#1193076 (C++23(gnu拡張gcc16)) No.3753 Certainly a Cretan

• 問題: No.3753 Certainly a Cretan
• ユーザー: ryoku
• 提出日時: 2026-10-14 13:23:05
• 言語: C++23(gnu拡張gcc16) (gcc 16.2.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 548 ms / 2,500 ms
• コード長: 21,671 bytes
• コンパイル時間: 6,012 ms
• コンパイル使用メモリ: 331,344 KB
• 実行使用メモリ: 39,736 KB
• 最終ジャッジ日時: 2026-10-14 13:23:21
• 合計ジャッジ時間: 13,261 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge5_0

ファイルパターン	結果
sample	AC * 2
other	AC * 46

ソースコード

// library begin: "lib/template.hpp"
#ifdef TEMPLATE
#else
#define TEMPLATE
# pragma GCC optimize("O3")
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <cassert>
#include <functional>
#include <iterator>
#include <utility>
#include <complex>
#include <bitset>
#include <chrono>
#include <random>
#include <limits>
#include <optional>
#include <variant>
#include <any>

#include <array>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <version>
using namespace std;
namespace ryoku{}
using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
using ld=long double;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using i128=__int128;
using u128=unsigned __int128;
template<class T>using vc=vector<T>;
template<class T>using vvc=vc<vc<T>>;
template<class T>using vvvc=vvc<vc<T>>;
template<class T>using smpq=priority_queue<T,vector<T>,greater<T>>;
template<class T>using bipq=priority_queue<T>;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++)
#define DREP(i,n,m) for(ll i=(n);i>=(m);i--)
#define drep(i,n) for(ll i=((n)-1);i>=0;i--)
#define rall(x) x.rbegin(),x.rend()
#define mp(...) make_pair(__VA_ARGS__)
#define pb push_back
#define fi first
#define se second
#define is insert
#define bg begin()
#define ed end()
#define all(x) x.begin(),x.end()
void scan(int&a) { cin >> a; }
void scan(ll&a) { cin >> a; }
void scan(string&a) { cin >> a; }
void scan(char&a) { cin >> a; }
void scan(uint&a) { cin >> a; }
void scan(ull&a) { cin >> a; }
void scan(bool&a) { cin >> a; }
void scan(ld&a){ cin>> a;}
template<class T> void scan(vector<T>&a) { for(auto&x:a) scan(x); }
void read() {}
template<class Head, class... Tail> void read(Head&head, Tail&... tail) { scan(head); read(tail...); }
#define INT(...) int __VA_ARGS__; read(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; read(__VA_ARGS__);
#define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__);
#define STR(...) string __VA_ARGS__; read(__VA_ARGS__);
#define VC(type, name, ...) vector<type> name(__VA_ARGS__); read(name);
#define VVC(type, name, size, ...) vector<vector<type>> name(size, vector<type>(__VA_ARGS__)); read(name);
template<class T>void print(T a) { cout << a; }
template<class T> void print(vector<T>a) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}}
void PRT() { cout <<endl; return ; }
template<class T> void PRT(T a) { print(a); cout <<endl; return; }
template<class Head, class... Tail> void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; }
template<class T,class F>
bool chmin(T &x, F y){
    if(x>y){
        x=y;
        return true;
    }
    return false;
}
template<class T, class F>
bool chmax(T &x, F y){
    if(x<y){
        x=y;
        return true;
    }
    return false;
}
template<typename T>
T floor(T a,T b){
    return a/b-(a%b&&((a<0)!=(b<0)));
}
template<typename T>
T ceil(T a,T b){
    return a/b+(a%b&&((a<0)==(b<0)));
}
template<typename T>
T bmod(T x,T y){
    return x-y*floor(x,y);
}
template<typename T>
pair<T,T>divmod(T x,T y){
    T q=floor(x,y);
    return{q,x-q*y};
}
void YesNo(bool b){
    cout<<(b?"Yes":"No")<<endl;
}
void YESNO(bool b){
    cout<<(b?"YES":"NO")<<endl;
}
void AliceBob(bool b){
    cout<<(b?"Alice":"Bob")<<endl;
}
void TakahashiAoki(bool b){
    cout<<(b?"Takahashi":"Aoki")<<endl;
}
void Yes(){
    cout<<"Yes"<<endl;
}
void No(){
    cout<<"No"<<endl;
}
vc<int>stovi(const string&s,const string&S){
    vc<int>v(s.size());
    rep(i,s.size()){
        auto t=S.find(s[i]);
        assert(t!=string::npos);
        v[i]=t;
    }
    return v;
}
template<class T=ll>
T isqrt(T x){
    T F=sqrtl(x);
    while((F+1)*(F+1)<=x)F++;
    while(F*F>x)F--;
    return F;
}
template<class T>
T tri(T x){return x*(x-1)/2;}

//[l,r)
template<class T>T tri(T l,T r){return (r-l)*(l+r-1)/2;}
//n を先頭に持ってくる
template<class T>
vc<T>rot(vc<T>v,int n){
    rotate(v.begin(),v.begin()+n,v.end());
    return v;
}
template<class Container>
auto rle(const Container&cv){
    using T=typename Container::value_type;
    vc<pair<T,int>>res;
    for(const auto&x:cv){
        if(res.empty()||res.back().fi!=x)res.pb({x,1});
        else res.back().se++;
    }
    return res;
}
template<class T>
vc<T>iota(int n){
    vc<T>v(n);rep(i,n)v[i]=i;
    return v;
}
template<class T,int minfirst>
vc<int>argsort(const vc<T>&a){
    auto idx=iota<int>(a.size());
    sort(all(idx),[&](int i,int j){
        return (minfirst?make_pair(a[i],i)<make_pair(a[j],j):make_pair(a[i],i)>make_pair(a[j],j));
    });
    return idx;
}
template<class T>
vvc<T>trans(const vvc<T>&a){
    assert(a.size()&&a[0].size());
    rep(i,a.size())assert(a[i].size()==a[0].size());
    vvc<T>b(a[0].size(),vc<T>(a.size()));
    rep(i,a.size())rep(j,a[0].size())b[j][i]=a[i][j];
    return b;
}
vc<string>trans(const vc<string>&a){
    assert(a.size()&&a[0].size());
    rep(i,a.size())assert(a[i].size()==a[0].size());
    vc<string>b(a[0].size(),string(a.size(),0));
    rep(i,a.size())rep(j,a[0].size())b[j][i]=a[i][j];
    return b;
}
template<class T>
int popcount(T n){
    return __builtin_popcountll(n);
}
template<class T,class L=ll>
L sum(const vc<T>&a){
    return accumulate(all(a),L(0));
}
template<class T>
struct subset_view{
    T s;
    struct iterator{
        T s,x;
        bool done;
        T operator*()const{return x;}
        iterator&operator++(){
            if(x==0)done=true;
            else x=(x-1)&s;
            return*this;
        }
        bool operator!=(const iterator&r)const{return done!=r.done;}
    };
    iterator begin()const{return{s,s,false};}
    iterator end()const{return{s,0,true};}
};
template<class T>
subset_view<T>subset(T s){
    return{s};
}
template<class T>
T max(vc<T>&a){
    return *max_element(all(a));
}
template<class T>
T min(vc<T>&a){
    return *min_element(all(a));
}
template<class T,class L=ll>
vc<L> presum(vc<T> &a){
    vc<L> ret(a.size()+1);
    rep(i,a.size())ret[i+1]=ret[i]+a[i];
    return ret;
}
template<class T, class F>
vc<T> &operator+=(vc<T> &a,F b){
    for (auto&v:a)v += b;
    return a;
}
template<class T, class F>
vc<T> &operator-=(vc<T>&a,F b){
    for (auto&v:a)v-=b;
    return a;
}
template<class T, class F>
vc<T> &operator*=(vc<T>&a,F b){
    for (auto&v:a)v*=b;
    return a;
}
template<class T=ll>
constexpr T pow(T a,T b){
    T res=1;
    while(b){
        if(b&1)res*=a;
        a*=a;
        b/=2;
    }
    return res;
}
constexpr ll ten(ll a){
    return pow<ll>(10,a);
}
template<typename T>constexpr T inf=numeric_limits<T>::max()/2-1;
template<>
constexpr pll inf<pll> ={inf<ll>,inf<ll>};
template<class T>
constexpr T neg_inf=-inf<T>;
template<>
constexpr pll neg_inf<pll> ={-inf<ll>,-inf<ll>};
template<class T>
int tbit(T x){
    using U=make_unsigned_t<T>;
    U y=(U)x;
    return y?(int)bit_width(y)-1:-1;
}
template<class T>
int lbit(T x){
    using U=make_unsigned_t<T>;
    U y=(U)x;
    return y?(int)countr_zero(y):-1;
}
template<class T>
int tbit(T x,int p){
    using U=make_unsigned_t<T>;
    constexpr int W=numeric_limits<U>::digits;
    U y=(U)x;
    if(p<0)return -1;
    if(p>=W-1)return tbit(y);
    return tbit(y&((U(1)<<(p+1))-1));
}
template<class T>
int lbit(T x,int p){
    using U=make_unsigned_t<T>;
    constexpr int W=numeric_limits<U>::digits;
    U y=(U)x;
    if(p<0)return lbit(y);
    if(p>=W)return -1;
    return lbit(y&(~U(0)<<p));
}
istream& operator>>(istream&is,i128&x){
    string s;is>>s;
    x=0;
    int i=0,neg=0;
    if(s[0]=='-')neg=1,i=1;
    for(;i<(int)s.size();i++)x=x*10+s[i]-'0';
    if(neg)x=-x;
    return is;
}
ostream& operator<<(ostream&os,i128 x){
    if(x==0)return os<<0;
    if(x<0)os<<"-";
    u128 y=x<0?-(u128)x:(u128)x;
    string s;
    while(y)s.pb('0'+y%10),y/=10;
    reverse(all(s));
    return os<<s;
}
#ifdef LOCAL
#include"lib/debug/local.hpp"
inline int dbging=1;
#else
#define dbg(...) ((void)0)
#endif

struct template_setup{
    template_setup(){
        #if defined(LOCAL)&&!defined(INTERACTIVE)
        freopen("input.txt","r",stdin);
        freopen("output.txt","w",stdout);
        
        #endif
        cin.tie(0)->sync_with_stdio(0);
        #ifdef LOCAL
        cout<<fixed<<setprecision(6);
        #else
        cout<<fixed<<setprecision(20);
        #endif
    }
};
inline template_setup template_setup;


#endif
// library end: "lib/template.hpp"
// library begin: "lib/ds/monoid/sum-prod.hpp"
// library include: "lib/template.hpp"

namespace ryoku{
template<class T>
struct Sum{
    using value_type=T;
    static constexpr bool commute=true;
    static value_type op(value_type a,value_type b){return a+b;}
    static value_type id(){return T(0);}
    static value_type e(){return id();}
};
template<class T>
struct Prod{
    using value_type=T;
    static constexpr bool commute=false;
    static value_type op(value_type a,value_type b){return a*b;}
    static value_type id(){return T(1);}
    static value_type e(){return id();}
};

}
// library end: "lib/ds/monoid/sum-prod.hpp"
// library begin: "lib/ds/ordered/adjacent-manager.hpp"
namespace ryoku{
template<class key>
struct adjacent_manager{
    set<key>sts;
    using F=function<void(const key&,const key&)>;
    F add,del;
    adjacent_manager(F add,F del):add(add),del(del){}
    bool insert(const key&x){
        auto r=sts.lower_bound(x);
        if(r!=sts.end()&&*r==x)return false;
        auto l=r==sts.begin()?sts.end():prev(r);
        if(l!=sts.end()&&r!=sts.end())del(*l,*r);
        auto it=sts.insert(r,x);
        if(l!=sts.end())add(*l,*it);
        if(r!=sts.end())add(*it,*r);
        return true;
    }
    bool erase(const key&x){
        auto it=sts.find(x);
        if(it==sts.end())return false;
        auto l=it==sts.begin()?sts.end():prev(it);
        auto r=next(it);
        if(l!=sts.end())del(*l,*it);
        if(r!=sts.end())del(*it,*r);
        sts.erase(it);
        if(l!=sts.end()&&r!=sts.end())add(*l,*r);
        return true;
    }
};
}
// library end: "lib/ds/ordered/adjacent-manager.hpp"
// library begin: "lib/math/modular/binom.hpp"
// library include: "lib/template.hpp"
namespace ryoku{
template<class,class=void>
struct binom_has_get_mod:false_type{};
template<class mint>
struct binom_has_get_mod<mint,void_t<decltype(mint::get_mod())>>:true_type{};
template<class mint>
struct binom{
private:
    static vector<mint>&fact_table(){static vector<mint>v={1};return v;}
    static vector<mint>&invfact_table(){static vector<mint>v={1};return v;}
    static vector<mint>&invs_table(){static vector<mint>v={0};return v;}
    static int&built_mod(){static int mod=-1;return mod;}
public:
    static void build(int n){
        auto&_fact=fact_table();
        auto&_invfact=invfact_table();
        auto&_invs=invs_table();
        if constexpr(binom_has_get_mod<mint>::value){
            auto mod=mint::get_mod();
            if(built_mod()!=mod){
                _fact={1};
                _invfact={1};
                _invs={0};
                built_mod()=mod;
            }
        }
        if(n<(int)_fact.size())return;
        int old=_fact.size();
        _fact.resize(n+1);
        _invfact.resize(n+1);
        _invs.resize(n+1);
        if constexpr(binom_has_get_mod<mint>::value){
            auto mod=mint::get_mod();
            for(int i=old;i<=n;i++){
                _fact[i]=_fact[i-1]*i;
                if(i==1)_invs[i]=1;
                else _invs[i]=-_invs[mod%i]*(mod/i);
                _invfact[i]=_invfact[i-1]*_invs[i];
            }
        }else{
            for(int i=old;i<=n;i++){
                _fact[i]=_fact[i-1]*i;
                _invs[i]=mint(1)/i;
                _invfact[i]=_invfact[i-1]*_invs[i];
            }
        }
    }
    static mint fact(int i){
        assert(i>=0);
        build(i);
        return fact_table()[i];
    }
    static mint invfact(int i){
        assert(i>=0);
        build(i);
        return invfact_table()[i];
    }
    static mint inv(int i){
        assert(i>0);
        build(i);
        return invs_table()[i];
    }
    static mint C(int a,int b){//aCb
        if(b==0)return 1;
        if(a<0||b<0||a-b<0)return mint(0);
        build(a);
        auto&_fact=fact_table();
        auto&_invfact=invfact_table();
        return _fact[a]*_invfact[b]*_invfact[a-b];
    }
    static mint iC(int a,int b){//1/aCb
        if(b==0)return 1;
        if(a<0||b<0||a-b<0)return mint(0);
        build(a);
        auto&_fact=fact_table();
        auto&_invfact=invfact_table();
        return _fact[b]*_fact[a-b]*_invfact[a];
    }
    static mint P(int a,int b){
        if(a<b||b<0)return 0;
        build(a);
        auto&_fact=fact_table();
        auto&_invfact=invfact_table();
        return _fact[a]*_invfact[a-b];
    }
    static mint H(int a,int b){
        return C(a+b-1,b);
    }

};
}
// library end: "lib/math/modular/binom.hpp"
// library begin: "lib/ds/segment_tree/segtree.hpp"
// library include: "lib/template.hpp"
/*
struct X{
    using value_type=pair<mint,mint>;
    static value_type op(value_type a,value_type b){
        return {a.first*b.first,b.first*a.second+b.second};
    }
    static value_type id(){
        return {1,0};
    }
};*/
namespace ryoku{
template<typename info>
struct segtree{
    using value_type=typename info::value_type;
    vc<value_type>node;
    int N;
    int n;
    int lg;
    void update(int i){
        assert(0<i&&i<n);
        node[i]=info::op(node[i*2],node[i*2+1]);
    }
    segtree(int N_=0,value_type leaf=info::id()){
        assert(N_>=0);
        N=N_;
        n=1;
        lg=0;
        while(n<N)n*=2,++lg;
        node.resize(n*2,info::id());
        REP(i,n,n+N)node[i]=leaf;
        DREP(i,n-1,1)update(i);
    }
    template<class F>requires is_invocable_r_v<value_type,F&,int>
    segtree(int N_,F f){
        assert(N_>=0);
        N=N_;
        n=1;
        lg=0;
        while(n<N)n*=2,++lg;
        node.resize(n*2,info::id());
        for(int i=n;i<n+N;i++){
            node[i]=f(i-n);
        }
        DREP(i,n-1,1)update(i);
    }
    template<class F>
    segtree(const vc<F>&val){
        *this=segtree(val.size(),[&](int i){
            return val[i];
        });
    }
    void push_back(value_type val){
        if(n==N){
            vc<value_type>vs(n+1);rep(i,n)vs[i]=node[i+n];
            vs[n]=val;
            (*this)=segtree(N+1,[&](auto i){
                return vs[i];
            });
        }else{
            node[N+n]=val;
            int i=N+n;
            while(i>>=1)update(i);N++;
        }
    }
    void set(int i,value_type val){
        assert(0<=i&&i<N);
        node[i+=n]=val;
        while(i>>=1)update(i);
    }
    void apply(int i,value_type val){
        assert(0<=i&&i<N);
        i+=n;
        node[i]=info::op(node[i],val);
        while(i>>=1)update(i);
    }
    value_type prod(int l,int r){
        assert(0<=l&&l<=r&&r<=N);
        l+=n,r+=n;
        value_type sml=info::id(),smr=info::id();
        while(l<r){
            if(l&1)sml=info::op(sml,node[l++]);
            if(r&1)smr=info::op(node[--r],smr);
            l/=2,r/=2;
        }
        return info::op(sml,smr);
    }
    value_type all_prod(){
        return node[1];
    }
    template<class F>
    int max_right(int L,F f){
        assert(0<=L&&L<=N);
        int l=n+L,w=1;
        value_type ansL=info::id();
        for(;L+w<=N;l>>=1,w<<=1)if(l&1){
            if(!f(info::op(ansL,node[l])))break;
            ansL=info::op(ansL,node[l++]);
            L+=w;
        }
        while(w>1){
            l<<=1,w>>=1;
            if(L+w<=N&&f(info::op(ansL,node[l]))){
                ansL=info::op(ansL,node[l++]);
                L+=w;
            }
        }
        return L;
    }
    template<class F>
    int min_left(int R,F f){
        assert(0<=R&&R<=N);
        int r=n+R,w=1;
        value_type ansR=info::id();
        for(;R-w>=0;r>>=1,w<<=1)if(r&1){
            if(!f(info::op(node[r-1],ansR)))break;
            ansR=info::op(node[--r],ansR);
            R-=w;
        }
        while(w>1){
            r<<=1,w>>=1;
            if(R-w>=0&&f(info::op(node[r-1],ansR))){
                ansR=info::op(node[r-1],ansR);
                R-=w;
                r--;
            }
        }
        return R;
    }
};

}

#ifdef LOCAL
#include"lib/debug/formatters/ds--segment_tree--segtree.hpp"
#endif
// library end: "lib/ds/segment_tree/segtree.hpp"
// library begin: "lib/math/modular/static-mod-int.hpp"
// library include: "lib/template.hpp"
namespace ryoku{
template<uint32_t mod>
struct static_modint{
    static_assert(0<mod&&mod<=(1u<<31)-1);
    using u32=uint32_t;
    using u64=uint64_t;
    u32 val;
    static_modint():val(0){}
    static_modint(ll x){
        ll v=x%mod;
        if(v<0)v+=mod;
        val=v;
    }
    constexpr static uint32_t get_mod(){
        return mod;
    }
    static static_modint raw(int v){
        assert(v>=0);
        static_modint mi;
        mi.val=v;
        return mi;
    }
    static_modint &operator+=(const static_modint&m){
        u32 x=val+m.val-mod;
        val=x+(mod&-(x>>31));
        return *this;
    }
    static_modint &operator-=(const static_modint&m){
        u32 x=val-m.val;
        val=x+(mod&-(x>>31));
        return *this;
    }
    static_modint &operator*=(const static_modint&m){
        val=u64(val)*m.val%mod;
        return *this;
    }
    static_modint &operator/=(const static_modint&m){
        val=u64(val)*m.inv().val%mod;
        return *this;
    }
    static_modint operator-() const{
        return static_modint(mod-val);
    }
    static_modint operator+() const {
        return *this;
    }
    friend static_modint operator+(static_modint lhs, const static_modint& rhs){
        return lhs+=rhs;
    }
    friend static_modint operator-(static_modint lhs, const static_modint& rhs){
        return lhs-=rhs;
    }
    friend static_modint operator*(static_modint lhs, const static_modint& rhs){
        return lhs*=rhs;
    }
    friend static_modint operator/(static_modint lhs,const static_modint&rhs){
        return lhs/=rhs;
    }
    bool operator==(const static_modint&p) const{
        return p.val==val;
    }
    bool operator!=(const static_modint&p) const{
        return p.val!=val;
    }
    static_modint pow(int64_t n) const{
        static_modint res(1),mul(val);
        while(n){
            if(n%2)res*=mul;
            mul*=mul;
            n/=2;
        }
        return res;
    }

    friend ostream&operator<<(ostream&os,const static_modint&p){
        os<<p.val;
        return os;
    }
    friend istream&operator>>(istream&is,static_modint&p){
        int64_t x;
        is>>x;
        p=static_modint(x);
        return is;
    }
    static_modint inv()const{
        int64_t a=val,b=mod,u=1,v=0,t;
        #ifdef LOCAL
        assert(gcd(a,b)==1);
        #endif
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);
            swap(u-=t*v,v);
        }
        return static_modint(u);
    }
};

}
// library end: "lib/math/modular/static-mod-int.hpp"
using namespace ryoku;
using mint=static_modint<998244353>;
using B=binom<mint>;
void solve(){
    LL(n,q); 
    STR(s); 
    segtree<Prod<mint>>seg(n);rep(i,n)seg.set(i,1);
    // x-1 | x で変化するという情報を入れておく
    //[l,r) でずっと same
    auto add=[&](int l,int r){

        if(r==n)return;
        mint ans=0;
        {
            int N=r-l;
            if(N%2)ans=0;
            else ans+=B::C(N,N/2)/(N/2+1);
        }
        seg.set(r,ans);
    };

    //[l,r) でずっと same
    auto erase=[&](int l,int r){
        if(r==n)return;
        seg.set(r,1);
    };
    adjacent_manager<ll>a(add,erase);
    a.insert(0);a.insert(n);
    vc<int>val(n);
    auto flip=[&](int i){
        if(i+1<n&&val[i+1]!=val[i]){
            a.erase(i+1);
        }
        if(i&&val[i-1]!=val[i]){
            a.erase(i);
        }
        val[i]^=1;
        if(i+1<n&&val[i+1]!=val[i]){
            a.insert(i+1);
        }
        if(i&&val[i-1]!=val[i]){
            a.insert(i);
        }
    };
    rep(i,n){
        if(s[i]=='Y')flip(i);
    }
    while(q--){
        INT(t);
        if(t==1){
            INT(i);--i;
            flip(i);
        }else{
            INT(k);k=(n-k)-k;
            dbg(k);
            {
                if(k<0&&val[n-1]){
                    PRT(0);
                    continue;
                }
                if(k>0&&val[n-1]==0){
                    PRT(0);
                    continue;
                }
            }
            int last_pos=*next(a.sts.rbegin());
            auto dp=seg.all_prod();
            mint ans=0;
            
            k=abs(k);
            rep(_,1){
                int w=n-last_pos;
                dbg(w,k,dp);
                //(0,0) -> (w,K) への dyck path
                if((w+k)%2)continue;
                int x=(w+k)/2,y=(w-k)/2;
                if(x<0||y<0)continue;
                if(x==0&&y==0){
                    ans+=dp;
                }else if(k>0){
                    ans+=dp*(B::C(w,y)-(y?B::C(w,y-1):mint(0)));
                }else{
                    assert(x==y);
                    ans+=dp*B::C(2*x,x)/(x+1);
                }
            }
            PRT(ans);
        }
    }
}
signed main(){
    int t=1;
    // cin >> t;
    while(t--)solve();
}