結果
問題 | No.2810 Have Another Go (Hard) |
ユーザー |
👑 ![]() |
提出日時 | 2024-07-12 22:59:34 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2,577 ms / 3,000 ms |
コード長 | 18,725 bytes |
コンパイル時間 | 2,844 ms |
コンパイル使用メモリ | 231,284 KB |
最終ジャッジ日時 | 2025-02-22 05:06:51 |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 61 |
ソースコード
//#define _GLIBCXX_DEBUG//#pragma GCC target("avx2")//#pragma GCC optimize("O3")//#pragma GCC optimize("unroll-loops")#include<bits/stdc++.h>using namespace std;#ifdef LOCAL#include <debug_print.hpp>#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else#define OUT(...) (static_cast<void>(0))#endif#define endl '\n'#define lfs cout<<fixed<<setprecision(15)#define ALL(a) (a).begin(),(a).end()#define ALLR(a) (a).rbegin(),(a).rend()#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())#define spa << " " <<#define fi first#define se second#define MP make_pair#define MT make_tuple#define PB push_back#define EB emplace_back#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)namespace template_tute{using ll = long long;using ld = long double;const ll MOD1 = 1e9+7;const ll MOD9 = 998244353;const ll INF = 1e18;using P = pair<ll, ll>;template<typename T> using PQ = priority_queue<T>;template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}ll median(ll a,ll b, ll c){return a+b+c-max<ll>({a,b,c})-min<ll>({a,b,c});}void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};template<typename T>void debug(const vector<T>&v){debug(v,v.size());}template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}template<typename T>void rearrange(vector<int>&ord, vector<T>&v){auto tmp = v;for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];}template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){rearrange(ord, head);rearrange(ord, tail...);}template<typename T> vector<int> ascend(const vector<T>&v){vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});return ord;}template<typename T> vector<int> descend(const vector<T>&v){vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});return ord;}template<typename T> vector<T> inv_perm(const vector<T>&ord){vector<T>inv(ord.size());for(int i=0;i<ord.size();i++)inv[ord[i]] = i;return inv;}ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}ll modulo(ll n,ll d){return (n%d+d)%d;};template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());int popcount(ll x){return __builtin_popcountll(x);};int poplow(ll x){return __builtin_ctzll(x);};int pophigh(ll x){return 63 - __builtin_clzll(x);};template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}std::ostream &operator<<(std::ostream &dest, __int128_t value) {std::ostream::sentry s(dest);if (s) {__uint128_t tmp = value < 0 ? -value : value;char buffer[128];char *d = std::end(buffer);do {--d;*d = "0123456789"[tmp % 10];tmp /= 10;} while (tmp != 0);if (value < 0) {--d;*d = '-';}int len = std::end(buffer) - d;if (dest.rdbuf()->sputn(d, len) != len) {dest.setstate(std::ios_base::badbit);}}return dest;}namespace converter{int dict[500];const string lower="abcdefghijklmnopqrstuvwxyz";const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string digit="0123456789";const string digit1="123456789";void regi_str(const string &t){for(int i=0;i<t.size();i++){dict[t[i]]=i;}}void regi_int(const string &t){for(int i=0;i<t.size();i++){dict[i]=t[i];}}vector<int>to_int(const string &s,const string &t){regi_str(t);vector<int>ret(s.size());for(int i=0;i<s.size();i++){ret[i]=dict[s[i]];}return ret;}vector<int>to_int(const string &s){auto t=s;sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());return to_int(s,t);}vector<vector<int>>to_int(const vector<string>&s,const string &t){regi_str(t);vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));for(int i=0;i<s.size();i++){for(int j=0;j<s[0].size();j++){ret[i][j]=dict[s[i][j]];}}return ret;}vector<vector<int>>to_int(const vector<string>&s){string t;for(int i=0;i<s.size();i++){t+=s[i];}sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());return to_int(s,t);}string to_str(const vector<int>&s,const string &t){regi_int(t);string ret;for(auto z:s)ret+=dict[z];return ret;}vector<string> to_str(const vector<vector<int>>&s,const string &t){regi_int(t);vector<string>ret(s.size());for(int i=0;i<s.size();i++){for(auto z:s[i])ret[i]+=dict[z];}return ret;}}template< typename T = int >struct edge {int to;T cost;int id;edge():to(-1),id(-1){};edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}operator int() const { return to; }};template<typename T>using Graph = vector<vector<edge<T>>>;template<typename T>Graph<T>revgraph(const Graph<T> &g){Graph<T>ret(g.size());for(int i=0;i<g.size();i++){for(auto e:g[i]){int to = e.to;e.to = i;ret[to].push_back(e);}}return ret;}template<typename T>Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){Graph<T> ret(n);for(int es = 0; es < m; es++){int u,v;T w=1;cin>>u>>v;u-=indexed,v-=indexed;if(weighted)cin>>w;ret[u].emplace_back(v,w,es);if(!directed)ret[v].emplace_back(u,w,es);}return ret;}template<typename T>Graph<T> readParent(int n,int indexed=1,bool directed=true){Graph<T>ret(n);for(int i=1;i<n;i++){int p;cin>>p;p-=indexed;ret[p].emplace_back(i);if(!directed)ret[i].emplace_back(p);}return ret;}}using namespace template_tute;template< int mod >struct ModInt {int x;ModInt() : x(0) {}ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}ModInt operator-() const { return ModInt(-x); }friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) += rhs;}friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) -= rhs;}friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) *= rhs;}friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) /= rhs;}bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ModInt(u);}ModInt pow(int64_t n) const {ModInt ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}pair<int,int>frac(){for(int j=1;j<=300;j++){for(int i=-300;i<=300;i++){if(ModInt(i)/j==*this){return make_pair(i,j);}}}return make_pair(-1,-1);}friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt &a) {int64_t t;is >> t;a = ModInt< mod >(t);return (is);}static int get_mod() { return mod; }};template< typename T >struct Combination {vector< T > _fact, _rfact, _inv;Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {_fact[0] = _rfact[sz] = _inv[0] = 1;for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;_rfact[sz] /= _fact[sz];for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];}inline T fact(ll k) const { return _fact[k]; }inline T rfact(ll k) const { return _rfact[k]; }inline T inv(ll k) const { return _inv[k]; }T P(ll n, ll r) const {if(r < 0 || n < r) return 0;return fact(n) * rfact(n - r);}T C(ll p, ll q) const {if(q < 0 || p < q) return 0;return fact(p) * rfact(q) * rfact(p - q);}T RC(ll p, ll q) const {if(q < 0 || p < q) return 0;return rfact(p) * fact(q) * fact(p - q);}T H(ll n, ll r) const {if(n < 0 || r < 0) return (0);return r == 0 ? 1 : C(n + r - 1, r);}//+1がm個、-1がn個で prefix sumが常にk以上T catalan(ll m,ll n,ll k){if(n>m-k)return 0;else return C(n+m,m)-C(n+m,n+k-1);}};using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);}//using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);}using Comb=Combination<modint>;template< class T>struct Kitamasa {ll n;const T zero = 0;//addの単位元const T iden = 1;//mulの単位元using arr = vector<T>;arr rec_f;const T add(T x, T y){return x + y;}const T mul(T x, T y){return x * y;}arr zeros(){arr ret(n);for(ll i=0;i<n;i++)ret[i]=zero;return ret;}Kitamasa(vector<T> v):n(v.size()){ //an=sum(v0*a_(n-k)+v_1*a_(n-k+1)+...rec_f = zeros();for(ll i=0;i<n;i++)rec_f[i]=v[i];}T calc(ll k, vector<T> a){//k項目を求める, a0...ak-1vector<ll>bit;while(k){if(k&1)bit.push_back(1);else bit.push_back(0);k>>=1;}reverse(bit.begin(),bit.end());arr now=zeros();now[0]=iden;for(ll i=0;i<bit.size();i++){now=twice(now);if(bit[i]==1)now=increment(now);}T ret=zero;for(ll i=0;i<n;i++)ret=add(ret,mul(now[i],a[i]));return ret;}arr increment(arr &v){arr ret=zeros();for(ll i=1;i<n;i++)ret[i]=add(v[i-1],mul(v[n-1],rec_f[i]));ret[0]=mul(v[n-1],rec_f[0]);return ret;}arr twice(arr &v){arr ret=zeros();arr tmp=v;for(ll i=0;i<n;i++){for(ll j=0;j<n;j++){ret[j]=add(ret[j],mul(v[i],tmp[j]));}tmp=increment(tmp);}return ret;}};template< class T >struct Matrix {vector< vector< T > > A;Matrix() {}Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}Matrix(size_t n) : A(n, vector< T >(n, 0)) {};Matrix(vector<vector<T>>v):A(v){};size_t height() const {return (A.size());}size_t width() const {return (A[0].size());}inline const vector< T > &operator[](int k) const {return (A.at(k));}inline vector< T > &operator[](int k) {return (A.at(k));}static Matrix I(size_t n) {Matrix mat(n);for(int i = 0; i < n; i++) mat[i][i] = 1;return (mat);}Matrix &operator+=(const Matrix &B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)(*this)[i][j] += B[i][j];return (*this);}Matrix &operator-=(const Matrix &B) {size_t n = height(), m = width();assert(n == B.height() && m == B.width());for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)(*this)[i][j] -= B[i][j];return (*this);}Matrix &operator*=(const Matrix &B) {size_t n = height(), m = B.width(), p = width();assert(p == B.height());vector< vector< T > > C(n, vector< T >(m, 0));for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)for(int k = 0; k < p; k++)C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);A.swap(C);return (*this);}Matrix &operator^=(long long k) {Matrix B = Matrix::I(height());while(k > 0) {if(k & 1) B *= *this;*this *= *this;k >>= 1LL;}A.swap(B.A);return (*this);}Matrix operator+(const Matrix &B) const {return (Matrix(*this) += B);}Matrix operator-(const Matrix &B) const {return (Matrix(*this) -= B);}Matrix operator*(const Matrix &B) const {return (Matrix(*this) *= B);}Matrix operator^(const long long k) const {return (Matrix(*this) ^= k);}bool operator==(const Matrix &B)const{return this->A == B.A;}bool operator!=(const Matrix &B)const{return this->A != B.A;}friend ostream &operator<<(ostream &os, Matrix p) {size_t n = p.height(), m = p.width();for(int i = 0; i < n; i++) {os << "[";for(int j = 0; j < m; j++) {os << p[i][j] << (j + 1 == m ? "]\n" : ",");}}return (os);}T determinant() {Matrix B(*this);assert(width() == height());T ret = 1;for(int i = 0; i < width(); i++) {int idx = -1;for(int j = i; j < width(); j++) {if(B[j][i] != 0) idx = j;}if(idx == -1) return (0);if(i != idx) {ret *= -1;swap(B[i], B[idx]);}ret *= B[i][i];T vv = B[i][i];for(int j = 0; j < width(); j++) {B[i][j] /= vv;}for(int j = i + 1; j < width(); j++) {T a = B[j][i];for(int k = 0; k < width(); k++) {B[j][k] -= B[i][k] * a;}}}return (ret);}};void solve(){ll res=0,buf=0;bool judge = true;ll n,m,k;cin>>n>>m>>k;vector<ll>c(k);rep(i,0,k)cin>>c[i];int sz=10;vector<modint>dp(sz+1);dp[0]=1;rep(i,0,sz)rep(j,1,7){if(i+j<=sz)dp[i+j]+=dp[i];}Kitamasa kit(vector<modint>{1,1,1,1,1,1});vector<modint> tmp(6);rep(i,0,6)tmp[i]=dp[i];//OUT(get(3));map<ll,modint>mp;rep(j,0,k){auto get=[&](ll d){if(mp.count(d))return mp[d];mp[d]=kit.calc(d,tmp);return mp[d];};Matrix<modint>mat(12,12);rep(i,0,6){modint sum=0;if(i<=c[j])sum+=get(c[j]-i);rep(r,n-6,n){if(i>r)continue;modint add1=0;if(c[j]<=r)add1=sum*get(r-c[j]);modint add0=get(r-i)-add1;rep(p,1,7)if(r+p>=n){int ir=r+p-n;mat[i][ir]+=add0;mat[i][ir+6]+=add1;mat[i+6][ir+6]+=add0+add1;}}}mat^=m;modint ret=0;rep(i,6,12)ret+=mat[0][i];cout<<ret<<endl;}}int main(){cin.tie(nullptr);ios_base::sync_with_stdio(false);ll res=0,buf=0;bool judge = true;int T = 1;//cin>>T;while(T--){solve();}return 0;}