i<c;i++)if(pow_mod(g,(x-1)/p[i],x)==1){
      ok=false;
      break;
    }
    if(ok)return g;
  }
}
#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);}
template<int m>
struct ntt_root{
  static constexpr int rank2=lsb(m-1);
  static constexpr int g=primitive_root_constexpr(m);
  std::array<int,rank2+1>root,invroot;
  std::array<int,std::max(0,rank2-1)>rate2,invrate2;
  std::array<int,std::max(0,rank2-2)>rate3,invrate3;
  constexpr ntt_root(){
    root[rank2]=pow_mod(g,m>>rank2,m);
    invroot[rank2]=pow_mod(root[rank2],m-2,m);
    for(int i=rank2-1;i>=0;i--){
      root[i]=(long long)root[i+1]*root[i+1]%m;
      invroot[i]=(long long)invroot[i+1]*invroot[i+1]%m;
    }
    int prod=1,invprod=1;
    for(int i=0;i<rank2-1;i++){
      rate2[i]=(long long)root[i+2]*prod%m;
      invrate2[i]=(long long)invroot[i+2]*invprod%m;
      prod=(long long)prod*invroot[i+2]%m;
      invprod=(long long)invprod*root[i+2]%m;
    }
    prod=invprod=1;
    for(int i=0;i<rank2-2;i++){
      rate3[i]=(long long)root[i+3]*prod%m;
      invrate3[i]=(long long)invroot[i+3]*invprod%m;
      prod=(long long)prod*invroot[i+3]%m;
      invprod=(long long)invprod*root[i+3]%m;
    }
  }
};
template<typename T>
void dft(std::vector<T>&a){
  #ifdef NTT_SIMD
  if((int)a.size()>=32){
    dft_simd(a);
    return;
  }
  #endif
  static constexpr ntt_root<T::mod()>r;
  static constexpr unsigned long long mod2=(unsigned long long)T::mod()*T::mod();
  int n=a.size();
  int h=lsb(n);
  int len=0;
  while(len<h){
    if(h-len==1){
      T rot=T::raw(1);
      for(int s=0;s<(1<<len);s++){
        int of=s*2;
        T u=a[of],v=a[of+1]*rot;
        a[of]=u+v;
        a[of+1]=u-v;
        rot*=T::raw(r.rate2[lsb(~(unsigned int)s)]);
      }
      len++;
    }
    else{
      int p=1<<(h-len-2);
      T rot=T::raw(1),imag=T::raw(r.root[2]);
      for(int s=0;s<(1<<len);s++){
        const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
        int of=s<<(h-len);
        for(int i=0;i<p;i++){
          const unsigned long long a0=a[i+of].val(),a1=(unsigned long long)a[i+of+p].val()*rot1,a2=(unsigned long long)a[i+of+p*2].val()*rot2,a3=(unsigned long long)a[i+of+p*3].val()*rot3;
          const unsigned long long m=(unsigned long long)T(a1+mod2-a3).val()*imag.val();
          const unsigned long long k=mod2-a2;
          a[i+of]=a0+a2+a1+a3;
          a[i+of+p]=a0+a2+(mod2*2-a1-a3);
          a[i+of+p*2]=a0+k+m;
          a[i+of+p*3]=a0+k+(mod2-m);
        }
        rot*=T::raw(r.rate3[lsb(~(unsigned int)s)]);
      }
      len+=2;
    }
  }
}
template<typename T>
void idft(std::vector<T>&a){
  #ifdef NTT_SIMD
  if((int)a.size()>=32){
    idft_simd(a);
    return;
  }
  #endif
  static constexpr ntt_root<T::mod()>r;
  int n=a.size();
  int h=lsb(n);
  int len=h;
  while(len){
    if(len==1){
      int p=1<<(h-1);
      for(int i=0;i<p;i++){
        T u=a[i],v=a[i+p];
        a[i]=u+v;
        a[i+p]=u-v;
      }
      len--;
    }
    else{
      int p=1<<(h-len);
      T rot=T::raw(1),imag=T::raw(r.invroot[2]);
      for(int s=0;s<(1<<(len-2));s++){
        const unsigned long long rot1=rot.val(),rot2=rot1*rot1%T::mod(),rot3=rot1*rot2%T::mod();
        int of=s<<(h-len+2);
        for(int i=0;i<p;i++){
          const unsigned long long a0=a[i+of].val(),a1=a[i+of+p].val(),a2=a[i+of+p*2].val(),a3=a[i+of+p*3].val();
          const unsigned long long k=T((T::mod()+a2-a3)*imag.val()).val();
          a[i+of]=a0+a1+a2+a3;
          a[i+of+p]=(a0+T::mod()-a1+k)*rot1;
          a[i+of+p*2]=(a0+a1+T::mod()*2-a2-a3)*rot2;
          a[i+of+p*3]=(a0+T::mod()*2-a1-k)*rot3;
        }
        rot*=T::raw(r.invrate3[lsb(~(unsigned int)s)]);
      }
      len-=2;
    }
  }
}
template<typename T>
std::vector<T>ntt_convolution(std::vector<T> a,std::vector<T> b){
  int n=a.size(),m=b.size(),s=n+m-1;
  if(std::min(n,m)<60){
    if(n==0||m==0)return {};
    std::vector<T>ret(s,0);
    if(n<m)for(int i=0;i<m;i++)for(int j=0;j<n;j++)ret[i+j]+=a[j]*b[i];
    else for(int i=0;i<n;i++)for(int j=0;j<m;j++)ret[i+j]+=a[i]*b[j];
    return ret;
  }
  int z=ceil_pow2(s);
  a.resize(z,0);
  b.resize(z,0);
  dft(a),dft(b);
  std::vector<T>c(z);
  for(int i=0;i<z;i++)c[i]=a[i]*b[i];
  idft(c);
  T g=T::raw(z).inv();
  for(int i=0;i<s;i++)c[i]*=g;
  return {c.begin(),c.begin()+s};
}
template<typename T>
void ntt_doubling(std::vector<T>&a){
  static constexpr ntt_root<T::mod()>r;
  int n=a.size()/2;
  std::vector<T>b(a.begin(),a.begin()+n);
  idft(b);
  T now=T::raw(n).inv(),zeta=T::raw(r.root[msb(n)+1]);
  for(int i=0;i<n;i++){
    b[i]*=now;
    now*=zeta;
  }
  dft(b);
  std::copy(b.begin(),b.end(),a.begin()+n);
}
template<typename T>
std::vector<T> fps_inv(const std::vector<T> &a,int deg=-1){
  int n=a.size();
  if(deg==-1)deg=n;
  const T zero=T::raw(0);
  assert(a[0]!=zero);
  std::vector<T> ret(ceil_pow2(deg));
  ret[0]=a[0].inv();
  for(int m=1;m<deg;m<<=1){
    std::vector<T> f(a.begin(),a.begin()+std::min(n,m*2));
    if(f.size()<m*2)f.resize(m*2,0);
    std::vector<T> g(ret);
    f.resize(m*2);
    dft(f);
    g.resize(m*2);
    dft(g);
    for(int i=0;i<m*2;i++)f[i]*=g[i];
    idft(f);
    T inv=T::raw(m*2).inv();
    for(int i=0;i<m;i++)f[i]=zero;
    for(int i=m;i<m*2;i++)f[i]*=inv;
    dft(f);
    for(int i=0;i<m*2;i++)f[i]*=g[i];
    idft(f);
    for(int i=0;i<m*2;i++)f[i]*=inv;
    for(int i=m;i<m*2;i++)ret[i]-=f[i];
  }
  ret.resize(deg);
  return ret;
}
template<typename T>
T bostan_mori(std::vector<T> p,std::vector<T> q,long long k){
  static constexpr ntt_root<T::mod()>r;
  int n=ceil_pow2((int)std::max(p.size()+1,q.size())*2-1);
  p.resize(n,T::raw(0));
  q.resize(n,T::raw(0));
  dft(p),dft(q);
  T inv2=T::raw(2).inv();
  int n2=n/2;
  while(k>=n){
    for(int i=0;i<n;i++)p[i]*=q[i^1];
    if(k&1){
      T prod=inv2;
      for(int i=0;i<n2;i++){
        p[i]=(p[i*2]-p[i*2+1])*prod;
        prod*=T::raw(r.invrate2[lsb(~i)]);
      }
    }
    else{
      for(int i=0;i<n2;i++){
        p[i]=(p[i*2]+p[i*2+1])*inv2;
      }
    }
    for(int i=0;i<n2;i++)q[i]=q[i*2]*q[i*2+1];
    ntt_doubling(p),ntt_doubling(q);
    k>>=1;
  }
  idft(p),idft(q);
  q=fps_inv(q,k+1);
  T res=T();
  for(int i=0;i<=k;i++)res+=p[i]*q[k-i];
  return res;
}
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{
        int 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];
}
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);
}
#pragma once
#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<std::signed_integral T>
struct CRT{
  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];
    }
  }
  T operator()(std::vector<T>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(v[i]<0)v[i]+=pe[i];
      T x=T2(v[i]-res)*T2(invs[i])%pe[i];
      res+=x*prod;
      prod*=pe[i];
      if(res<0)res+=prod;
    }
    return res;
  }
};
#include<optional>
constexpr int carmichael_constexpr(int n){
  if(n==998244353)return 998244352;
  if(n==1000000007)return 1000000006;
  if(n<=1)return n;
  int res=1;
  int t=0;
  while(n%2==0){
    n/=2;
    t++;
  }
  if(t==2)res=2;
  else if(t>=3)res=1<<(t-2);
  for(int i=3;i*i<=n;i++)if(n%i==0){
    int c=0;
    while(n%i==0){
      n/=i;
      c++;
    }
    int prod=i-1;
    for(int j=0;j<c-1;j++)prod*=i;
    res=std::lcm(res,prod);
  }
  if(n!=1)res=std::lcm(res,n-1);
  return res;
}
template<typename T>
std::enable_if_t<std::is_integral_v<T>,T>carmichael(T n){
  T res=1;
  for(auto [p,e]:factorize(n)){
    if(p==2){
      if(e==2)res=2;
      else if(e>=3)res=T(1)<<(e-2);
    }
    else{
      T prod=p-1;
      for(int i=0;i<e-1;i++)prod*=p;
      res=std::lcm(res,prod);
    }
  }
  return res;
}
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;
  }
};
template<int id>
struct arbitrary_modint{
private:
  using uint=unsigned int;
  using mint=arbitrary_modint;
  uint v;
  static uint umod;
  static int car;
  static BarrettReduction 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++;
      int m2=umod-1,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(1<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;e=j;
      }
      return x;
    }
    else if(umod%8==5){
      mint ret=this->pow((umod+3)/8);
      if((ret*ret).val()==this->val())return ret;
      else return ret*mint::raw(2).pow((umod-1)/4);
    }
    else{
      return this->pow((umod+1)/4);
    }
  }
public:
  using value_type=uint;
  arbitrary_modint():v(0){}
  template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
  arbitrary_modint(T x):v(br.rem(x)){}
  template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
  arbitrary_modint(T x){
    x%=(int)umod;
    if(x<0)x+=(int)umod;
    v=x;
  }
  static void set_mod(int m_){
    assert(1<=m_);
    umod=m_;
    car=carmichael(umod);
    br=BarrettReduction(umod);
  }
  static int mod(){return umod;}
  static mint raw(int x){
    mint res;
    res.v=x;
    return res;
  }
  inline uint 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){
    this->v=br.rem((unsigned long long)this->v*b.v);
    return *this;
  }
  inline mint &operator/=(const mint &b){
    *this*=b.inv();
    return *this;
  }
  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;}
  friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
  friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
  friend inline bool operator<(const mint&a,const mint&b){return a.val()<b.val();}
  friend inline bool operator>(const mint&a,const mint&b){return a.val()>b.val();}
  friend inline bool operator<=(const mint&a,const mint&b){return a.val()<=b.val();}
  friend inline bool operator>=(const mint&a,const mint&b){return a.val()>=b.val();}
  inline mint operator++(int){
    mint ret=*this;
    *this+=mint::raw(1);
    return ret;
  }
  inline mint operator--(int){
    mint ret=*this;
    *this-=mint::raw(1);
    return ret;
  }
  mint pow(long long n)const{
    mint ret=mint::raw(1),a(*this);
    while(n){
      if(n&1)ret*=a;
      a*=a;
      n>>=1;
    }
    return ret;
  }
  inline mint inv()const{
    return pow(car-1);
  }
  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;
  }
  static unsigned int order(){return car;}
  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<int id>typename arbitrary_modint<id>::uint arbitrary_modint<id>::umod=2;
template<int id>int arbitrary_modint<id>::car=1;
template<int id>BarrettReduction arbitrary_modint<id>::br;
template<int id>
struct std::hash<arbitrary_modint<id>>{
  std::size_t operator()(arbitrary_modint<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<20260702>;
  CRT<int>crt(T::mod());
  std::vector<std::vector<int>>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<int>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;
}
template<typename T,int p1,int p2,int p3>
T crt3(int a1,int a2,int a3){
  static_assert(p1<p2&&p2<p3);
  static constexpr long long x=pow_mod<int>(p1,p2-2,p2);
  static constexpr long long y=pow_mod<int>((long long)p1*p2%p3,p3-2,p3);
  long long c=(a2-a1+p2)*x%p2;
  long long c2=a1+c*p1;
  c=(a3-c2%p3+p3)*y%p3;
  return T(c2)+T(c)*T(p1)*T(p2);
}
template<int m>
struct mod_int{
private:
  static constexpr unsigned int umod=static_cast<unsigned int>(m);
  static constexpr unsigned int car=carmichael_constexpr(m);
  using uint=unsigned int;
  using mint=mod_int;
  uint v;
  static_assert(m<uint(1)<<31);
  mint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if constexpr(m%8==1){
      mint b=2;
      while(b.pow((m-1)/2).val()==1)b++;
      int m2=m-1,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(1<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;e=j;
      }
      return x;
    }
    else if constexpr(m%8==5){
      mint ret=this->pow((m+3)/8);
      if((ret*ret).val()==this->val())return ret;
      else return ret*mint::raw(2).pow((m-1)/4);
    }
    else{
      return this->pow((m+1)/4);
    }
  }
public:
  using value_type=uint;
  mod_int():v(0){}
  template<typename T,std::enable_if_t<std::is_signed_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a){
    a%=m;
    if(a<0)v=a+umod;
    else v=a;
  }
  template<typename T,std::enable_if_t<std::is_unsigned_v<T>,std::nullptr_t> =nullptr>
  mod_int(T a):v(a%umod){}
  static constexpr mint raw(int a){
    mint ret;
    ret.v=a;
    return ret;
  }
  inline uint val()const{return this->v;}
  static constexpr int mod(){return m;}
  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){
    this->v=((unsigned long long)this->v*b.v)%umod;
    return *this;
  }
  inline mint &operator/=(const mint &b){
    *this*=b.inv();
    return *this;
  }
  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;}
  friend inline bool operator==(const mint &a,const mint &b){return a.val()==b.val();}
  friend inline bool operator!=(const mint &a,const mint &b){return !(a==b);}
  friend inline bool operator<(const mint &a,const mint &b){return a.val()<b.val();}
  friend inline bool operator>(const mint &a,const mint &b){return a.val()>b.val();}
  friend inline bool operator<=(const mint &a,const mint &b){return a.val()<=b.val();}
  friend inline bool operator>=(const mint &a,const mint &b){return a.val()>=b.val();}
  inline mint operator++(int){
    mint ret=*this;
    *this+=mint::raw(1);
    return ret;
  }
  inline mint operator--(int){
    mint ret=*this;
    *this-=mint::raw(1);
    return ret;
  }
  mint pow(long long n)const{
    mint ret=mint::raw(1),a(*this);
    while(n){
      if(n&1)ret*=a;
      a*=a;
      n>>=1;
    }
    return ret;
  }
  inline mint inv()const{
    assert(this->v!=0);
    return pow(car-1);
  }
  std::optional<mint>sqrt()const{
    if(this->val()<=1||this->pow((m-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  static constexpr unsigned int order(){return car;}
  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<int m>
struct std::hash<mod_int<m>>{
  std::size_t operator()(mod_int<m>x)const{
    return std::hash<unsigned int>()(x.val());
  }
};
using mint998=mod_int<998244353>;
using mint107=mod_int<1000000007>;
template<typename T>
std::vector<T>arbitrary_mod_convolution(const std::vector<T>&a,const std::vector<T>&b){
  if(a.empty()||b.empty())return std::vector<T>{};
  if(std::min(a.size(),b.size())<60){
    std::vector<T>ret(a.size()+b.size()-1,0);
    for(int i=0;i<a.size();i++)for(int j=0;j<b.size();j++)ret[i+j]+=a[i]*b[j];
    return ret;
  }
  using mint1=mod_int<167772161>;
  using mint2=mod_int<469762049>;
  using mint3=mod_int<998244353>;
  std::vector<mint1>a1(a.size()),b1(b.size());
  std::vector<mint2>a2(a.size()),b2(b.size());
  std::vector<mint3>a3(a.size()),b3(b.size());
  for(int i=0;i<a.size();i++){
    a1[i]=a[i].val();
    a2[i]=a[i].val();
    a3[i]=a[i].val();
  }
  for(int i=0;i<b.size();i++){
    b1[i]=b[i].val();
    b2[i]=b[i].val();
    b3[i]=b[i].val();
  }
  a1=ntt_convolution(a1,b1),a2=ntt_convolution(a2,b2),a3=ntt_convolution(a3,b3);
  std::vector<T>ret(a.size()+b.size()-1);
  for(int i=0;i<ret.size();i++)ret[i]=crt3<T,mint1::mod(),mint2::mod(),mint3::mod()>(a1[i].val(),a2[i].val(),a3[i].val());
  return ret;
}
template<typename T>
T kth_term(std::vector<T>p,long long k){
  std::vector<T>q=find_linear_recurrence(p);
  if constexpr(is_static_modint_v<T>){
    if((T::mod()-1)%(ceil_pow2(q.size()*2-1))==0){
      p=ntt_convolution(p,q);
      p.resize(q.size()-1);
      return bostan_mori(p,q,k);
    }
  }
  p=arbitrary_mod_convolution(p,q);
  int n=q.size();
  p.resize(n-1);
  std::vector<T>mq(n);
  while(k){
    for(int i=0;i<n;i++)mq[i]=i&1?-q[i]:q[i];
    p=arbitrary_mod_convolution(p,mq);
    q=arbitrary_mod_convolution(q,mq);
    std::vector<T>u(n-1),v(n);
    if(k&1)for(int i=0;i<n-1;i++)u[i]=p[i*2+1];
    else for(int i=0;i<n-1;i++)u[i]=p[i*2];
    for(int i=0;i<n;i++)v[i]=q[i*2];
    p=std::move(u),q=std::move(v);
    k>>=1;
  }
  if(p.empty())return 0;
  else return p[0];
}
using mint=mint998;
void SOLVE(){
  int k;
  ll l,r;
  cin>>k>>l>>r;
  vector<mint>dp(k*2+10);
  dp[0]=1;
  rep(i,1,dp.size()){
    dp[i]=dp[i-1]*k+mint(i-1).pow(k)+mint(k).pow(i-1);
  }
  rep(i,1,dp.size())dp[i]+=dp[i-1];
  mint ans=kth_term(dp,r);
  if(l!=0)ans-=kth_term(dp,l-1);
  cout<<ans<<endl;
}