//#pragma GCC optimize ("-O3") #include using namespace std; //@起動時 struct initon { initon() { cin.tie(0); ios::sync_with_stdio(false); cout.setf(ios::fixed); cout.precision(16); srand((unsigned) clock() + (unsigned) time(NULL)); }; } __initon; //衝突対策 #define ws ___ws struct T { int f, s, t; T() { f = -1, s = -1, t = -1; } T(int f, int s, int t) : f(f), s(s), t(t) {} bool operator<(const T &r) const { return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t; //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順 } bool operator>(const T &r) const { return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順 } bool operator==(const T &r) const { return f == r.f && s == r.s && t == r.t; } bool operator!=(const T &r) const { return f != r.f || s != r.s || t != r.t; } int operator[](int i) { assert(i < 3); return i == 0 ? f : i == 1 ? s : t; } }; #define int long long #define ll long long //#define double long double #define ull unsigned long long using dou = double; using itn = int; using str = string; using bo= bool; #define au auto using P = pair; #define fi first #define se second #define vec vector #define beg begin #define rbeg rbegin #define con continue #define bre break #define brk break #define is == //マクロ省略系 コンテナ using vi = vector; #define _overloadvvi(_1, _2, _3, _4, name, ...) name #define vvi0() vec #define vvi1(a) vec a #define vvi2(a, b) vec a(b) #define vvi3(a, b, c) vec a(b,vi(c)) #define vvi4(a, b, c, d) vec a(b,vi(c,d)) #define vvi(...) _overloadvvi(__VA_ARGS__,vvi4,vvi3,vvi2 ,vvi1,vvi0)(__VA_ARGS__) using vl = vector; #define _overloadvvl(_1, _2, _3, _4, name, ...) name #define vvl1(a) vec a #define vvl2(a, b) vec a(b) #define vvl3(a, b, c) vec a(b,vl(c)) #define vvl4(a, b, c, d) vec a(b,vl(c,d)) #define vvl(...) _overloadvvl(__VA_ARGS__,vvl4,vvl3,vvl2 ,vvl1)(__VA_ARGS__) using vb = vector; #define _overloadvvb(_1, _2, _3, _4, name, ...) name #define vvb1(a) vec a #define vvb2(a, b) vec a(b) #define vvb3(a, b, c) vec a(b,vb(c)) #define vvb4(a, b, c, d) vec a(b,vb(c,d)) #define vvb(...) _overloadvvb(__VA_ARGS__,vvb4,vvb3,vvb2 ,vvb1)(__VA_ARGS__) using vs = vector; #define _overloadvvs(_1, _2, _3, _4, name, ...) name #define vvs1(a) vec a #define vvs2(a, b) vec a(b) #define vvs3(a, b, c) vec a(b,vs(c)) #define vvs4(a, b, c, d) vec a(b,vs(c,d)) #define vvs(...) _overloadvvs(__VA_ARGS__,vvs4,vvs3,vvs2 ,vvs1)(__VA_ARGS__) using vd = vector; #define _overloadvvd(_1, _2, _3, _4, name, ...) name #define vvd1(a) vec a #define vvd2(a, b) vec a(b) #define vvd3(a, b, c) vec a(b,vd(c)) #define vvd4(a, b, c, d) vec a(b,vd(c,d)) #define vvd(...) _overloadvvd(__VA_ARGS__,vvd4,vvd3,vvd2 ,vvd1)(__VA_ARGS__) using vc=vector; #define _overloadvvc(_1, _2, _3, _4, name, ...) name #define vvc1(a) vec a #define vvc2(a, b) vec a(b) #define vvc3(a, b, c) vec a(b,vc(c)) #define vvc4(a, b, c, d) vec a(b,vc(c,d)) #define vvc(...) _overloadvvc(__VA_ARGS__,vvc4,vvc3,vvc2 ,vvc1)(__VA_ARGS__) using vp = vector

; #define _overloadvvp(_1, _2, _3, _4, name, ...) name #define vvp1(a) vec a #define vvp2(a, b) vec a(b) #define vvp3(a, b, c) vec a(b,vp(c)) #define vvp4(a, b, c, d) vec a(b,vp(c,d)) using vt = vector; #define _overloadvvt(_1, _2, _3, _4, name, ...) name #define vvt1(a) vec a #define vvt2(a, b) vec a(b) #define vvt3(a, b, c) vec a(b,vt(c)) #define vvt4(a, b, c, d) vec a(b,vt(c,d)) #define v3i(a, b, c, d) vector> a(b, vector(c, vi(d))) #define v3d(a, b, c, d) vector> a(b, vector(c, vd(d))) #define v3m(a, b, c, d) vector> a(b, vector(c, vm(d))) #define _vvi vector #define _vvl vector #define _vvb vector #define _vvs vector #define _vvd vector #define _vvc vector #define _vvp vector #define PQ priority_queue, greater > #define tos to_string using mapi = map; using mapd = map; using mapc = map; using maps = map; using seti = set; using setd = set; using setc = set; using sets = set; using qui = queue; #define bset bitset #define uset unordered_set #define mset multiset #define umap unordered_map #define umapi unordered_map #define umapp unordered_map #define mmap multimap //マクロ 繰り返し #define _overloadrep(_1, _2, _3, _4, name, ...) name # define _rep(i, n) for(int i = 0,_lim=n; i < _lim ; i++) #define repi(i, m, n) for(int i = m,_lim=n; i < _lim ; i++) #define repadd(i, m, n, ad) for(int i = m,_lim=n; i < _lim ; i+= ad) #define rep(...) _overloadrep(__VA_ARGS__,repadd,repi,_rep,)(__VA_ARGS__) #define _rer(i, n) for(int i = n; i >= 0 ; i--) #define reri(i, m, n) for(int i = m,_lim=n; i >= _lim ; i--) #define rerdec(i, m, n, dec) for(int i = m,_lim=n; i >= _lim ; i-=dec) #define rer(...) _overloadrep(__VA_ARGS__,rerdec,reri,_rer,)(__VA_ARGS__) #define fora(a, b) for(auto&& a : b) //マクロ 定数 #define k3 1010 #define k4 10101 #define k5 101010 #define k6 1010101 #define k7 10101010 const int inf = (int) 1e9 + 100; const ll linf = (ll) 1e18 + 100; const double eps = 1e-9; const double PI = 3.1415926535897932384626433832795029L; ll ma = numeric_limits::min(); ll mi = numeric_limits::max(); const int y4[] = {-1, 1, 0, 0}; const int x4[] = {0, 0, -1, 1}; const int y8[] = {0, 1, 0, -1, -1, 1, 1, -1}; const int x8[] = {1, 0, -1, 0, 1, -1, 1, -1}; //マクロ省略形 関数等 #define arsz(a) (sizeof(a)/sizeof(a[0])) #define sz(a) ((int)(a).size()) #define rs resize #define mp make_pair #define pb push_back #define pf push_front #define eb emplace_back #define all(a) (a).begin(),(a).end() #define rall(a) (a).rbegin(),(a).rend() inline void sort(string &a) { sort(a.begin(), a.end()); } template inline void sort(vector &a) { sort(a.begin(), a.end()); }; template inline void sort(vector &a, int len) { sort(a.begin(), a.begin() + len); }; template inline void sort(vector &a, F f) { sort(a.begin(), a.end(), [&](T l, T r) { return f(l) < f(r); }); }; enum ___pcomparator { fisi, fisd, fdsi, fdsd, sifi, sifd, sdfi, sdfd }; inline void sort(vector

&a, ___pcomparator type) { switch (type) { case fisi: sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se < r.se; }); break; case fisd: sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se > r.se; }); break; case fdsi: sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se < r.se; }); break; case fdsd: sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se > r.se; }); break; case sifi: sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi < r.fi; }); break; case sifd: sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi > r.fi; }); break; case sdfi: sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi < r.fi; }); break; case sdfd: sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi > r.fi; }); break; } }; inline void sort(vector &a, ___pcomparator type) { switch (type) { case fisi: sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s < r.s; }); break; case fisd: sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s > r.s; }); break; case fdsi: sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s < r.s; }); break; case fdsd: sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s > r.s; }); break; case sifi: sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f < r.f; }); break; case sifd: sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f > r.f; }); break; case sdfi: sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f < r.f; }); break; case sdfd: sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f > r.f; }); break; } }; template inline void rsort(vector &a) { sort(a.begin(), a.end(), greater()); }; template inline void rsort(vector &a, int len) { sort(a.begin(), a.begin() + len, greater()); }; template inline void rsort(vector &a, F f) { sort(a.begin(), a.end(), [&](U l, U r) { return f(l) > f(r); }); }; template inline void sortp(vector &a, vector &b) { vp c; int n = sz(a); assert(n == sz(b)); rep(i, n)c.eb(a[i], b[i]); sort(c); rep(i, n) { a[i] = c[i].first; b[i] = c[i].second;; } }; //F = T //例えばreturn p.fi + p.se; template inline void sortp(vector &a, vector &b, F f) { vp c; int n = sz(a); assert(n == sz(b)); rep(i, n)c.eb(a[i], b[i]); sort(c, f); rep(i, n) { a[i] = c[i].first; b[i] = c[i].second; } }; template inline void sortp(vector &a, vector &b, char type) { vp c; int n = sz(a); assert(n == sz(b)); rep(i, n)c.eb(a[i], b[i]); sort(c, type); rep(i, n) { a[i] = c[i].first; b[i] = c[i].second; } }; template inline void rsortp(vector &a, vector &b) { vp c; int n = sz(a); assert(n == sz(b)); rep(i, n)c.eb(a[i], b[i]); rsort(c); rep(i, n) { a[i] = c[i].first; b[i] = c[i].second; } }; template inline void rsortp(vector &a, vector &b, F f) { vp c; int n = sz(a); assert(n == sz(b)); rep(i, n)c.eb(a[i], b[i]); rsort(c, f); rep(i, n) { a[i] = c[i].first; b[i] = c[i].second; } }; template inline void sortt(vector &a, vector &b, vector &c) { vt r; int n = sz(a); assert(n == sz(b)); assert(n == sz(c)); rep(i, n)r.eb(a[i], b[i], c[i]); sort(r); rep(i, n) { a[i] = r[i].f; b[i] = r[i].s; c[i] = r[i].t; } }; template inline void sortt(vector &a, vector &b, vector &c, F f) { vt r; int n = sz(a); assert(n == sz(b)); assert(n == sz(c)); rep(i, n)r.eb(a[i], b[i], c[i]); sort(r, f); rep(i, n) { a[i] = r[i].f; b[i] = r[i].s; c[i] = r[i].t; } }; template inline void rsortt(vector &a, vector &b, vector &c, F f) { vt r; int n = sz(a); assert(n == sz(b)); assert(n == sz(c)); rep(i, n)r.eb(a[i], b[i], c[i]); rsort(r, f); rep(i, n) { a[i] = r[i].f; b[i] = r[i].s; c[i] = r[i].t; } }; template inline void sort2(vector> &a) { for (int i = 0, n = a.size(); i < n; i++)sort(a[i]); } template inline void rsort2(vector> &a) { for (int i = 0, n = a.size(); i < n; i++)rsort(a[i]); } template void fill(A (&a)[N], const T &v) { rep(i, N)a[i] = v; } template void fill(A (&a)[N][O], const T &v) { rep(i, N)rep(j, O)a[i][j] = v; } template void fill(A (&a)[N][O][P], const T &v) { rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v; } template void fill(A (&a)[N][O][P][Q], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v; } template void fill(A (&a)[N][O][P][Q][R], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v; } template void fill(A (&a)[N][O][P][Q][R][S], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v; } template void fill(V &xx, const T vall) { xx = vall; } template void fill(vector &vecc, const T vall) { for (auto &&vx: vecc) fill(vx, vall); } //@汎用便利関数 入力 template T _in() { T x; cin >> x; return (x); } #define _overloadin(_1, _2, _3, _4, name, ...) name #define in0() _in() #define in1(a) cin>>a #define in2(a, b) cin>>a>>b #define in3(a, b, c) cin>>a>>b>>c #define in4(a, b, c, d) cin>>a>>b>>c>>d #define in(...) _overloadin(__VA_ARGS__,in4,in3,in2 ,in1,in0)(__VA_ARGS__) #define _overloaddin(_1, _2, _3, _4, name, ...) name #define din1(a) int a;cin>>a #define din2(a, b) int a,b;cin>>a>>b #define din3(a, b, c) int a,b,c;cin>>a>>b>>c #define din4(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d #define din(...) _overloadin(__VA_ARGS__,din4,din3,din2 ,din1)(__VA_ARGS__) #define _overloaddind(_1, _2, _3, _4, name, ...) name #define din1d(a) int a;cin>>a;a-- #define din2d(a, b) int a,b;cin>>a>>b;a--,b-- #define din3d(a, b, c) int a,b,c;cin>>a>>b>>c;a--,b--,c-- #define din4d(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d;;a--,b--,c--,d-- #define dind(...) _overloaddind(__VA_ARGS__,din4d,din3d,din2d ,din1d)(__VA_ARGS__) string sin() { return _in(); } ll lin() { return _in(); } #define na(a, n) a.resize(n); rep(i,n) cin >> a[i]; #define nao(a, n) a.resize(n+1); rep(i,n) cin >> a[i+1]; #define nad(a, n) a.resize(n); rep(i,n){ cin >> a[i]; a[i]--;} #define na2(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i]; #define na2d(a, b, n) a.resize(n),b.resize(n);rep(i, n){cin >> a[i] >> b[i];a[i]--,b[i]--;} #define na3(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n)cin >> a[i] >> b[i] >> c[i]; #define na3d(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n){cin >> a[i] >> b[i] >> c[i];a[i]--,b[i]--,c[i]--;} #define nt(a, h, w) resize(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi]; #define ntd(a, h, w) rs(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--; #define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi]; //デバッグ #define sp << " " << #define debugName(VariableName) # VariableName #define _deb1(x) cerr << debugName(x)<<" = "< void rev(vector &a) { reverse(all(a)); } void rev(string &a) { reverse(all(a)); } ll ceil(ll a, ll b) { if (b == 0) { debugline("ceil"); deb(a, b); ole(); return -1; } else return (a + b - 1) / b; } ll sqrt(ll a) { if (a < 0) { debugline("sqrt"); deb(a); ole(); } ll res = (ll) std::sqrt(a); while (res * res < a)res++; return res; } double log(double e, double x) { return log(x) / log(e); } ll sig(ll t) { return (1 + t) * t / 2; } ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; } vi divisors(int v) { vi res; double lim = std::sqrt(v); for (int i = 1; i <= lim; ++i) { if (v % i == 0) { res.pb(i); if (i != v / i)res.pb(v / i); } } return res; } vb isPrime; vi primes; void setPrime() { int len = 4010101; isPrime.resize(4010101); fill(isPrime, true); isPrime[0] = isPrime[1] = false; for (int i = 2; i <= sqrt(len) + 5; ++i) { if (!isPrime[i])continue; for (int j = 2; i * j < len; ++j) { isPrime[i * j] = false; } } rep(i, len)if (isPrime[i])primes.pb(i); } vi factorization(int v) { int tv = v; vi res; if (isPrime.size() == 0)setPrime(); for (auto &&p :primes) { if (v % p == 0)res.push_back(p); while (v % p == 0) { v /= p; } if (v == 1 || p * p > tv)break; } if (v > 1)res.pb(v); return res; } inline bool inside(int h, int w, int H, int W) { return h >= 0 && w >= 0 && h < H && w < W; } inline bool inside(int v, int l, int r) { return l <= v && v < r; } #define ins inside ll u(ll a) { return a < 0 ? 0 : a; } template vector u(const vector &a) { vector ret = a; fora(v, ret)v = u(v); return ret; } #define MIN(a) numeric_limits::min() #define MAX(a) numeric_limits::max() void yn(bool a) { if (a)cout << "yes" << endl; else cout << "no" << endl; } void Yn(bool a) { if (a)cout << "Yes" << endl; else cout << "No" << endl; } void YN(bool a) { if (a)cout << "YES" << endl; else cout << "NO" << endl; } void fyn(bool a) { if (a)cout << "yes" << endl; else cout << "no" << endl; exit(0); } void fYn(bool a) { if (a)cout << "Yes" << endl; else cout << "No" << endl; exit(0); } void fYN(bool a) { if (a)cout << "YES" << endl; else cout << "NO" << endl; exit(0); } void Possible(bool a) { if (a)cout << "Possible" << endl; else cout << "Impossible" << endl; exit(0); } void POSSIBLE(bool a) { if (a)cout << "POSSIBLE" << endl; else cout << "IMPOSSIBLE" << endl; exit(0); } template set &operator+=(set &a, U v) { a.insert(v); return a; } template vector &operator+=(vector &a, U v) { a.pb(v); return a; } template T sum(vector &v, int s = 0, int t = inf) { T ret = 0; rep(i, s, min(sz(v), t))ret += v[i]; return ret; } void mod(int &a, int m) { a = (a % m + m) % m; } template inline int mgr(int ok, int ng, F f) { #define _mgrbody int mid = (ok + ng) / 2; if (f(mid))ok = mid; else ng = mid; if (ok < ng)while (ng - ok > 1) { _mgrbody } else while (ok - ng > 1) { _mgrbody } return ok; } template inline int mgr(int ok, int ng, int second, F f) { #define _mgrbody2 int mid = (ok + ng) / 2; if (f(mid, second))ok = mid; else ng = mid; if (ok < ng) while (ng - ok > 1) { _mgrbody2 } else while (ok - ng > 1) { _mgrbody2 } return ok; } template ostream &operator<<(ostream &os, vector &m) { for (auto &&v:m) os << v << " "; return os; } constexpr bool bget(ll m, int keta) { return (m >> keta) & 1; } int bget(ll m, int keta, int sinsuu) { m /= (ll) pow(sinsuu, keta); return m % sinsuu; } ll bit(int n) { return (1LL << (n)); } ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); } int mask(int n) { return (1ll << n) - 1; } #define bcou __builtin_popcountll template vector ruiv(vector &a) { vector ret(a.size() + 1); rep(i, a.size())ret[i + 1] = ret[i] + a[i]; return ret; } template inline bool chma(T &a, const U &b) { if (a < b) { a = b; return true; } return false; } template inline bool chma(const U &b) { return chma(ma, b); } template inline bool chmi(T &a, const U &b) { if (b < a) { a = b; return true; } return false; } template inline bool chmi(const U &b) { return chmi(mi, b); } #define unique(v) v.erase( unique(v.begin(), v.end()), v.end() ); int max(vi &a) { int res = a[0]; fora(v, a) { res = max(res, v); } return res; } int min(vi &a) { int res = a[0]; fora(v, a) { res = min(res, v); } return res; } template void out(T &&head, U &&... tail) { cout << head << " "; out2(tail...); cout << "" << endl; } template void out(T &&head) { cout << head << endl; } void out() { cout << "" << endl; } int N, M, H, W; vi A, B, C; //@formatter:off template T minv(T a, T m); template T minv(T a); template class Modular { public: using Type = typename decay::type; constexpr Modular() : value() {} template Modular(const U &x) { value = normalize(x); } template static Type normalize(const U &x) { Type v; if (-mod() <= x && x < mod()) v = static_cast(x); else v = static_cast(x % mod()); if (v < 0) v += mod(); return v; } const Type &operator()() const { return value; } templateexplicit operator U() const { return static_cast(value); } constexpr static Type mod() { return T::value; } Modular &operator+=(const Modular &other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular &operator-=(const Modular &other) { if ((value -= other.value) < 0) value += mod(); return *this; } template Modular &operator+=(const U &other) { return *this += Modular(other); } template Modular &operator-=(const U &other) { return *this -= Modular(other); } Modular &operator++() { return *this += 1; } Modular &operator--() { return *this -= 1; } Modular operator++(signed) { Modular result(*this); *this += 1; return result; } Modular operator--(signed) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); } templatetypename enable_if::Type, signed>::value, Modular>::type &operator*=(const Modular &rhs) { #ifdef _WIN32 uint64_t x = static_cast(value) * static_cast(rhs.value);uint32_t xh = static_cast(x >> 32), xl = static_cast(x), d, m;asm("divl %4; \n\t": "=a" (d), "=d" (m): "d" (xh), "a" (xl), "r" (mod()));value = m; #else value = normalize(static_cast(value) * static_cast(rhs.value)); #endif return *this; } template typename enable_if::Type, int64_t>::value, Modular>::type &operator*=(const Modular &rhs) { int64_t q = static_cast(static_cast(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template typename enable_if::Type>::value, Modular>::type &operator*=(const Modular &rhs) { value = normalize(value * rhs.value); return *this; } Modular &operator/=(const Modular &other) { return *this *= Modular(minv(other.value)); } template friend bool operator==(const Modular &lhs, const Modular &rhs); template friend bool operator<(const Modular &lhs, const Modular &rhs); template friend std::istream &operator>>(std::istream &stream, Modular &number); operator int() { return value; }private: Type value; }; template bool operator==(const Modular &lhs, const Modular &rhs) { return lhs.value == rhs.value; }template bool operator==(const Modular &lhs, U rhs) { return lhs == Modular(rhs); }template bool operator==(U lhs, const Modular &rhs) { return Modular(lhs) == rhs; }template bool operator!=(const Modular &lhs, const Modular &rhs) { return !(lhs == rhs); }template bool operator!=(const Modular &lhs, U rhs) { return !(lhs == rhs); }template bool operator!=(U lhs, const Modular &rhs) { return !(lhs == rhs); }template bool operator<(const Modular &lhs, const Modular &rhs) { return lhs.value < rhs.value; }template Modular operator+(const Modular &lhs, const Modular &rhs) { return Modular(lhs) += rhs; }template Modular operator+(const Modular &lhs, U rhs) { return Modular(lhs) += rhs; }template Modular operator+(U lhs, const Modular &rhs) { return Modular(lhs) += rhs; }template Modular operator-(const Modular &lhs, const Modular &rhs) { return Modular(lhs) -= rhs; }template Modular operator-(const Modular &lhs, U rhs) { return Modular(lhs) -= rhs; }template Modular operator-(U lhs, const Modular &rhs) { return Modular(lhs) -= rhs; }template Modular operator*(const Modular &lhs, const Modular &rhs) { return Modular(lhs) *= rhs; }template Modular operator*(const Modular &lhs, U rhs) { return Modular(lhs) *= rhs; }template Modular operator*(U lhs, const Modular &rhs) { return Modular(lhs) *= rhs; }template Modular operator/(const Modular &lhs, const Modular &rhs) { return Modular(lhs) /= rhs; }template Modular operator/(const Modular &lhs, U rhs) { return Modular(lhs) /= rhs; }template Modular operator/(U lhs, const Modular &rhs) { return Modular(lhs) /= rhs; } constexpr signed MOD = // 998244353; 1e9 + 7;//MOD using mint = Modular::type, MOD>>; constexpr int mint_len = 1400001; vi fac, finv, inv; vi p2; mint com(int n, int r) { if (r < 0 || r > n) return 0; /*nが大きくてrが小さい場合、nを上からr個掛ける*/ if (n >= mint_len) { int fa = finv[r]; rep(i, r)fa *= n - i, fa %= MOD; return mint(fa); } return mint(finv[r] * fac[n] % MOD * finv[n - r]);} mint pom(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - r]);} mint npr(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - r]);} int nprin(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return fac[n] * finv[n - r] % MOD;} int icom(int n, int r) { const int NUM_ = 1400001; static ll fac[NUM_ + 1], finv[NUM_ + 1], inv[NUM_ + 1]; if (fac[0] == 0) { inv[1] = fac[0] = finv[0] = 1; for (int i = 2; i <= NUM_; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; for (int i = 1; i <= NUM_; ++i) fac[i] = fac[i - 1] * i % MOD, finv[i] = finv[i - 1] * inv[i] % MOD; } if (r < 0 || r > n) return 0; return ((finv[r] * fac[n] % MOD) * finv[n - r]) % MOD;} #define ncr com #define ncri icom //n個の場所にr個の物を置く mint nhr(int n, int r) { if(n==0&&r==0)return 1; else return com(n + r - 1, r); } mint hom(int n, int r) { if(n==0&&r==0)return 1; else return com(n + r - 1, r); } int nhri(int n, int r) { if(n==0&&r==0)return 1; else return icom(n + r - 1, r); } //グリッドで0-indexedの最短経路 pascal mint pas(int h,int w){return com(h+w,w);} template T minv(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;} template T minv(T a) { if (a < mint_len)return inv[a]; T u = 0, v = 1; T m = MOD; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;} template Modular mpow(const Modular &a, const U &b) { assert(b >= 0); int x = a(), res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;} template mint mpow(const T a, const U b, const V m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;} //-k乗出来る template mint mpow(const T a, const U b) {/* assert(b >= 0);*/ if(b<0){ return minv(mpow(a,-b)); } int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;} template int mpowi(const T &a, const U &b, const V &m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;} template string to_string(const Modular &number) { return to_string(number());} #ifdef _DEBUG void yuri(const mint &a) { stringstream st; rep(i, 300) { rep(j, 300) { if ((mint) i / j == a) { st << i << " / " << j; i=2000;break;}}} string val = st.str(); if(val!=""){ deb(val); return; } rep(i, 1000) { rep(j, 1000) { if ((mint) i / j == a) { st << i << " / " << j;i=2000; break;}}} val = st.str(); deb(val);} #else #define yuri(...) ; #endif template std::ostream &operator<<(std::ostream &stream, const Modular &number) {stream << number(); #ifdef _DEBUG // stream << " -> " << yuri(number); #endif return stream; } //@formatter:off template std::istream &operator>>(std::istream &stream, Modular &number) { typename common_type::Type, int64_t>::type x; stream >> x; number.value = Modular::normalize(x); return stream;} using PM = pair; using vm = vector; using mapm = map; //using umapm = umap; #define vvm(...) over4(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(mint,__VA_ARGS__) #define vnm(name, ...) auto name = make_v(__VA_ARGS__) string out_m2(mint a) { stringstream st; st<<(int)a ; rep(i, 300) { rep(j, 2, 300) { if ((i%j)&&(mint) i / j == a) { st <<"("<< i << "/" << j<<")"; i = 2000; break; } } } return st.str();} struct setmod{ setmod() { p2.resize(mint_len);p2[0] = 1; for (int i = 1; i < mint_len; ++i) p2[i] = p2[i - 1] * 2 % MOD; fac.resize(mint_len); finv.resize(mint_len); inv.resize(mint_len); inv[1] = fac[0] = finv[0] = 1; for (int i = 2; i < mint_len; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; for (int i = 1; i < mint_len; ++i) fac[i] = fac[i - 1] * i % MOD, finv[i] = finv[i - 1] * inv[i] % MOD; } }setmodv; //@formatter:on //nhr n個の場所にr個の物を分ける mint m1 = (mint) 1; mint half = (mint) 1 / 2; /*@formatter:off*/ namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); signed base = 1; vector rts = {{0, 0}, {1, 0}}; vector rev = {0, 1}; void ensure_base(signed nbase) {if (nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for (signed i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while (base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for (signed i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector &a, signed n) { assert((n & (n - 1)) == 0); signed zeros = __builtin_ctz(n); ensure_base(zeros); signed shift = base - zeros; for (signed i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (signed k = 1; k < n; k <<= 1) { for (signed i = 0; i < n; i += 2 * k) { for (signed j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector multiply(const vector &a, const vector &b) { signed need = (signed) a.size() + (signed) b.size() - 1; signed nbase = 1; while ((1 << nbase) < need) nbase++; ensure_base(nbase); signed sz = 1 << nbase; vector fa(sz); for (signed i = 0; i < sz; i++) { signed x = (i < (signed) a.size() ? a[i] : 0); signed y = (i < (signed) b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for (signed i = 0; i <= (sz >> 1); i++) { signed j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for (signed i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector ret(need); for (signed i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; }}; templatestruct ArbitraryModConvolution {using real = FastFourierTransform::real;using C = FastFourierTransform::C;ArbitraryModConvolution() = default;vector multiply(const vector &a, const vector &b, signed need = -1) { if (need == -1) need = a.size() + b.size() - 1; signed nbase = 0; while ((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); signed sz = 1 << nbase; vector fa(sz); for (signed i = 0; i < a.size(); i++) { fa[i] = C((signed) a[i] & ((1 << 15) - 1), (signed) a[i] >> 15); } fft(fa, sz); vector fb(sz); if (a == b) { fb = fa; } else { for (signed i = 0; i < b.size(); i++) { fb[i] = C((signed) b[i] & ((1 << 15) - 1), (signed) b[i] >> 15); } fft(fb, sz); } real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for (signed i = 0; i <= (sz >> 1); i++) { signed j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if (i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector ret(need); for (signed i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa), bb = T(bb), cc = T(cc); ret[i] = aa + (bb << 15) + (cc << 30); } return ret; }}; templatestruct FormalPowerSeries : vector { using vector< T >::vector; using P = FormalPowerSeries; using MULT = function< P(P, P) >; static MULT &get_mult() { static MULT mult = nullptr; return mult; } static void set_fft(MULT f) { get_mult() = f; } template< typename E > FormalPowerSeries(const vector< E > &x) : vector< T >(begin(x), end(x)) {} void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i]; shrink(); return *this; } P &operator-=(const T &r) {if(this->empty()) this->resize(1); (*this)[0] -= r; shrink(); return *this; } P &operator*=(const T &v) { const int n = (int) this->size(); for(int k = 0; k < n; k++) (*this)[k] *= v; return *this; } P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } assert(get_mult() != nullptr); return *this = get_mult()(*this, r); } P &operator%=(const P &r) {return *this -= *this / r * r;} P operator-() const { P ret(this->size()); for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i]; return ret; } //謎が多い あまり使いたくない P &operator/=(P r) { while((*this).back()==T(0))(*this).pop_back(); while(r.back()==T(0))r.pop_back(); 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 pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); } P operator>>(int sz) const { if(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; } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } P diff() const { const int n = (int) this->size(); P ret(max(0ll, 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; } // 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 ret({T(1) / (*this)[0]}); for(int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } return ret.pre(deg); } // 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(); } P sqrt(int deg = -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) << (i / 2); if(ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); }P ret({T(1)}); 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); } // F(0) must be 0 P exp(int deg = -1) const { assert((*this)[0] == T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1)}); for(int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } 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 C(*this * rev); P D(n - i); for(int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log() * k).exp() * mpow((*this)[i],(k)); P E(deg); if(i * k > deg) return E; auto S = i * k; for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j]; return E; } } return *this; } T eval(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } // *x^x P& rshift(int k){ int an= this->size(); this->resize(an+k); rer(i, an+k-1,k){ (*this)[i] = (*this)[i-k]; } rep(i,k){ (*this)[i] = 0; } return (*this); } // /x^k P& lshift(int k){ int an= this->size(); rep(i,an-k){ (*this)[i] =(*this)[i+k]; } this->resize(an-k); return (*this); } //x = rx^dを代入する P &assign(int r, int d, int msize) { P ret(msize + 1); T rv = 1; rep(i, min((int)this->size(), msize / d + 1)) { ret[i * d] = (*this)[i] * rv; rv *= r; } return *this = ret; } }; ArbitraryModConvolution fft; using fps = FormalPowerSeries; struct FPS_init {FPS_init() {fps::set_fft([](const fps::P &a, const fps::P &b) { return fft.multiply(a, b); });};} initooonv; fps operator+(const fps &l, const fps &r) { auto ret=l; ret+= r;return ret; } fps operator+(const fps &l, const mint &r) { auto ret=l; ret+= r;return ret; } fps operator-(const fps &l, const fps &r) { auto ret=l; ret-= r;return ret; } fps operator-(const fps &l, const mint &r) { auto ret=l; ret-= r;return ret; } fps operator*(const fps &l, const fps &r) { auto ret=l; ret*= r;return ret; } fps operator*(const fps &l, const mint &r) { auto ret=l; ret*= r;return ret; } fps operator/(const fps &l, const fps &r) { auto ret=l; ret/= r;return ret; } fps operator%(const fps &l, const fps &r) { auto ret=l; ret%= r;return ret; } //vectorとして使える fps operator+(fps &l, signed v) { fps ret = l; ret[0] += v; return ret;}fps operator+(fps &l, ll v) { fps ret = l; ret[0] += v; return ret;}fps operator+=(fps &l, signed v) { l[0] += v; return l;}fps operator+=(fps &l, ll v) { l[0] += v; return l;}fps operator-(fps &l, signed v) { return operator+(l, -v); }fps operator-(fps &l, ll v) { return operator+(l, -v); }fps operator-=(fps &l, signed v) { return operator+=(l, -v); }fps operator-=(fps &l, ll v) { return operator+=(l, -v); }fps operator*(fps &l, signed v) { fps ret = l; for (int i = 0; i < l.size(); i++)ret[i] *= v; return ret;}fps operator*(fps &l, ll v) { fps ret = l; for (int i = 0; i < l.size(); i++)ret[i] *= v; return ret;}fps operator*=(fps &l, signed v) { for (int i = 0; i < l.size(); i++)l[i] *= v; return l;}fps operator*=(fps &l, ll v) { for (int i = 0; i < l.size(); i++)l[i] *= v; return l;}fps operator/(fps &l, signed v) { return operator*(l, minv(v)); }fps operator/(fps &l, ll v) { return operator*(l, minv(v)); }fps operator/=(fps &l, signed v) { return operator*=(l, minv(v)); }fps operator/=(fps &l, ll v) { return operator*=(l, minv(v)); }fps operator+(signed l, fps &v) { return operator+(v, l); }fps operator+(ll l, fps &v) { return operator+(v, l); }fps operator-(signed l, fps v) {v *= -1;return operator+(v, l);}fps operator-(ll l, fps v) {v *= -1;return operator+(v, l);}fps operator*(signed l, fps &v) { return operator*(v, l); }fps operator*(ll l, fps &v) { return operator*(v, l); }fps operator/(signed l, fps v) { v = v.inv(); return operator*(v, l);}fps operator/(ll l, fps v) { v = v.inv(); return operator*(v, l);}fps cut(fps l, fps r) { fps ret = l; ret *= r; ret.resize(max(l.size(), r.size())); return ret;} template fps cut(fps l, T... r) { return cut(l, cut(r...));} //initializerlist operatorに fps cutf(fps &l, fps &r) { fps ret = l; ret *= r; ret.resize(max(l.size(), r.size())); return ret;} //合計がSになる組合せを返す template T fft_get(vector &a, vector &b, int S) { int bn = sz(b); T res = 0; rep(l, sz(a) + 1) { int r = S - l; if (r >= bn || r < 0)con; res += a[l] * b[r]; } return res;} //右から疎なfpsを掛ける、O(N) * 右の項数 fps mul_sparse(const fps& l,const fps& r,int msize){ vi inds; rep(i, r.size()){ if(r[i]){ inds.push_back(i); } } assert(sz(inds)); int n = l.size()+inds.back(); if(msize==-1){ msize = n-1; } fps ret(msize+1); rep(i, l.size()){ for(auto d : inds){ if(i+d> msize)break; ret[i+d] += l[i] * r[d]; } } return ret;} //右から疎なfpsで割る、O(N) * 右の項数 fps div_sparse(const fps& a,const fps &r, int msize) {fps l = a; vi inds; rep(i, r.size()) { if (r[i]) { inds.push_back(i); }} assert(sz(inds)); int n = l.size(); if (msize == -1) { msize = n - 1; } msize = min(msize, n - 1); fps ret(msize + 1); rep(i, l.size()) { if (l[i]) { assert(i >= inds[0]); mint dec_k = l[i] / r[inds[0]]; if(i-inds[0] > msize)break; ret[i - inds[0]] += dec_k; for (auto d : inds) { if (i + d - inds[0] >= n)break; l[i + d - inds[0]] -= dec_k * r[d]; } } } return ret;} fps pow_sparse(const fps& a, int k, int msize){ fps ret = a; k--; while(k--){ ret = mul_sparse(ret, a, msize); } return ret; } fps div_sparse_n(const fps& a,const fps& b, int k, int msize){ fps ret = a; while(k--){ ret = div_sparse(ret, b, msize); } return ret; } //Π(1-x^n) (1<=n<=inf) = 1 + Σ -1^i * (x^(i*(3i-1)/2) + x^(i*(3i+1)/2) (1<=i<=inf)http://math.josai.ac.jp/~oshima/s2004.pdf P2 fps pow_sigma(int msize){vi reti(msize+1); reti[0] = 1; for (int i = 2; i < inf ; i+=2){ int a = (i*(3*i-1))>>1 ; if(a > msize)break; reti[a]++; a = (i*(3*i+1))>>1 ; if(a > msize)continue; reti[a]++; } for (int i = 1; i < inf ; i+=2){ int a = (i*(3*i-1))>>1 ; if(a > msize)break; reti[a]--; a = (i*(3*i+1))>>1 ; if(a > msize)continue; reti[a]--; } return reti;} //閉区間 sigma x^(0~r) = (1 - x^(r+1)) / (1 - x) //N乗はcombinationで分かる //Σx^(0~r) = (1-x^(r+1)) / (1-x) // // (1-x^r)^nを返す sigma x^(0~r) = (1 - x^(r+1)) / (1 - x)に注意! (0~rは r+1乗になる) fps pow_term2(int r, int n, int msize) { fps ret(msize + 1); rep(i, n + 1) { if (i * r <= msize) { ret[i * r] = com(n, i); if (i & 1)ret[i * r] = -ret[i * r]; } } return ret;} // (x^l - x^r)^n fps pow_term2(int l,int r,int n,int msize){ fps ret = pow_term2(r-l,n,msize); /*(x^l)^n * (1-x^(r-l))^n*/ ret.rshift(l*n); if(sz(ret)>msize+1)ret.resize(msize+1); return ret;} //1/(1-rx)^nを返す [x^i]f = nhi * r^i fps pow_term2_inv(int r, int n, int msize) {/*http://math.josai.ac.jp/~oshima/s2004.pdf P2 */ /*wolfram Series (1/(1-r*x)^m) 級数表現*/ fps ret(msize + 1); if (r == 1) { for (int i = 0; i < msize + 1; i++)ret[i] = nhr(n, i); return ret; } mint rb = 1; for (int i = 0; i < msize + 1; i++) { ret[i] = nhr(n, i) * rb; rb *= r; } return ret;} //1/(1-x)^n fps pow_term2_inv(int n,int msize){return pow_term2_inv(1,n,msize);} //1/(1-rx^d)^nを返す 1/(1-rx)^n にx=x^dを代入 fps pow_term2_inv(int r, int d, int n, int msize) { fps ret = pow_term2_inv(r, n, msize); ret.assign(1, d, msize); return ret;}/*@formatter:on*/ //割り算の使い方が怪しい //逆元は使えるため、逆元を掛けたほうがいいかも //invは長さが元のだけ必要 //Σx^(0~r) = (1-x^(r+1)) / (1-x) //vector はatcoderエラーなので vvmとする //undef long double /*@formatter:on*/ template struct fps1 { T k;/*係数*/ static T pow(T a, int k) { T res = 1; T x = a; while (k) { if (k & 1)res *= x; x *= x; k >>= 1; } return res; } fps1(T k = 1) : k(k) {} fps operator^(int sz) { fps ret(sz + 1); if (k == 1)ret[sz] = 1; else ret[sz] = fps1::pow(k, sz); return ret; } }; template fps operator-(int l, const fps1 &r) { fps ret(2); ret[0] = l; ret[1] = -r.k; return ret; } template fps operator-(const fps1 &l, const fps &r) { fps ret(2); ret[1] = l.k; ret -= r; return ret; } /*@formatter:off*/ fps1 X; /*@formatter:on*/ signed main() { in(N); din(D, K); fps S = X ^0;//todo (X^1)をXに置き換えるとバグる S = pow_sparse(X - (X ^ (D + 1)), N, K + 1); S = div_sparse_n(S, 1 - X, N, K + 1); out(S[K]); }