#ifndef MYLOCAL
//# pragma GCC target("avx2")//yukiではNG
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
#endif
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
using namespace std;
using ll=long long;
using dd=long double;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll,ll>;
using qll=tuple<ll,ll,ll,ll>;
using namespace chrono;
constexpr ll INF = 1201001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define EXPAND( x ) x//VS用おまじない
#define overload3(_1,_2,_3,name,...) name
#define overload4(_1,_2,_3,_4,name,...) name
#define overload5(_1,_2,_3,_4,_5,name,...) name
#define rep1(N)          for (ll dmyi = 0; dmyi < (N); dmyi++)
#define rep2(i, N)       for (ll i = 0; i < (N); i++)
#define rep3(i, S, E)    for (ll i = (S); i <= (E); i++)
#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))
#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))
#define dep3(i, E, S)    for (ll i = (E); i >= (S); i--)
#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))
#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))
#define ALL1(v)     (v).begin(),     (v).end()
#define ALL2(v,E)   (v).begin(),     (v).begin()+((E)+1)
#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)
#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> [[nodiscard]] inline T limithi(T a,T b){ return min(a,b); }
template<class T> [[nodiscard]] inline T limitlo(T a,T b){ return max(a,b); }
template<class T> inline bool chlimithi(T &a,T b){ return chmin(a,b); }
template<class T> inline bool chlimitlo(T &a,T b){ return chmax(a,b); }
template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }
template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }
template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }
template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }
template<class T,class U=typename remove_reference<T>::type::value_type>
inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}
template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}
template<class T> inline ll sz(T &&v){ return (ll)v.size(); }

//cin
struct cinutil{
    template<class T> static void cin1core(T &a){ cin>>a; }
    template<class T,class S> static void cin1core(pair<T,S> &a){
        cin1core(a.first),cin1core(a.second);
    }
    template<class... Args> static void cin1core(tuple<Args...> &a){
        cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);
    }
    template<class T,size_t N>
    static void cin1core(array<T,N> &a){ for (int i=0; i<(int)N; ++i) cin>>a[i]; }
private:
    template<class Tpl,int i> struct cinTplRec{
        void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }
    };
    template<class Tpl> struct cinTplRec<Tpl,0>{
        void operator()(Tpl &a){ cin1core(get<0>(a)); }
    };
};
template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }
template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }

//cout
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
template<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); }
template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i];  return os; }

inline struct{
  system_clock::time_point st = system_clock::now();
  ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;


template<long long MOD> struct mll_{
    using Int = long long;
    using ll = long long;
    ll val_=0;
    /*---- utility ----*/
    mll_ &norm(){ return normR().normS(); }//正規化
    mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
    mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
    mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
    mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
    ll modinv(int a){//a^-1 mod MOD
        int ypre=0,y=1,apre=MOD;
        while (a>1){
            int t=apre/a;
            apre-=a*t,swap(a,apre);
            ypre-=y*t,swap(y,ypre);
        }
        return y<0 ? y+MOD : y;
    }
    /*---- I/F ----*/
    mll_(){}
    mll_(ll v): val_(v){ norm(); }
    mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
    Int val()const{ return (Int)val_; }
    bool isnone() const { return val_==-1; } //true:値なし
    mll_ &none() { val_=-1; return *this; } //値なしにする
    mll_ &inv(){ val_=modinv((int)val_); return *this; }
    mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
    mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
    mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
    mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
    mll_ &operator+=(ll b){ return *this+=mll_(b); }
    mll_ &operator-=(ll b){ return *this-=mll_(b); }
    mll_ &operator*=(ll b){ return *this*=mll_(b); }
    mll_ &operator/=(ll b){ return *this/=mll_(b); }
    mll_ operator-()const{ return mll_(*this).invsg(); }
    mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
    mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
    mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
    mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
    mll_ operator+(ll b)const{ return mll_(*this)+=b; }
    mll_ operator-(ll b)const{ return mll_(*this)-=b; }
    mll_ operator*(ll b)const{ return mll_(*this)*=b; }
    mll_ operator/(ll b)const{ return mll_(*this)/=b; }
    friend mll_ operator+(ll a,mll_ b){ return b+a; }
    friend mll_ operator-(ll a,mll_ b){ return -b+a; }
    friend mll_ operator*(ll a,mll_ b){ return b*a; }
    friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
    bool operator==(mll_ b)const{ return val_==b.val_; }
    bool operator!=(mll_ b)const{ return val_!=b.val_; }
    bool operator==(ll b)const{ return *this==mll_(b); }
    bool operator!=(ll b)const{ return *this!=mll_(b); }
    friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }
    friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
    friend ostream &operator<<(ostream &os,mll_  a){ return os << a.val_; }
    friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
    mll_ pow(ll k)const{
        mll_ ret(1,false),a(*this);
        for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
        return ret;
    }
    static constexpr int mod() { return MOD; }
    //enum{ modll=MOD };
};


template<class T> struct Vector: vector<T>{
  using Int = long long;
  using vT=vector<T>;
  using cvT=const vector<T>;
  using cT=const T;
  using vT::vT; //親クラスのコンストラクタの隠蔽を回避
  using vT::begin,vT::end,vT::insert,vT::erase;
  auto it(Int i){ return begin()+i; }
  auto it(Int i)const{ return begin()+i; }
  Vector(cvT& b):vT(b){}
  Vector(vT&& b):vT(move(b)){}
  Vector(int n,cT& x):vT(n,x){}// ┬ 型推論のためラッパー
  Vector(long long n,cT& x):vT(n,x){}
  template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}
  template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}
  Vector(Int n,T s,T d){ iota(n,s,d); }
  Vector(Int n,function<T(Int)> g):vT(n){ for(Int i=0;i<n;++i) (*this)[i]=g(i); }
  Vector &operator+=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]+=b[i]; return *this; }
  Vector &operator-=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]-=b[i]; return *this; }
  Vector &operator*=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]*=b[i]; return *this; }
  Vector &operator/=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]/=b[i]; return *this; }
  Vector &operator%=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]%=b[i]; return *this; }
  Vector &operator+=(const Vector<T> &b){ return *this+=(cvT&)b; }
  Vector &operator-=(const Vector<T> &b){ return *this-=(cvT&)b; }
  Vector &operator*=(const Vector<T> &b){ return *this*=(cvT&)b; }
  Vector &operator/=(const Vector<T> &b){ return *this/=(cvT&)b; }
  Vector &operator%=(const Vector<T> &b){ return *this%=(cvT&)b; }
  Vector operator+(cvT &b){ return Vector(*this)+=b; }
  Vector operator-(cvT &b){ return Vector(*this)-=b; }
  Vector operator*(cvT &b){ return Vector(*this)*=b; }
  Vector operator/(cvT &b){ return Vector(*this)/=b; }
  Vector operator%(cvT &b){ return Vector(*this)%=b; }
  Vector operator+(const Vector<T> &b){ return Vector(*this)+=b; }
  Vector operator-(const Vector<T> &b){ return Vector(*this)-=b; }
  Vector operator*(const Vector<T> &b){ return Vector(*this)*=b; }
  Vector operator/(const Vector<T> &b){ return Vector(*this)/=b; }
  Vector operator%(const Vector<T> &b){ return Vector(*this)%=b; }
  template<class S> Vector &operator+=(S x){ for(T &e: *this) e+=x;  return *this; }
  template<class S> Vector &operator-=(S x){ for(T &e: *this) e-=x;  return *this; }
  template<class S> Vector &operator*=(S x){ for(T &e: *this) e*=x;  return *this; }
  template<class S> Vector &operator/=(S x){ for(T &e: *this) e/=x;  return *this; }
  template<class S> Vector &operator%=(S x){ for(T &e: *this) e%=x;  return *this; }
  template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }
  template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }
  template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }
  template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }
  template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }
  Vector &operator--(int){ return *this-=1; }
  Vector &operator++(int){ return *this+=1; }
  Vector operator-()const{ return Vector(*this)*=-1; }
  template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
  T& at(Int i){ assert(i>=0); if(n()<=i)vT::resize(i+1); return vT::operator[](i); }
  Vector slice(Int l,Int r,Int d=1)const{
    Vector ret;
    for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);
    return ret;
  }
  Int size()const{ return (Int)vT::size(); }
  Int n()const{ return size(); }
  Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }
  Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }
  Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }
  Vector &pop_front(Int n=1){ erase(0,n-1); return *this; }
  T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }
  T pull_front(){ T x=move(vT::front()); erase(0); return x; }
  Vector &insert(Int i,cT& x,Int n=1){ insert(it(i),n,x); return *this; }
  Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }
  Vector &erase(Int i){ erase(it(i)); return *this; }
  Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }
  Vector &erase(const Vector<Int> &idxs){
      for (Int I=0; I<idxs.n(); ++I){
          Int l=idxs[I]+1, r = (I<idxs.n()-1) ? idxs[I+1] : this->n();
          copy(it(l),it(r),it(l-I-1));//[l,r)を前にI+1個ずらす
      }
      vT::resize(this->n()-idxs.n());
      return *this;
  }
  Vector &eraseall(cT& x){ return eraseall(0,size()-1,x); }
  Vector &eraseall(Int l,Int r,cT& x){ erase(remove(it(l),it(r+1),x),it(r+1)); return *this; }
  template<class Pr> Vector &eraseif(Pr pr){ return eraseif(0,size()-1,pr); }
  template<class Pr> Vector &eraseif(Int l,Int r,Pr pr){ erase(remove_if(it(l),it(r+1),pr),it(r+1)); return *this; }
  Vector &concat(cvT &b,Int n=1){
    cvT B = (&b==this) ? *this : vT{};
    for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);
    return *this;
  }
  Vector repeat(Int n){ return Vector{}.concat(*this,n); }
  Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }
  Vector &rotate(Int m){ return rotate(0,size()-1,m); }
  Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }
  Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }
  Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }
  template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }
  template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }
  template<int key> Vector &sortbykey(Int l=0,Int r=-1){
    r+=r<0?size():0;
    sort(l,r,[](cT &x,cT &y){return get<key>(x)<get<key>(y);});
    return *this;
  }
  Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
  Vector &sortq(){ return sort().uniq(); }
  Vector &fill(cT& x){ return fill(0,size()-1,x); }
  Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
  Vector &copy(Int i,cvT &b,Int n=1){//A[i]スタートでbをn回分コピー
      for (int t=0; t<n; ++t) for (int j=0; j<(int)b.size(); ++j){
          if (i>=size()) return *this;
          if (i>=0) (*this)[i]=b[j];
          i++;
      }
      return *this;
  }
  template<class S=Int> Vector &iota(Int n,T s=0,S d=1){
    vT::resize(n);
    if(n==0) return *this;
    (*this)[0]=s;
    for(int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;
    return *this;
  }
  Int count(cT& x)const{ return count(0,size()-1,x); }
  Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }
  template<class Pr> Int countif(Pr pr)const{ return countif(0,size()-1,pr); }
  template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }
  Int find(cT& x)const{ return find(0,size()-1,x); }
  Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
  Int rfind(cT& x)const{ return rfind(0,size()-1,x); }
  Int rfind(Int l,Int r,cT& x)const{
      for (int i=r;i>=l;--i) if ((*this)[i]==x) return i;
      return l-1;
  }
  template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }
  template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }
  Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }
  Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }
  template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }
  template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{
    Vector<Int> ret;
    for(Int i=l;i<=r;++i) if(pr((*this)[i])) ret.push_back(i);
    return ret;
  }
  Int  flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }
  Int   ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }
  Int  leftnmof(cT& x)const{ return flooridx(x)+1; }
  Int rightnmof(cT& x)const{ return size()-ceilidx(x); }
  bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }
  template<class Pr> Int  flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }
  template<class Pr> Int   ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }
  template<class Pr> Int  leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }
  template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }
  template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }

  template<class S> using VV    = Vector<Vector<S>>; template<class S> using sVV    = vector<vector<S>>;
  template<class S> using VVV   = Vector<VV<S>>;     template<class S> using sVVV   = vector<sVV<S>>;
  template<class S> using VVVV  = Vector<VVV<S>>;    template<class S> using sVVVV  = vector<sVVV<S>>;
  template<class S> using VVVVV = Vector<VVVV<S>>;   template<class S> using sVVVVV = vector<sVVVV<S>>;
  auto tostd()const{ return tov(*this); }
  template <class S> static vector<S> tov(const Vector<S>&v){ return v; }
  template <class S> static sVV<S>    tov(const VV<S>    &v){ sVV<S>    ret; for(auto&& e:v) ret.push_back(e);         return ret; }
  template <class S> static sVVV<S>   tov(const VVV<S>   &v){ sVVV<S>   ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
  template <class S> static sVVVV<S>  tov(const VVVV<S>  &v){ sVVVV<S>  ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
  template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
};


#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;



namespace SolvingSpace{

template<class T> using vector = Vector<T>;
using    vll=vector<   ll>; using    vmll=vector<   mll>; using    vdd=vector<   dd>;
using   vvll=vector<  vll>; using   vvmll=vector<  vmll>; using   vvdd=vector<  vdd>;
using  vvvll=vector< vvll>; using  vvvmll=vector< vvmll>; using  vvvdd=vector< vvdd>;
using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;
using   vpll=vector<  pll>; using    vtll=vector<   tll>; using   vqll=vector<  qll>;
using  vvpll=vector< vpll>; using   vvtll=vector<  vtll>; using  vvqll=vector< vqll>;
using vss=vector<string>;
template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }
template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }

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template<int DIM> struct rangeNd{
    using Int = long long;
    using NInt = array<Int,DIM>;
    NInt sv,ev,lv,dv; //各変数の初期値,終了値,項数,公差(通常±1)
    Int size_=1;
    NInt cyclemask;
    rangeNd(const NInt &sv_,const NInt &ev_,Int cycle=-1): sv(sv_),ev(ev_){
        for (ll i=0; i<DIM; ++i) lv[i]=abs(sv[i]-ev[i])+1;
        for (ll i=0; i<DIM; ++i) dv[i]=sign(ev[i]-sv[i]);
        for (ll i=0; i<DIM; ++i) size_*=lv[i];
        for (ll i=0; i<DIM; ++i) cyclemask[i]=~0;
        if (cycle!=-1) cyclemask[0]=cycle-1;
    }
    Int size()const{ return size_; }
    Int csize()const{ return size_/lv[0]; }
    bool isCycle()const{ return cyclemask[0]!=~0; }
    Int cycle()const{ return isCycle() ? cyclemask[0]+1 : -1; }
    tuple<Int,Int,Int,Int> SELDx()const{ return SELDof(0); }
    tuple<Int,Int,Int,Int> SELDy()const{ return SELDof(1); }
    tuple<Int,Int,Int,Int> SELDz()const{ return SELDof(2); }
    tuple<Int,Int,Int,Int> SELDw()const{ return SELDof(3); }
    array<NInt,2> rngs()const{ return {sv,dv}; }
    NInt ls()const{ return lv; }
    NInt v2i(const NInt &vx)const{
        NInt ret;
        for (Int i=0; i<DIM; ++i) ret[i]=(vx[i]-sv[i])*dv[i];
        return ret;
    }
    auto toID(){
        return [this](const NInt &vx)->Int{
            Int id=0;
            for (Int i=0; i<DIM; ++i){
                Int x=vx[i],s=sv[i],l=lv[i],d=dv[i],xx=(x-s)*d;
                if (xx<0 || l<=xx) return -1;
                id=id*l+(xx&cyclemask[i]);
            }
            return id;
        };
    }
    auto fromID(){
        return [this](Int id)->NInt{
            NInt ret;
            for (Int i=DIM-1; i>=0; --i){
                Int s=sv[i],l=lv[i],d=dv[i],nid=id/l,xx=id-nid*l;
                ret[i]=s+xx*d;
                id=nid;
            }
            return ret;
        };
    }
    bool out(const NInt &vx){
        for (Int i=0; i<DIM; ++i){
            Int x=vx[i],s=sv[i],l=lv[i],d=dv[i];
            Int xx=(x-s)*d;
            if (xx<0 || l<=xx) return true;
        }
        return false;
    }
    NInt start(Int xx=0)const{
        NInt ret=sv;
        ret[0]=sv[0]+dv[0]*xx;
        return ret;
    }
    bool next(NInt &vx,Int dMn=0)const{ //次へ進める 対象:第dMn以降 @return true:次有
        for (int d=DIM-1; d>=dMn; --d){
            if (vx[d]==ev[d]) vx[d]=sv[d];
            else{ vx[d]+=dv[d]; return true; }
        }
        return false;
    }
private:
    tuple<Int,Int,Int,Int> SELDof(Int i)const{
        if (i>=DIM) return {-1,-1,-1,-1};
        return {sv[i],ev[i],lv[i],dv[i]};
    }
    static Int sign(Int x){ return x>=0 ? 1 : -1; }
};


template<class STATE,class VAL,class Ope,class Tran,class ToID,class FromID>
struct PushBasedDP{
    using Int = long long;
    using ll = long long;
    Ope ope; //配るときの演算
    Tran tran;
    ToID toID;
    FromID fromID;
    VAL ini,dmy; //ini:dpテーブルの初期値
    const bool isinf; //true:iniは配らない(ini=±INFを想定)
    vector<VAL> dp_;
    bool autoResize = true;
    bool nextdp = false; //true:nextDP
    //-------- コンストラクタ --------
    PushBasedDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,FromID fromID_,
        VAL ini_,bool isinf_)
        : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),
        ini(ini_),dmy(ini_),isinf(isinf_){
    }
    //事前メモリ確保用コンストラクタ
    template<class RNG> PushBasedDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,
        FromID fromID_,VAL ini_,bool isinf_,const RNG &rng)
        : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),
        ini(ini_),dmy(ini_),isinf(isinf_),
        dp_(rng.isCycle() ? rng.csize()*rng.cycle() : rng.size(),ini),
        autoResize(false),nextdp(rng.isCycle()){
    }
    //-------- アクセス・計算実行 --------
    template<class... Args> VAL &operator()(Args&&... args){ return Dp(STATE{args...}); }
    template<class... Args> void calc(Args&&... args){ calcSt({args...}); }
    template<class RNG> void calcall(const RNG &rng){
        if (nextdp) calcallNextDp(rng);
        else        calcallNormal(rng);
    }
    using   vVAL = vector<  VAL>;  using   vvVAL = vector<  vVAL>;
    using vvvVAL = vector<vvVAL>;  using vvvvVAL = vector<vvvVAL>;
    vVAL    tov(array<Int,1> ls){ return tov(ls[0]); }
    vvVAL   tov(array<Int,2> ls){ return tov(ls[0],ls[1]); }
    vvvVAL  tov(array<Int,3> ls){ return tov(ls[0],ls[1],ls[2]); }
    vvvvVAL tov(array<Int,4> ls){ return tov(ls[0],ls[1],ls[2],ls[3]); }
    vVAL tov(Int xl){
        dp_.resize(xl,ini);  return vVAL(dp_);
    }
    vvVAL tov(Int xl,Int yl){
        dp_.resize(xl*yl,ini);
        vvVAL ret(xl,vVAL(yl));
        for (ll i=0; i<xl; ++i) for (ll j=0; j<yl; ++j) ret[i][j]=dp_[i*yl+j];
        return ret;
    }
    vvvVAL tov(Int xl,Int yl,Int zl){
        dp_.resize(xl*yl*zl,ini);
        vvvVAL ret(xl,vvVAL(yl,vVAL(zl)));
        for (ll i=0; i<xl; ++i) for (ll j=0; j<yl; ++j) for (ll k=0; k<zl; ++k){
            ret[i][j][k]=dp_[i*yl*zl+j*zl+k];
        }
        return ret;
    }
    vvvvVAL tov(Int xl,Int yl,Int zl,Int wl){
        dp_.resize(xl*yl*zl*wl,ini);
        vvvvVAL ret(xl,vvvVAL(yl,vvVAL(zl,vVAL(wl))));
        for (ll i=0; i<xl; ++i) for (ll j=0; j<yl; ++j) for (ll k=0; k<zl; ++k){
            for (ll l=0; l<wl; ++l) ret[i][j][k][l]=dp_[i*yl*zl*wl+j*zl*wl+k*wl+l];
        }
        return ret;
    }
private:
    VAL &Dp(const STATE &vx){
        ll id=toID(vx);
        if (autoResize && (ll)dp_.size()<=id) dp_.resize(id+1,ini);
        return id<0 ? (dmy=ini) : dp_[id];
    }
    void calcSt(const STATE &vx){
        auto dstVal=[&](const STATE &nvx,VAL val){
            VAL &DpNvx=Dp(nvx);
            VAL nval=ope(DpNvx,val);
            if (DpNvx!=nval) DpNvx=nval,preRenew(nvx,vx);
        };
        VAL va=Dp(vx);
        if (!(isinf && va==ini)) tran(vx,va,dstVal);
    }
    template<class RNG> void calcallNormal(const RNG &rng){
        STATE vx=rng.start();
        do calcSt(vx); while (rng.next(vx));
    }
    template<class RNG> void calcallNextDp(const RNG &rng){
        auto [sx,ex,xl,dx]=rng.SELDx();
        for (ll xx=0; xx<xl; ++xx){
            //1つ前を消去
            if (xx>0){
                ll id=toID(rng.start(xx-1));
                auto it=dp_.begin()+id;
                fill(it,it+rng.csize(),ini);//dp_[id～id+csize-1]を消去
            }
            //現在位置xxを処理
            STATE vx=rng.start(xx);
            do calcSt(vx); while (rng.next(vx,1));
        }
    }
    //-------- ダンプ --------
public:
#if 0
    template<int N>
    void dump(rangeNd<N> &rng,vector<string> labels={},const vector<ll> axes={0,1,2,3}){
        auto ls=rng.ls();
        if (nextdp) ls[0]=rng.cycle();
        dumpstring::dumpNd("",tov(ls).tostd(),args().rngs(rng.rngs()).labels(labels).tr(axes));
    }
#endif
    //-------- 最適パス --------
#if 0
private:
    vector<ll> pre;
    ll preini=-1,predmy=-1;
    ll &Pre(const STATE &vx){
        ll id=toID(vx);
        if ((ll)pre.size()<=id) pre.resize(id+1,preini);
        return id<0 ? (predmy=preini) : pre[id];
    }
public:
    void preRenew(const STATE &vx,const STATE &src){ Pre(vx)=toID(src); }

    template<class... Args> vector<STATE> pathget(Args&&... endargs){
        vector<ll> ids{toID({endargs...})};
        while (ids.back()<(ll)pre.size() && pre[ids.back()]!=preini) ids.push_back(pre[ids.back()]);
        reverse(ids.begin(),ids.end());
        vector<STATE> path;
        for (auto&& id: ids) path.push_back(fromID(id));
        return path;
    }
#else
    void preRenew(const STATE &vx,const STATE &src)const{ (void)vx,(void)src; }
#endif
};



template<class T> struct mat_: std::vector<std::vector<T>>{
    using P=std::vector<std::vector<T>>;
    mat_(){}
    mat_(initializer_list<initializer_list<T>> a): P(a.begin(),a.end()){
        assert(all_of(this->begin(),this->end(),[&](auto &x){return (ll)x.size()==w(); }));
    }
    mat_(ll h,ll w,T x=T()): P(h,std::vector<T>(w,x)){}
    mat_(ll n): P(n,std::vector<T>(n)){}
    mat_(ll n,const string &c): P(n,std::vector<T>(n)){ if (c=="E")E(); }
    mat_(std::vector<T> &v,bool istranspose=false){
        if (istranspose){
            P::resize(1,std::vector<T>((ll)v.size()));
            for (ll j=0; j<w(); ++j) (*this)[0][j]=v[j];
        }
        else{
            P::resize((ll)v.size(),std::vector<T>(1));
            for (ll i=0; i<h(); ++i) (*this)[i][0]=v[i];
        }
    }
    ll h() const { return (ll)P::size(); }
    ll w() const { return h()==0 ? 0 : (ll)(*this)[0].size(); }
    mat_ &operator+=(const mat_ &b){ for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]+=b[i][j]; return *this; }
    mat_ &operator-=(const mat_ &b){ for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]-=b[i][j]; return *this; }
    mat_ &operator*=(T b)          { for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]*=b;       return *this; }
    mat_ operator+(const mat_ &b) const { return mat_(*this)+=b; }
    mat_ operator-(const mat_ &b) const { return mat_(*this)-=b; }
    mat_ operator*(T b)           const { return mat_(*this)*=b; }
    friend mat_ operator*(T a,const mat_ &b) { return b*a; }
    mat_ &operator*=(const mat_ &b){ return *this=*this*b; }
    mat_ operator*(const mat_ &b) const {//行列*行列
        mat_ ret(h(),b.w());
        for (ll i=0; i<h(); ++i) for (ll j=0; j<b.w(); ++j) for (ll k=0; k<w(); ++k){
            ret[i][j]+=(*this)[i][k]*b[k][j];
        }
        return ret;
    }
    std::vector<T> operator*(const std::vector<T> &v) const {//行列*ベクトル
        std::vector<T> ret(h());
        for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) ret[i]+=(*this)[i][j]*v[j];
        return ret;
    }
    mat_ pow(const ll n) const {
        mat_ ret(h(),"E"),a(*this);
        for (ll i=n; i>0; i>>=1,a*=a){ if (i&1) ret*=a; }
        return ret;
    }
    mat_ t() const {
        mat_ ret(w(),h());
        for (ll i=0; i<w(); ++i) for (ll j=0; j<h(); ++j) ret[i][j]=(*this)[j][i];
        return ret;
    }
    void E(){ for (ll i=0; i<min(h(),w()); ++i) (*this)[i][i]=1; }
};
using mat=mat_<mll>;
/*
mat m={{2,3,4},{1,0,5}};
.    ↓2x2正方行列、all0
mat m(2);
.      ↓2x2 単位行列
mat m(2,"E");
.     ↓vectorを縦(n×1)のmat型に変換
mat m(v);
.     ↓vectorを横(1×n)のmat型に変換
mat m(v,true);
.      ↓定数倍
m*=mll(2);
mat mm=m.pow(i);
*/



template<class T> struct findchar{
    using Int = long long;
    using ll = long long;
    using S = typename T::value_type;
    T data;
    vector<vector<Int>> idxss; //idxss[x]: data[i]=xであるiの配列
    S offset=0;//vの要素の最小値
    findchar(){}
    findchar(const T& v,S offset_=0){ init(v,offset_); }
    void init(const T& v,S offset_=0){
        data=v;
        offset=offset_;
        if (data.empty()) return;
        auto [mnit,mxit]=minmax_element(v.begin(),v.end());
        assert(offset<=*mnit && *mxit<offset+100000000LL);
        idxss.resize((*mxit)-offset+1);
        for (Int i=0; i<size(); ++i) idxsOf(v[i]).push_back(i);
    }
    bool empty()const{ return data.empty(); }
    Int size()const{ return (Int)data.size(); }
    void clear(){ data.clear(); idxss.clear(); }
    bool contains(S c)const{ return !out(c) && !idxsOf(c).empty(); }
    Int       ceilIdxOf(S c,Int i,ll d=1)const{ return  ceilIdxOfCore(c,i,d,false); }
    Int      floorIdxOf(S c,Int i,ll d=1)const{ return floorIdxOfCore(c,i,d,false); }
    Int  cycleCeilIdxOf(S c,Int i,ll d=1)const{ return  ceilIdxOfCore(c,i,d,true); }
    Int cycleFloorIdxOf(S c,Int i,ll d=1)const{ return floorIdxOfCore(c,i,d,true); }
    Int      nextIdxOf(Int i,ll d=1)const{ return  ceilIdxOfCore(data[i],i+1,d,false); }
    Int      prevIdxOf(Int i,ll d=1)const{ return floorIdxOfCore(data[i],i-1,d,false); }
    Int cycleNextIdxOf(Int i,ll d=1)const{ return  ceilIdxOfCore(data[i],i+1,d,true); }
    Int cyclePrevIdxOf(Int i,ll d=1)const{ return floorIdxOfCore(data[i],i-1,d,true); }
    Int numOf(S c,Int l,Int r)const{ return numOf(c,r)-numOf(c,l-1); }
    Int idxOf(S c,Int r)const{//r番目(0-indexed)のcの位置 なければ-1
        if (out(c))return -1;
        const vector<Int> &idxs=idxsOf(c);
        return (Int)idxs.size()<=r ? -1 : idxs[r];
    }
    Int rankOf(Int i)const{ return numOf(data[i],i)-1; }
    void push_back(S c){
        assert(offset<=c);
        if ((S)idxss.size()<=c-offset) idxss.resize(c-offset+1);
        idxsOf(c).push_back(size());
        data.push_back(c);
    }
    void push_back(const T& v){ for (S c : v) push_back(c); }
    void pop_back(){
        if (empty())return;
        idxsOf(data.back()).pop_back();
        data.pop_back();
    }
private:
    bool out(S c)const{ return c<offset || offset+(S)idxss.size()<=c; }
    vector<Int> &idxsOf(S c){ return idxss[c-offset]; }
    const vector<Int> &idxsOf(S c)const{ return idxss[c-offset]; }
    Int numOf(S c,Int r)const{//区間[0,r]のcの個数
        if (out(c))return 0;
        const vector<Int> &idxs=idxsOf(c);
        return upper_bound(idxs.begin(),idxs.end(),r) - idxs.begin();
    }
    /* 位置i以降d個目の文字c位置 ないとき-1 cycle=trueなら循環 */
    Int ceilIdxOfCore(S c,Int i,ll d,bool cycle)const{
        if (!contains(c)) return -1;
        const vector<Int> &idxs=idxsOf(c);
        ll I=ll(lower_bound(idxs.begin(),idxs.end(),i)-idxs.begin()) + d-1;
        if (cycle) return idxs[I%(ll)idxs.size()];
        else      return I<idxs.size() ? idxs[I] : -1;
    }
    /* 位置i以前d個目の文字c位置 ないとき-1 cycle=trueなら循環 */
    Int floorIdxOfCore(S c,Int i,ll d,bool cycle)const{
        if (!contains(c)) return -1;
        const vector<Int> &idxs=idxsOf(c);
        ll I=ll(upper_bound(idxs.begin(),idxs.end(),i)-idxs.begin())-1 -(d-1);
        if (cycle){
            ll m=(ll)idxs.size(),Im=I%m;
            return idxs[Im>=0 ? Im : Im+m];
        }
        else return I>=0 ? idxs[I] : -1;
    }
};
/*
- 定義      ↓string,vll等
findchar fc(s);
.              ↓最小要素指定
findchar fc(s,'a');
findchar fc(v,-100);
- 複数定義
vector<findchar<vll>> vfc(n);
vector<findchar<string>> vfc(n);
for (auto &&e: vfc) e.init("",'a'); //後から初期化
- 使用
ll n=fc.size();
bool b=fc.empty();
fc.clear();
ll nm=fc.numOf(c,l,r);       //区間[l,r]の文字cの個数
ll j=fc.idxOf(c,r);          //r番目の文字cの位置(0-indexed)
ll r=fc.rankOf(i);           //位置iはその文字の何番目か(0-indexed) i=0~N-1
bool b=fc.contains(c);       //文字cがある
ll j=fc.nextIdxOf(i);          //位置iと同じ文字の次の位置 なければ-1 i=0~N-1
ll j=fc.prevIdxOf(i);          //位置iと同じ文字の前の位置 なければ-1 i=0~N-1
ll j=fc.cycleNextIdxOf(i);     //位置iと同じ文字の次の位置(循環)      i=0~N-1
ll j=fc.cyclePrevIdxOf(i);     //位置iと同じ文字の前の位置(循環)      i=0~N-1
ll j=fc.ceilIdxOf(c,i);        //位置i以降の文字c位置 なければ-1
ll j=fc.floorIdxOf(c,i);       //位置i以前の文字c位置 なければ-1
ll j=fc.cycleCeilIdxOf(c,i);   //位置i以降の文字c位置(循環) なければ-1
ll j=fc.cycleFloorIdxOf(c,i);  //位置i以前の文字c位置(循環) なければ-1
ll j=fc.nextIdxOf(i,d);        //┐
ll j=fc.prevIdxOf(i,d);        //│
ll j=fc.cycleNextIdxOf(i,d);   //│
ll j=fc.cyclePrevIdxOf(i,d);   //├↑の同名関数のd個先/d個前版 d≧1
ll j=fc.ceilIdxOf(c,i,d);      //│
ll j=fc.floorIdxOf(c,i,d);     //│
ll j=fc.cycleCeilIdxOf(c,i,d); //│
ll j=fc.cycleFloorIdxOf(c,i,d);//┘
fc.push_back(c); //末尾に文字c追加
fc.push_back(s); //string,vll等でまとめて末尾追加
fc.pop_back();   //末尾削除
*/


namespace MomentMultiset{

template<class T,class S> struct moment{
    using MM=moment<T,S>;
    T n=0; //要素の個数
    S s=0; //要素の和
    moment() = default;
    moment(S x): n(1),s(x){}
    moment(T n,S s): n(n),s(s){}

    //--------- 各種演算 --------
    [[nodiscard]] MM minkowskiSum(const MM &b)const{
        T nx=this->n,ny=b.n;
        S sx=this->s,sy=b.s;
        return {nx*ny, ny*sx+nx*sy};
    }

    [[nodiscard]] MM minkowskiProd(const MM &b)const{
        return {this->n*b.n, this->s*b.s};
    }

    [[nodiscard]] MM Union(const MM &b)const{
        return {this->n+b.n, this->s+b.s};
    }

    //--------- operator 行列累乗時セットする --------
    MM operator*(const MM &b)const{
        //適切な演算をセット
        return minkowskiProd(b);
        //return minkowskiSum(b);
    }
    MM operator+(const MM &b)const{
        //適切な演算をセット
        return Union(b);
    }
    MM &operator*=(const MM &b){ return *this=(*this)*b; }
    MM &operator+=(const MM &b){ return *this=(*this)+b; }
    auto operator<=>(const MM& b) const = default; //辞書順比較を自動生成
#if 0 //デバグ時ON
    string to_string()const{
        return stringfx(n)+","+stringfx(s);
    }
#endif
};


template<class T,class S,class R> struct moment2{
    using MM=moment2<T,S,R>;
    T n=0; //要素の個数
    S s=0; //要素の和
    R s2=0;//要素の2乗和
    moment2() = default;
    moment2(S x): n(1),s(x),s2(x*x) {}
    moment2(T n,S s,R s2): n(n),s(s),s2(s2) {}

    //--------- 各種演算 --------
    [[nodiscard]] MM minkowskiSum(const MM &b)const{
        T nx= this->n,ny =b.n;
        S sx= this->s,sy =b.s;
        R sx2=this->s2,sy2=b.s2;
        return {nx*ny, ny*sx+nx*sy, ny*sx2 + 2*sx*sy + nx*sy2};
    }

    [[nodiscard]] MM minkowskiProd(const MM &b)const{
        return {this->n*b.n, this->s*b.s, this->s2*b.s2};
    }

    [[nodiscard]] MM Union(const MM &b)const{
        return {this->n+b.n, this->s+b.s, this->s2+b.s2};
    }

    //--------- operator 行列累乗時セットする --------
    MM operator*(const MM &b)const{
        //適切な演算をセット
        return minkowskiProd(b);
        //return minkowskiSum(b);
    }
    MM operator+(const MM &b)const{
        //適切な演算をセット
        return Union(b);
    }
    MM &operator*=(const MM &b){ return *this=(*this)*b; }
    MM &operator+=(const MM &b){ return *this=(*this)+b; }
    auto operator<=>(const MM& b) const = default; //辞書順比較を自動生成
#if 0 //デバグ時ON
    string to_string()const{
        return stringfx(n)+","+stringfx(s)+","+stringfx(s2);
    }
#endif
};
}
using MomentMultiset::moment;
using MomentMultiset::moment2;
/*
DPで、条件を満たす要素の多重集合の個数・和・2乗和を求めたいとき、
valueに本クラスを使う。

- ---- 型定義 ----
using mom = moment <mll,mll>;     //個数・和
using mom = moment2<mll,mll,mll>; //個数・和・2乗和
- ---- 定義 ----
mom m;        //空集合のmoment(単位元)
mom m(x);     //{x}(要素がx一つの集合)のmoment
mom m(n,s,s2);//要素数n,和s,2乗和s2のmoment
- ---- アクセス ----
ll n=m.n;   //個数n
ll s=m.s;   //和s
ll s2=m.s2; //2乗和s2
- ---- 演算 ----
mom mZ=mX.minkowskiSum(mom(c));  //多重集合Xの全要素に+c
mom mZ=mX.minkowskiProd(mom(k)); //多重集合Xの全要素をk倍
mom mZ=mX.Union(mY);         //┬直和X+Y (X={1,3},Y={1,4}ならX+Y={1,1,3,4})
mom mZ=mX+mY;                //┘
mom mZ=mX.minkowskiSum(mY);  //ミンコフスキー和 Z=X⊕Y={x+y|x∈X,y∈Y}
mom mZ=mX.minkowskiProd(mY); //ミンコフスキー積 Z=X⊗Y={x*y|x∈X,y∈Y}
mom mZ=mX*mY;                //default:ミンコフスキー積、適宜変更する
- ---- operator *,+,*=,+= ----
行列累乗にしたいときは+と*を適切に定める。
*/
using mom = moment <mll,mll>;     //個数・和
using vmom=vector<mom>;


template <class T> T sumPowers(T a,T e,long long n){
    T ret=e;
    T b=e; //e+x+x^2+…+x^(2ベキ)
    for (;n>0;n>>=1,b=b*a+b,a*=a){
        if (n&1) ret=ret*a+b;
    }
    return ret;
}
/*
mll x=sumPowers(a,1,n);  //1+a+a^2+…+a^n
mat B=sumPowers(A,E,n);  //E+A+A^2+…+A^n
.                ↑単位元
*/


void cin2solve()
{
    auto S=cin1<string>();
    ll N=sz(S);
    auto K=cin1<ll>();
    findchar fc(S);

    ll G=10;
    ll D=20;

    auto dpcalc=[&](ll st,ll cs/*0:個数、1:和*/){
        //数字stの個数/和 の寄与を計算
        //戻り
        //ret:{c0,s0,c1,s1,…,c9,s9}
        //sm :「N内で終わるものの和」への寄与 dp(*).s を全部足す

        using STATE=array<ll,1>;
        using VAL=mom;
        auto operation=[&](VAL a,VAL b){return a+b; };
        VAL ini=mom();  bool isinf=false;

        vmom ret(G);

        auto transition=[&](const STATE &vx,VAL va,auto dstVal){
            const auto [i]=vx;
            rep(dg,0,9){
                if (i==-1 and dg!=st)continue;
                //i+1以降でdgが初めに出てくる位置 j
                ll j=fc.ceilIdxOf(char('0'+dg),i+1);//位置i以降の文字c位置 なければ-1
                if (j==-1)
                    ret[dg]+=va;
                else{
                    mom vaZ=va .minkowskiProd(mom(10)); //多重集合Xの全要素をk倍
                    mom vaY=vaZ.minkowskiSum(mom(dg));  //多重集合Xの全要素に+c
                    dstVal(STATE{j},vaY);
                }
            }
        };

        auto [s1,e1]=pll{-1,N-1}; //1つ目の変数の範囲
        rangeNd<1> rng({s1,},{e1,});
        PushBasedDP dp(STATE(),VAL(),operation,transition,rng.toID(),rng.fromID(),ini,isinf,rng);
        
        if (cs==0)
            dp(-1)=mom(1,0);
        else
            dp(-1)=mom(0,1);
        dp.calcall(rng);


        mll sm;
        rep(i,0,N-1)
            sm+=dp(i).s;
        
        vmll retv(D);
        rep(i,0,9){
            retv[2*i+0]=ret[i].n;
            retv[2*i+1]=ret[i].s;
        }
        return make_pair(retv,sm);
    };

    mat A(D);
    vmll u(D);
    rep(st,0,9){
        {
            auto [retv,sm]=dpcalc(st,0);
            rep(i,0,D-1)
                A[i][2*st+0]=retv[i];
            u[2*st+0]=sm;
        }
        {
            auto [retv,sm]=dpcalc(st,1);
            rep(i,0,D-1)
                A[i][2*st+1]=retv[i];
            u[2*st+1]=sm;
        }
    }

    vmll v{0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,};
    mat B=sumPowers(A,mat(D,"E"),K-1);
    vmll v2=B*v;
    mat U(u,true);
    mll ans=(U*v2)[0];
    cout << ans << '\n';

    return;
}

}//SolvingSpace

//////////////////////////////////////////


int main(){
#if defined(RANDOM_TEST)
    //SolvingSpace::cin2solve();
    SolvingSpace::generand();
#else
  #if 1
    //SolvingSpace::labo();'
    SolvingSpace::cin2solve();
  #else
    ll t;  cin >> t;
    rep(i,0,t-1){
        SolvingSpace::cin2solve();
    }
  #endif
#endif
    cerr << timeget() <<"ms"<< '\n';
    return 0;
}