結果
| 問題 |
No.3213 depth max K
|
| ユーザー |
 Taiki0715
|
| 提出日時 | 2025-07-25 22:28:44 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 27 ms / 2,000 ms |
| コード長 | 20,786 bytes |
| コンパイル時間 | 3,530 ms |
| コンパイル使用メモリ | 310,160 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-07-25 22:28:51 |
| 合計ジャッジ時間 | 5,155 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 |
ソースコード
#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>
#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<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);}
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>;
#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<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;
}
}
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){
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){
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){
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};
}
#include<initializer_list>
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>
struct F{
private:
static int capacity;
static std::vector<T>fact,factinv,inv;
public:
static void resize(int n){
if(capacity>=n)return;
fact.resize(n+1),factinv.resize(n+1),inv.resize(n+1);
for(int i=capacity+1;i<=n;i++){
fact[i]=fact[i-1]*T::raw(i);
if constexpr(is_uso_modint_v<T>)inv[i]=T(1)/T(i);
else inv[i]=-inv[T::mod()%i]*(T::mod()/i);
factinv[i]=factinv[i-1]*inv[i];
}
capacity=n;
}
static T C(int n,int k){
if(n<k)return 0;
if(k<0)return 0;
resize(n);
return fact[n]*factinv[k]*factinv[n-k];
}
static T P(int n,int k){
if(n<k)return 0;
if(k<0)return 0;
resize(n);
return fact[n]*factinv[n-k];
}
static T H(int n,int k){
if(n==0&&k==0)return 1;
return C(n+k-1,k);
}
static T factorial(int n){
resize(n);
return fact[n];
}
static T factorial_inv(int n){
resize(n);
return factinv[n];
}
static T inverse(int n){
resize(n);
return inv[n];
}
static T S(long long n,int k){
if(n<0)return 0;
if(n<k)return 0;
T ret=0;
resize(k);
for(int i=0;i<=k;i++){
ret+=fact[k]*factinv[i]*factinv[k-i]*T::raw(i).pow(n)*((k-i)&1?-1:1);
}
return ret*factinv[k];
}
template<typename... INT>
static T O(INT...k){
int n=0;
for(int i:std::initializer_list<int>{k...}){
if(i<0)return 0;
n+=i;
}
resize(n);
T ret=fact[n];
for(int i:std::initializer_list<int>{k...})ret*=factinv[i];
return ret;
}
};
template<typename T>int F<T>::capacity=1;
template<typename T>std::vector<T>F<T>::fact{1,1};
template<typename T>std::vector<T>F<T>::factinv{1,1};
template<typename T>std::vector<T>F<T>::inv{0,1};
//lower[i]<=A[i]<=upper[i]
template<typename T>
T counting_increasing_sequence(std::vector<int>lower,std::vector<int>upper){
assert(lower.size()==upper.size());
int n=lower.size();
for(int i=1;i<n;i++)if(lower[i-1]>lower[i])lower[i]=lower[i-1];
for(int i=n-2;i>=0;i--)if(upper[i]>upper[i+1])upper[i]=upper[i+1];
for(int i=0;i<n;i++)if(lower[i]>upper[i])return 0;
int f=lower[0];
for(int i=0;i<n;i++){
lower[i]-=f;
upper[i]-=f;
}
lower.insert(lower.begin(),0);
upper.push_back(upper.back());
int m=upper[n];
std::vector<T>red(n+1),blue(m+1);
//下限同じ、上限単調増加(愚直)
auto naive1=[&](int lx,int rx,int ly,int ry)->void {
std::vector<std::vector<T>>dp(rx-lx+1,std::vector<T>(ry-ly+1,0));
for(int i=lx;i<=rx;i++)dp[i-lx][0]=red[i];
for(int j=ly+1;j<=upper[lx];j++)dp[0][j-ly]=dp[0][j-ly-1];
for(int i=lx+1;i<=rx;i++){
for(int j=ly+1;j<=upper[i];j++)dp[i-lx][j-ly]=dp[i-lx-1][j-ly]+dp[i-lx][j-ly-1];
}
for(int j=ly;j<=ry;j++)blue[j]=dp.back()[j-ly];
};
//下限単調増加、上限同じ(愚直)
auto naive2=[&](int lx,int rx,int ly,int ry)->void {
std::vector<std::vector<T>>dp(rx-lx+1,std::vector<T>(ry-ly+1,0));
for(int j=ly;j<=ry;j++)dp[0][j-ly]=blue[j];
for(int i=lx+1;i<=rx;i++){
dp[i-lx][lower[i]-ly]=dp[i-lx-1][lower[i]-ly];
for(int j=lower[i]+1;j<=ry;j++){
dp[i-lx][j-ly]=dp[i-lx-1][j-ly]+dp[i-lx][j-ly-1];
}
}
for(int i=lx;i<=rx;i++)red[i]=dp[i-lx].back();
};
auto calc_naive=[&](int lx,int rx,int ly,int ry)->void {
std::vector<std::vector<T>>dp(rx-lx+1,std::vector<T>(ry-ly+1,0));
for(int i=lx;i<=rx;i++)dp[i-lx][0]=red[i];
for(int i=ly;i<=ry;i++)dp[0][i-ly]=blue[i];
for(int i=1;i<=rx-lx;i++)for(int j=1;j<=ry-ly;j++){
dp[i][j]=dp[i-1][j]+dp[i][j-1];
}
for(int i=lx;i<=rx;i++)red[i]=dp[i-lx][ry-ly];
for(int i=ly;i<=ry;i++)blue[i]=dp[rx-lx][i-ly];
};
//長方形の寄与を畳み込みで計算
auto calc=[&](int lx,int rx,int ly,int ry){
std::vector<T>l(blue.begin()+ly,blue.begin()+ry+1);
std::vector<T>d(red.begin()+lx,red.begin()+rx+1);
for(int i=lx;i<=rx;i++)red[i]=0;
for(int i=ly;i<=ry;i++)blue[i]=0;
int x=rx-lx,y=ry-ly;
for(int i=x;i>=1;i--)d[i]-=d[i-1];
for(int i=y;i>=1;i--)l[i]-=l[i-1];
int s=ceil_pow2(x+y+2);
T invs=T(s).inv();
d[0]=0;
{//下から上
vector<T>coef(x+1);
for(int i=0;i<=x;i++)coef[i]=F<T>::C(y+i,i);
coef=ntt_convolution(coef,d);
for(int i=0;i<=x;i++)red[i+lx]+=coef[i];
}
{//左から右
vector<T>coef(y+1);
for(int i=0;i<=y;i++)coef[i]=F<T>::C(x+i,i);
coef=ntt_convolution(coef,l);
for(int i=0;i<=y;i++)blue[i+ly]+=coef[i];
}
vector<T>coef(s,0);
for(int i=0;i<=x+y;i++)coef[i]=F<T>::factorial(i);
dft(coef);
{//下から右
for(int i=0;i<=x;i++)d[i]*=F<T>::factorial_inv(x-i);
d.resize(s,0);
dft(d);
for(int i=0;i<s;i++)d[i]*=coef[i];
idft(d);
for(int i=0;i<=y;i++)blue[i+ly]+=d[i+x]*F<T>::factorial_inv(i)*invs;
}
{//左から上
for(int i=0;i<=y;i++)l[i]*=F<T>::factorial_inv(y-i);
l.resize(s,0);
dft(l);
for(int i=0;i<s;i++)l[i]*=coef[i];
idft(l);
for(int i=0;i<=x;i++)red[i+lx]+=l[i+y]*F<T>::factorial_inv(i)*invs;
}
};
//下限同じ、上限単調増加(分割統治)
auto dfs1=[&](auto self,int lx,int rx,int ly,int ry)->void {
if((long long)(rx-lx)*(ry-ly)<=150){
naive1(lx,rx,ly,ry);
return;
}
int mid=-1;
long long s=0;
for(int i=lx;i<=rx;i++){
long long now=(long long)(rx-i)*(upper[i]-ly);
if(s<now)mid=i,s=now;
}
if(mid==-1){
for(int i=ly;i<=ry;i++)blue[i]=red[rx];
return;
}
int y=upper[mid];
self(self,lx,mid,ly,y);
red[mid]=blue[ly];
calc(mid,rx,ly,y);
self(self,mid,rx,y,ry);
};
//下限単調増加、上限同じ(分割統治)
auto dfs2=[&](auto self,int lx,int rx,int ly,int ry)->void {
if((long long)(rx-lx)*(ry-ly)<=150){
naive2(lx,rx,ly,ry);
return;
}
int mid=-1;
long long s=0;
for(int i=lx;i<=rx;i++){
long long now=(long long)(i-lx)*(ry-lower[i]);
if(s<now)mid=i,s=now;
}
if(mid==-1){
for(int i=lx;i<=rx;i++)red[i]=blue[ry];
return;
}
int y=lower[mid];
self(self,lx,mid,ly,y);
blue[y]=red[lx];
calc(lx,mid,y,ry);
self(self,mid,rx,y,ry);
};
int x=0,y=0;
red[0]=1;
while(x<n&&lower[x+1]==y)red[x+1]=red[x],x++;
int lx=0,ly=0;
while(true){
ly=y;
y=upper[x];
dfs1(dfs1,lx,x,ly,y);
if(x==n)break;
lx=x;
while(x<n&&lower[x+1]<=y)x++;
dfs2(dfs2,lx,x,ly,y);
}
return blue.back();
}
using mint=mint998;
mint solve(int n,int k){
if(k==0)return 0;
vector<int>l(n),r(n);
rep(i,n){
l[i]=max(0,i-k+1);
r[i]=i;
}
return counting_increasing_sequence<mint>(l,r);
}
void SOLVE(){
int n,k;
cin>>n>>k;
cout<<solve(n,k)-solve(n,k-1)<<endl;
}