結果
問題 | No.2164 Equal Balls |
ユーザー | 👑 tute7627 |
提出日時 | 2022-12-15 00:43:28 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 890 ms / 5,000 ms |
コード長 | 23,207 bytes |
コンパイル時間 | 2,925 ms |
コンパイル使用メモリ | 221,228 KB |
実行使用メモリ | 14,800 KB |
最終ジャッジ日時 | 2024-04-26 04:36:12 |
合計ジャッジ時間 | 23,527 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 8 ms
6,784 KB |
testcase_01 | AC | 8 ms
6,784 KB |
testcase_02 | AC | 9 ms
6,912 KB |
testcase_03 | AC | 8 ms
6,912 KB |
testcase_04 | AC | 9 ms
6,912 KB |
testcase_05 | AC | 8 ms
6,784 KB |
testcase_06 | AC | 9 ms
6,912 KB |
testcase_07 | AC | 9 ms
6,912 KB |
testcase_08 | AC | 84 ms
9,004 KB |
testcase_09 | AC | 66 ms
8,120 KB |
testcase_10 | AC | 41 ms
7,808 KB |
testcase_11 | AC | 151 ms
9,856 KB |
testcase_12 | AC | 90 ms
9,044 KB |
testcase_13 | AC | 56 ms
8,000 KB |
testcase_14 | AC | 72 ms
8,368 KB |
testcase_15 | AC | 146 ms
9,672 KB |
testcase_16 | AC | 82 ms
8,896 KB |
testcase_17 | AC | 24 ms
7,296 KB |
testcase_18 | AC | 108 ms
9,272 KB |
testcase_19 | AC | 184 ms
11,328 KB |
testcase_20 | AC | 97 ms
8,992 KB |
testcase_21 | AC | 19 ms
7,168 KB |
testcase_22 | AC | 18 ms
7,040 KB |
testcase_23 | AC | 342 ms
9,936 KB |
testcase_24 | AC | 333 ms
12,344 KB |
testcase_25 | AC | 286 ms
8,832 KB |
testcase_26 | AC | 248 ms
12,020 KB |
testcase_27 | AC | 398 ms
13,352 KB |
testcase_28 | AC | 403 ms
12,916 KB |
testcase_29 | AC | 142 ms
8,776 KB |
testcase_30 | AC | 332 ms
11,028 KB |
testcase_31 | AC | 398 ms
9,984 KB |
testcase_32 | AC | 412 ms
12,884 KB |
testcase_33 | AC | 215 ms
8,448 KB |
testcase_34 | AC | 297 ms
9,752 KB |
testcase_35 | AC | 62 ms
7,296 KB |
testcase_36 | AC | 634 ms
14,252 KB |
testcase_37 | AC | 461 ms
10,240 KB |
testcase_38 | AC | 890 ms
14,800 KB |
testcase_39 | AC | 839 ms
14,672 KB |
testcase_40 | AC | 832 ms
14,668 KB |
testcase_41 | AC | 833 ms
14,672 KB |
testcase_42 | AC | 845 ms
14,744 KB |
testcase_43 | AC | 829 ms
14,780 KB |
testcase_44 | AC | 836 ms
14,796 KB |
testcase_45 | AC | 837 ms
14,544 KB |
testcase_46 | AC | 828 ms
14,672 KB |
testcase_47 | AC | 832 ms
14,800 KB |
testcase_48 | AC | 832 ms
14,544 KB |
testcase_49 | AC | 608 ms
9,856 KB |
testcase_50 | AC | 607 ms
9,856 KB |
testcase_51 | AC | 596 ms
9,856 KB |
testcase_52 | AC | 606 ms
9,856 KB |
testcase_53 | AC | 602 ms
9,856 KB |
ソースコード
//#define _GLIBCXX_DEBUG #include<bits/stdc++.h> using namespace std; #define endl '\n' #define lfs cout<<fixed<<setprecision(10) #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--) 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({a,b,c})-min({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;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} 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){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;} template< typename T = int > struct edge { int to; T cost; int id; edge():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; } 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; } 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 pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);} //using modint=ld; using Comb=Combination<modint>; template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { static vector< Mint > dw, idw; static int max_base; static Mint root; NumberTheoreticTransformFriendlyModInt() = default; static void init() { const unsigned mod = Mint::get_mod(); assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(root.pow((mod - 1) >> 1) == 1) root += 1; assert(root.pow(mod - 1) == 1); dw.resize(max_base); idw.resize(max_base); for(int i = 0; i < max_base; i++) { dw[i] = -root.pow((mod - 1) >> (i + 2)); idw[i] = Mint(1) / dw[i]; } } static void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = n; m >>= 1;) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; a[i] = x + y, a[j] = x - y; } w *= dw[__builtin_ctz(++k)]; } } } static void intt(vector< Mint > &a, bool f = true) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = 1; m < n; m *= 2) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * w; } w *= idw[__builtin_ctz(++k)]; } } if(f) { Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } } static vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); return a; } }; template< typename Mint > vector< Mint > NumberTheoreticTransformFriendlyModInt<Mint>::dw = vector< Mint >(); template< typename Mint > vector< Mint > NumberTheoreticTransformFriendlyModInt< Mint >::idw = vector< Mint >(); template< typename Mint > int NumberTheoreticTransformFriendlyModInt< Mint >::max_base = 0; template< typename Mint > Mint NumberTheoreticTransformFriendlyModInt< Mint >::root = 2; //ret[i-j]=x[i]*y[j] template<typename Conv, typename T> vector<T>multiply_minus(vector<T>x,vector<T>y){ reverse(y.begin(),y.end()); auto tmp = Conv::multiply(x,y); vector<modint>ret(x.size()); for(int i = 0; i < x.size(); i++){ ret[i] = tmp[y.size() - 1 + i]; } return ret; } template< typename T > struct FormalPowerSeriesFriendlyNTT : vector< T > { using vector< T >::vector; using P = FormalPowerSeriesFriendlyNTT; using NTT = NumberTheoreticTransformFriendlyModInt< T >; P pre(int deg) const { return P(begin(*this), begin(*this) + min((int) this->size(), deg)); } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } P operator/(const P &r) const { return P(*this) /= r; } P operator%(const P &r) const { return P(*this) %= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < (int) r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < (int) r.size(); i++) (*this)[i] -= r[i]; return *this; } // https://judge.yosupo.jp/problem/convolution_mod P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } auto ret = NTT::multiply(*this, r); return *this = {begin(ret), end(ret)}; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P &operator%=(const P &r) { *this -= *this / r * r; shrink(); return *this; } // https://judge.yosupo.jp/problem/division_of_polynomials pair< P, P > div_mod(const P &r) { P q = *this / r; P x = *this - q * r; x.shrink(); return make_pair(q, x); } P operator-() const { P ret(this->size()); for(int i = 0; i < (int) this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; return *this; } P &operator*=(const T &v) { for(int i = 0; i < (int) this->size(); i++) (*this)[i] *= v; return *this; } P dot(P r) const { P ret(min(this->size(), r.size())); for(int i = 0; i < (int) ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } P operator>>(int sz) const { if((int) this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } T operator()(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } P diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } P integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } // https://judge.yosupo.jp/problem/inv_of_formal_power_series // F(0) must not be 0 P inv(int deg = -1) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P res(deg); res[0] = {T(1) / (*this)[0]}; for(int d = 1; d < deg; d <<= 1) { P f(2 * d), g(2 * d); for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j]; for(int j = 0; j < d; j++) g[j] = res[j]; NTT::ntt(f); NTT::ntt(g); f = f.dot(g); NTT::intt(f); for(int j = 0; j < d; j++) f[j] = 0; NTT::ntt(f); for(int j = 0; j < 2 * d; j++) f[j] *= g[j]; NTT::intt(f); for(int j = d; j < min(2 * d, deg); j++) res[j] = -f[j]; } return res; } // https://judge.yosupo.jp/problem/log_of_formal_power_series // F(0) must be 1 P log(int deg = -1) const { assert((*this)[0] == T(1)); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const { const int n = (int) this->size(); if(deg == -1) deg = n; if((*this)[0] == T(0)) { for(int i = 1; i < n; i++) { if((*this)[i] != T(0)) { if(i & 1) return {}; if(deg - i / 2 <= 0) break; auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt); if(ret.empty()) return {}; ret = ret << (i / 2); if((int) ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); } auto sqr = T(get_sqrt((*this)[0])); if(sqr * sqr != (*this)[0]) return {}; P ret{sqr}; T inv2 = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg); } P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const { return sqrt(deg, get_sqrt); } // https://judge.yosupo.jp/problem/exp_of_formal_power_series // F(0) must be 0 P exp(int deg = -1) const { if(deg == -1) deg = this->size(); assert((*this)[0] == T(0)); P inv; inv.reserve(deg + 1); inv.push_back(T(0)); inv.push_back(T(1)); auto inplace_integral = [&](P &F) -> void { const int n = (int) F.size(); auto mod = T::get_mod(); while((int) inv.size() <= n) { int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), T(0)); for(int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](P &F) -> void { if(F.empty()) return; F.erase(begin(F)); T coeff = 1, one = 1; for(int i = 0; i < (int) F.size(); i++) { F[i] *= coeff; coeff += one; } }; P b{1, 1 < (int) this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for(int m = 2; m < deg; m *= 2) { auto y = b; y.resize(2 * m); NTT::ntt(y); z1 = z2; P z(m); for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i]; NTT::intt(z); fill(begin(z), begin(z) + m / 2, T(0)); NTT::ntt(z); for(int i = 0; i < m; ++i) z[i] *= -z1[i]; NTT::intt(z); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c; z2.resize(2 * m); NTT::ntt(z2); P x(begin(*this), begin(*this) + min< int >(this->size(), m)); inplace_diff(x); x.push_back(T(0)); NTT::ntt(x); for(int i = 0; i < m; ++i) x[i] *= y[i]; NTT::intt(x); x -= b.diff(); x.resize(2 * m); for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0); NTT::ntt(x); for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i]; NTT::intt(x); x.pop_back(); inplace_integral(x); for(int i = m; i < min< int >(this->size(), 2 * m); ++i) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, T(0)); NTT::ntt(x); for(int i = 0; i < 2 * m; ++i) x[i] *= y[i]; NTT::intt(x); b.insert(end(b), begin(x) + m, end(x)); } return P{begin(b), begin(b) + deg}; } // https://judge.yosupo.jp/problem/pow_of_formal_power_series P pow(int64_t k, int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k)); if(i * k > deg) return P(deg, T(0)); ret = (ret << (i * k)).pre(deg); if((int) ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return *this; } P mod_pow(int64_t k, P g) const { P modinv = g.rev().inv(); auto get_div = [&](P base) { if(base.size() < g.size()) { base.clear(); return base; } int n = base.size() - g.size() + 1; return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n); }; P x(*this), ret{1}; while(k > 0) { if(k & 1) { ret *= x; ret -= get_div(ret) * g; ret.shrink(); } x *= x; x -= get_div(x) * g; x.shrink(); k >>= 1; } return ret; } // https://judge.yosupo.jp/problem/polynomial_taylor_shift P taylor_shift(T c) const { int n = (int) this->size(); vector< T > fact(n), rfact(n); fact[0] = rfact[0] = T(1); for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i); rfact[n - 1] = T(1) / fact[n - 1]; for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i); P p(*this); for(int i = 0; i < n; i++) p[i] *= fact[i]; p = p.rev(); P bs(n, T(1)); for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1]; p = (p * bs).pre(n); p = p.rev(); for(int i = 0; i < n; i++) p[i] *= rfact[i]; return p; } }; template< typename Mint > using FPS = FormalPowerSeriesFriendlyNTT< Mint >; template<typename Poly> Poly multiply_all(vector<Poly>&fs){ queue<Poly>que; for(auto f:fs)que.push(f); while(que.size()>=2){ auto p=que.front(); que.pop(); auto q=que.front(); que.pop(); que.push(p*q); } return que.front(); } int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); NumberTheoreticTransformFriendlyModInt<modint>::init(); ll res=0,buf=0; bool judge = true; ll n,m;cin>>n>>m; vector<ll>a(n),b(n); rep(i,0,n)cin>>a[i]; rep(i,0,n)cin>>b[i]; Comb comb(300005); int sz=605; vector<FPS<modint>>fs; ll off=302; rep(i,0,m){ FPS<modint> add(sz,1); for(ll j=i;j<n;j+=m){ rep(o,0,sz){ add[o]*=comb.C(a[j]+b[j],b[j]-(o-off)); } } //debug(add); fs.PB(add); } auto ret=multiply_all(fs); cout<<ret[off*fs.size()]<<endl; return 0; }