結果
問題 | No.8046 yukicoderの過去問 |
ユーザー | ttttan2 |
提出日時 | 2022-06-08 23:54:07 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 446 ms / 2,000 ms |
コード長 | 56,725 bytes |
コンパイル時間 | 4,636 ms |
コンパイル使用メモリ | 259,324 KB |
実行使用メモリ | 30,896 KB |
最終ジャッジ日時 | 2024-09-21 05:17:11 |
合計ジャッジ時間 | 9,271 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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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 | 435 ms
30,404 KB |
testcase_01 | AC | 432 ms
30,424 KB |
testcase_02 | AC | 437 ms
30,400 KB |
testcase_03 | AC | 433 ms
30,404 KB |
testcase_04 | AC | 433 ms
30,608 KB |
testcase_05 | AC | 435 ms
30,400 KB |
testcase_06 | AC | 446 ms
30,896 KB |
testcase_07 | AC | 440 ms
30,672 KB |
testcase_08 | AC | 443 ms
30,812 KB |
ソースコード
#include <algorithm> #include <bitset> #include <complex> #include <deque> #include <exception> #include <fstream> #include <functional> #include <iomanip> #include <ios> #include <iosfwd> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <locale> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <set> #include <sstream> #include <stack> #include <stdexcept> #include <streambuf> #include <string> #include <typeinfo> #include <utility> #include <valarray> #include <vector> #if __cplusplus >= 201103L #include <array> #include <atomic> #include <chrono> #include <condition_variable> #include <forward_list> #include <future> #include <initializer_list> #include <mutex> #include <random> #include <ratio> #include <regex> #include <scoped_allocator> #include <system_error> #include <thread> #include <tuple> #include <typeindex> #include <type_traits> #include <unordered_map> #include <unordered_set> #endif using namespace std; typedef long long ll; typedef unsigned long long ull; typedef unsigned int ui; typedef pair<int,int> pii; typedef pair<pii,int> ppii; typedef pair<int,pii> pipi; typedef pair<ll,ll> pll; typedef pair<pll,ll> ppll; typedef pair<ll,pll> plpl; typedef pair<pii,pii> pippi; typedef tuple<ll,ll,ll> tl; typedef pair<long double,long double> pdd; //typedef vector<vector<ll>> mat; const ll mod=1000000007; const ll mod2=998244353; const ll mod3=1000000009; ll inf=numeric_limits<ll>::max()/2; int iinf=numeric_limits<int>::max()/2; double pi=3.14159265358979323846; double eps=1e-10; #define rep(i,m,n) for(ll i=m;i<n;i++) #define rrep(i,n,m) for(ll i=n;i>=m;i--) #define srep(itr,st) for(auto itr=st.begin();itr!=st.end();itr++) #define mrep(itr,mp) for(auto& itr:mp) #define Max(a,b) a=max(a,b) #define Min(a,b) a=min(a,b) int dh[4]={1,0,-1,0}; int dw[4]={0,1,0,-1}; int ddh[8]={-1,-1,-1,0,0,1,1,1}; int ddw[8]={-1,0,1,-1,1,-1,0,1}; struct custom_hash { static uint64_t splitmix64(uint64_t x) { x+=0x9e3779b97f4a7c15;x=(x^(x>>30))*0xbf58476d1ce4e5b9;x=(x^(x>>27))*0x94d049bb133111eb; return x^(x>>31);} size_t operator()(uint64_t x) const { static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); return splitmix64(x + FIXED_RANDOM);} }; #define umh unordered_map<int,ll,custom_hash> ll gcd(ll a,ll b){ if(a<0)a=-a;if(b<0)b=-b;if(a<b)swap(a,b);if(b==0)return a;if(a%b==0)return b;return gcd(b,a%b);} ll lcm(ll a,ll b){if(a==0)return b;if(b==0)return a;ll c=gcd(a,b);a/=c;a*=b;return a;} ll Pow(ll n,ll k){ if(k<0)return 0;ll ret=1;ll now=n;while(k>0){if(k&1)ret*=now;now*=now;k/=2;}return ret; } ll beki(ll n,ll k,ll md){ ll ret=1;ll now=n;now%=md; while(k>0){ if(k%2==1){ret*=now;ret%=md;} now*=now;now%=md;k=k>>1;}return ret; } ll gyaku(ll n,ll md){return beki(n,md-2,md);} ll popcount(ll n){ll ret=0;ll u=n;while(u>0){ret+=u%2;u/=2;}return ret;} #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { int ceil_pow2(int n) { int x = 0;while ((1U << x) < (unsigned int)(n)) x++;return x;} int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif }}} #endif #ifndef ATCODER_INTERNAL_MATH_HPP #define ATCODER_INTERNAL_MATH_HPP 1 #include <utility> namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x%=m;if(x<0)x+=m;return x;} struct barrett { unsigned int _m; unsigned long long im; barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a;z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n<=1) return false; if (n==2||n==7||n==61) return true; if (n%2==0) return false; long long d = n - 1; while (d%2==0)d/=2; for (long long a : {2, 7, 61}) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n;t <<= 1;} if (y != n - 1 && t % 2 == 0) {return false;} } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i;} } } if (x > 1) {divs[cnt++] = x;} for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false;break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); } } #endif #ifndef ATCODER_INTERNAL_QUEUE_HPP #define ATCODER_INTERNAL_QUEUE_HPP 1 #include <vector> namespace atcoder { namespace internal { template <class T> struct simple_queue { std::vector<T> payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear();pos = 0;} void pop() { pos++; } }; } } #endif #ifndef ATCODER_INTERNAL_SCC_HPP #define ATCODER_INTERNAL_SCC_HPP 1 #include <algorithm> #include <utility> #include <vector> namespace atcoder { namespace internal { template <class E> struct csr { std::vector<int> start; std::vector<E> elist; csr(int n, const std::vector<std::pair<int, E>>& edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) {start[e.first + 1]++;} for (int i = 1; i <= n; i++) {start[i] += start[i - 1];} auto counter = start; for (auto e : edges) {elist[counter[e.first]++] = e.second;} } }; struct scc_graph { public: scc_graph(int n) : _n(n) {} int num_vertices() { return _n; } void add_edge(int from, int to) { edges.push_back({from, {to}}); } std::pair<int, std::vector<int>> scc_ids() { auto g = csr<edge>(_n, edges); int now_ord = 0, group_num = 0; std::vector<int> visited, low(_n), ord(_n, -1), ids(_n); visited.reserve(_n); auto dfs = [&](auto self, int v) -> void { low[v] = ord[v] = now_ord++; visited.push_back(v); for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto to = g.elist[i].to; if (ord[to] == -1) { self(self, to);low[v] = std::min(low[v], low[to]); } else {low[v] = std::min(low[v], ord[to]);} } if (low[v] == ord[v]) { while (true) { int u = visited.back(); visited.pop_back();ord[u] = _n;ids[u] = group_num;if (u == v) break; } group_num++; } }; for (int i = 0; i < _n; i++) {if (ord[i] == -1) dfs(dfs, i);} for (auto& x : ids) {x = group_num - 1 - x;} return {group_num, ids}; } std::vector<std::vector<int>> scc() { auto ids = scc_ids(); int group_num = ids.first; std::vector<int> counts(group_num); for (auto x : ids.second) counts[x]++; std::vector<std::vector<int>> groups(ids.first); for (int i = 0; i < group_num; i++) { groups[i].reserve(counts[i]); } for (int i = 0; i < _n; i++) { groups[ids.second[i]].push_back(i); } return groups; } private: int _n; struct edge { int to; }; std::vector<std::pair<int, edge>> edges; }; } } #endif #ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP #define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1 #include <cassert> #include <numeric> #include <type_traits> namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } } #endif #ifndef ATCODER_MODINT_HPP #define ATCODER_MODINT_HPP 1 #include <cassert> #include <numeric> #include <type_traits> #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } static_modint(bool v) { _v = ((unsigned int)(v) % umod()); } unsigned int val() const { return _v; } mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;} mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;} mint operator++(int) {mint result = *this;++*this;return result;} mint operator--(int) {mint result = *this;--*this;return result;} mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;} mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;} mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt = 998244353; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; } } #endif #ifndef ATCODER_CONVOLUTION_HPP #define ATCODER_CONVOLUTION_HPP 1 #include <algorithm> #include <array> #include <cassert> #include <type_traits> #include <vector> namespace atcoder { namespace internal { template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_e[30]; if (first) { first = false; mint es[30], ies[30]; int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_e[i] = es[i] * now; now *= ies[i]; } } for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p] * now; a[i + offset] = l + r; a[i + offset + p] = l - r; } now *= sum_e[bsf(~(unsigned int)(s))]; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly_inv(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_ie[30]; if (first) { first = false; mint es[30], ies[30]; int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_ie[i] = ies[i] * now; now *= es[i]; } } for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val(); } inow *= sum_ie[bsf(~(unsigned int)(s))]; } } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) { if (n < m) { std::swap(n, m); std::swap(a, b); } std::vector<mint> ans(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; } } return ans; } int z = 1 << internal::ceil_pow2(n + m - 1); a.resize(z); internal::butterfly(a); b.resize(z); internal::butterfly(b); for (int i = 0; i < z; i++) { a[i] *= b[i]; } internal::butterfly_inv(a); a.resize(n + m - 1); mint iz = mint(z).inv(); for (int i = 0; i < n + m - 1; i++) a[i] *= iz; return a; } template <unsigned int mod = 998244353, class T, std::enable_if_t<internal::is_integral<T>::value>* = nullptr> std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; using mint = static_modint<mod>; std::vector<mint> a2(n), b2(m); for (int i = 0; i < n; i++) { a2[i] = mint(a[i]); } for (int i = 0; i < m; i++) { b2[i] = mint(b[i]); } auto c2 = convolution(move(a2), move(b2)); std::vector<T> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); } return c; } std::vector<long long> convolution_ll(const std::vector<long long>& a, const std::vector<long long>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; static constexpr unsigned long long MOD1 = 754974721; static constexpr unsigned long long MOD2 = 167772161; static constexpr unsigned long long MOD3 = 469762049; static constexpr unsigned long long M2M3 = MOD2 * MOD3; static constexpr unsigned long long M1M3 = MOD1 * MOD3; static constexpr unsigned long long M1M2 = MOD1 * MOD2; static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3; static constexpr unsigned long long i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second; static constexpr unsigned long long i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second; static constexpr unsigned long long i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second; auto c1 = convolution<MOD1>(a, b); auto c2 = convolution<MOD2>(a, b); auto c3 = convolution<MOD3>(a, b); std::vector<long long> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { unsigned long long x = 0; x += (c1[i] * i1) % MOD1 * M2M3; x += (c2[i] * i2) % MOD2 * M1M3; x += (c3[i] * i3) % MOD3 * M1M2; long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1)); if (diff < 0) diff += MOD1; static constexpr unsigned long long offset[5] = { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3}; x -= offset[diff % 5]; c[i] = x; } return c; } } #endif #ifndef ATCODER_DSU_HPP #define ATCODER_DSU_HPP 1 #include <algorithm> #include <cassert> #include <vector> namespace atcoder { struct dsu { public: dsu() : _n(0) {} dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector<std::vector<int>> groups() { std::vector<int> leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector<std::vector<int>> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector<int>& v) { return v.empty(); }), result.end()); return result; } private: int _n; std::vector<int> parent_or_size; }; } #endif #ifndef ATCODER_FENWICKTREE_HPP #define ATCODER_FENWICKTREE_HPP 1 #include <cassert> #include <vector> namespace atcoder { template <class T> struct fenwick_tree { using U = internal::to_unsigned_t<T>; public: fenwick_tree() : _n(0) {} fenwick_tree(int n) : _n(n), data(n) {} void add(int p, T x) { assert(0 <= p && p < _n); p++; while (p <= _n) { data[p - 1] += U(x); p += p & -p; } } void change(int p,T x){ add(p,x-data[p]); } T sum(int l, int r) { assert(0 <= l && l <= r && r <= _n); return sum(r) - sum(l); } int lb(T w){ if(w<=0)return 0; int x=0; int u=1;while(u<_n)u*=2; for(int k=u;k>0;k/=2){ if(x+k<=_n&&data[x+k-1]<w){ w-=data[x+k-1]; x+=k; } } return x; } private: int _n; std::vector<U> data; U sum(int r) { U s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } }; } #endif #ifndef ATCODER_LAZYSEGTREE_HPP #define ATCODER_LAZYSEGTREE_HPP 1 #include <algorithm> #include <cassert> #include <iostream> #include <vector> namespace atcoder { template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()> struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {} lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector<S>(2 * size, e()); lz = std::vector<F>(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push(r >> i); } S sml = e(), smr = e(); while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template <bool (*g)(S)> int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template <class G> int max_right(int l, G g) { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template <bool (*g)(S)> int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template <class G> int min_left(int r, G g) { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector<S> d; std::vector<F> lz; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } #endif #ifndef ATCODER_MAXFLOW_HPP #define ATCODER_MAXFLOW_HPP 1 #include <algorithm> #include <cassert> #include <limits> #include <queue> #include <vector> namespace atcoder { template <class Cap> struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector<edge> edges() { int m = int(pos.size()); std::vector<edge> result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); std::vector<int> level(_n), iter(_n); internal::simple_queue<int> que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) break; } return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); while (flow < flow_limit) { Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } } return flow; } std::vector<bool> min_cut(int s) { std::vector<bool> visited(_n); internal::simple_queue<int> que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector<std::pair<int, int>> pos; std::vector<std::vector<_edge>> g; }; } #endif #ifndef ATCODER_MINCOSTFLOW_HPP #define ATCODER_MINCOSTFLOW_HPP 1 #include <algorithm> #include <cassert> #include <limits> #include <queue> #include <vector> namespace atcoder { template <class Cap, class Cost> struct mcf_graph { public: mcf_graph() {} mcf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); g[from].push_back(_edge{to, int(g[to].size()), cap, cost}); g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{ pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost, }; } std::vector<edge> edges() { int m = int(pos.size()); std::vector<edge> result(m); for (int i = 0; i < m; i++) { result[i] = get_edge(i); } return result; } std::pair<Cap, Cost> flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); } std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector<std::pair<Cap, Cost>> slope(int s, int t) { return slope(s, t, std::numeric_limits<Cap>::max()); } std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector<Cost> dual(_n, 0), dist(_n); std::vector<int> pv(_n), pe(_n); std::vector<bool> vis(_n); auto dual_ref = [&]() { std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max()); std::fill(pv.begin(), pv.end(), -1); std::fill(pe.begin(), pe.end(), -1); std::fill(vis.begin(), vis.end(), false); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::priority_queue<Q> que; dist[s] = 0; que.push(Q{0, s}); while (!que.empty()) { int v = que.top().to; que.pop(); if (vis[v]) continue; vis[v] = true; if (v == t) break; for (int i = 0; i < int(g[v].size()); i++) { auto e = g[v][i]; if (vis[e.to] || !e.cap) continue; Cost cost = e.cost - dual[e.to] + dual[v]; if (dist[e.to] - dist[v] > cost) { dist[e.to] = dist[v] + cost; pv[e.to] = v; pe[e.to] = i; que.push(Q{dist[e.to], e.to}); } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; dual[v] -= dist[t] - dist[v]; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost = -1; std::vector<std::pair<Cap, Cost>> result; result.push_back({flow, cost}); while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = pv[v]) { c = std::min(c, g[pv[v]][pe[v]].cap); } for (int v = t; v != s; v = pv[v]) { auto& e = g[pv[v]][pe[v]]; e.cap -= c; g[v][e.rev].cap += c; } Cost d = -dual[s]; flow += c; cost += c * d; if (prev_cost == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost = cost; } return result; } private: int _n; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector<std::pair<int, int>> pos; std::vector<std::vector<_edge>> g; }; } #endif #ifndef ATCODER_SEGTREE_HPP #define ATCODER_SEGTREE_HPP 1 #include <algorithm> #include <cassert> #include <vector> namespace atcoder { template <class S, S (*op)(S, S), S (*e)()> struct segtree { public: segtree() : segtree(0) {} segtree(int n) : segtree(std::vector<S>(n, e())) {} segtree(const std::vector<S>& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector<S>(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } template <bool (*f)(S)> int max_right(int l) { return max_right(l, [](S x) { return f(x); }); } template <class F> int max_right(int l, F f) { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template <bool (*f)(S)> int min_left(int r) { return min_left(r, [](S x) { return f(x); }); } template <class F> int min_left(int r, F f) { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector<S> d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } #endif using namespace atcoder; #define endl "\n" //using mint=static_modint<mod2>; //mintに注意 //除算はa[0]!=0でないとできない template < int MOD > struct mint { public: long long x; mint(long long x = 0) : x((x % MOD + MOD) % MOD) {} mint(std::string &s) { long long z = 0; for (int i = 0; i < s.size(); i++) { z *= 10; z += s[i] - '0'; z %= MOD; } this->x = z; } mint &operator+=(const mint &a) { if ((x += a.x) >= MOD) x -= MOD; return *this; } mint &operator-=(const mint &a) { if ((x += MOD - a.x) >= MOD) x -= MOD; return *this; } mint &operator*=(const mint &a) { (x *= a.x) %= MOD; return *this; } mint &operator/=(const mint &a) { long long n = MOD - 2; mint u = 1, b = a; while (n > 0) { if (n & 1) { u *= b; } b *= b; n >>= 1; } return *this *= u; } mint operator+(const mint &a) const { mint res(*this); return res += a; } mint operator-() const { return mint() -= *this; } mint operator-(const mint &a) const { mint res(*this); return res -= a; } mint operator*(const mint &a) const { mint res(*this); return res *= a; } mint operator/(const mint &a) const { mint res(*this); return res /= a; } friend std::ostream &operator<<(std::ostream &os, const mint &n) { return os << n.x; } friend std::istream &operator>>(std::istream &is, mint &n) { long long x; is >> x; n = mint(x); return is; } bool operator==(const mint &a) const { return this->x == a.x; } bool operator!=(const mint &a) const { return this->x != a.x; } mint pow(long long k) const { mint ret = 1; mint p = this->x; while (k > 0) { if (k & 1) { ret *= p; } p *= p; k >>= 1; } return ret; } }; //constexpr int MOD = mod; //any=false:NTT friendly any=true:not NTT friendly template < const int MOD, bool any = false > struct FormalPowerSeries { private: using P = FormalPowerSeries< MOD, any >; template < class T, class F = multiplies< T > > T power(T a, long long n, F op = multiplies< T >(), T e = {1}) const { assert(n >= 0); T res = e; while (n) { if (n & 1) res = op(res, a); if (n >>= 1) a = op(a, a); } return res; } template < int _MOD > void ntt(vector< mint< _MOD > > &a, bool inverse) { static vector< mint< _MOD > > dw(30), idw(30); if (dw[0] == 0) { mint< _MOD > root = 2; while (power(root, (_MOD - 1) / 2) == 1) root += 1; for (int i = 0; i < 30; i++) dw[i] = -power(root, (_MOD - 1) >> (i + 2)), idw[i] = mint< _MOD >(1) / dw[i]; } int n = a.size(); assert((n & (n - 1)) == 0); if (not inverse) { for (int m = n; m >>= 1;) { mint< _MOD > 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; if (x.x >= _MOD) x.x -= _MOD; a[i].x = x.x + y.x, a[j].x = x.x + (_MOD - y.x); } w *= dw[__builtin_ctz(++k)]; } } } else { for (int m = 1; m < n; m *= 2) { mint< _MOD > 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 = x.x + (_MOD - y.x), a[j] *= w; } w *= idw[__builtin_ctz(++k)]; } } } auto c = mint< _MOD >(1) / mint< _MOD >(inverse ? n : 1); for (auto &&e : a) e *= c; } template < int _MOD > vector< mint< _MOD > > convolution(vector< mint< _MOD > > l, vector< mint< _MOD > > r) { if (l.empty() || r.empty()) return {}; int n = l.size(), m = r.size(), sz = 1 ; while(sz<=2*(n+m-1)-1)sz*=2; if (min(n, m) < 30) { vector< long long > res(n + m - 1); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) res[i + j] += (l[i] * r[j]).x; return {begin(res), end(res)}; } bool eq = l == r; l.resize(sz), ntt(l, false); if (eq) r = l; else r.resize(sz), ntt(r, false); for (int i = 0; i < sz; i++) l[i] *= r[i]; ntt(l, true), l.resize(n + m - 1); return l; } P pre(const P &p, int sz) const { P ret; ret.a = vector< mint< MOD > >(p.a.begin(), p.a.begin() + min((int)p.a.size(), sz)); return ret; } public: vector< mint< MOD > > a; FormalPowerSeries(int sz = 0) { this->a.resize(sz, 0); } P resize(int k) const { return pre(*this, k); } FormalPowerSeries(std::initializer_list< mint< MOD > > v) { this->a = v; } size_t size() const { return this->a.size(); } bool operator<(const P &r) const { return this->a.size() < r.a.size(); } bool operator>(const P &r) const { return this->a.size() > r.a.size(); } P operator+(const P &a) const { return P(*this) += a; } //定数を足す P operator+(const long long a) const { return P(*this) += a; } P operator-(const P &a) const { return P(*this) -= a; } P operator*(const P &a) const { return P(*this) *= a; } P operator*(const long long a) const { return P(*this) *= a; } P operator/(const P &a) const { return P(*this) /= a; } P &operator+=(const P &r) { this->a.resize(max(this->a.size(), r.size())); for (int i = 0; i < (int)r.size(); i++) this->a[i] += r.a[i]; return *this; } P &operator+=(const long long v) { if (this->a.size() == 0) this->a.resize(1, (v % MOD + MOD) % MOD); else this->a[0] += v; return *this; } P &operator-=(const P &r) { this->a.resize(max(this->a.size(), r.size())); for (int i = 0; i < (int)r.size(); i++) this->a[i] -= r.a[i]; return *this; } P &operator*=(const P &b) { if (!any) { this->a = convolution(this->a, b.a); return *this; } else { if (this->a.empty() || b.a.empty()) { this->a.clear(); return *this; } int n = this->a.size(), m = b.a.size(); static constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617; using Mint0 = mint< mod0 >; using Mint1 = mint< mod1 >; using Mint2 = mint< mod2 >; vector< Mint0 > l0(n), r0(m); vector< Mint1 > l1(n), r1(m); vector< Mint2 > l2(n), r2(m); for (int i = 0; i < n; i++) l0[i] = this->a[i].x, l1[i] = this->a[i].x, l2[i] = this->a[i].x; for (int j = 0; j < m; j++) r0[j] = b.a[j].x, r1[j] = b.a[j].x, r2[j] = b.a[j].x; l0 = convolution(l0, r0); l1 = convolution(l1, r1); l2 = convolution(l2, r2); this->a.resize(n + m - 1); static const Mint1 im0 = Mint1(1) / Mint1(mod0); static const Mint2 im1 = Mint2(1) / Mint2(mod1), im0m1 = im1 / mod0; static const mint< MOD > m0 = mod0, m0m1 = m0 * mod1; for (int i = 0; i < n + m - 1; i++) { int y0 = l0[i].x; int y1 = (im0 * (l1[i] - y0)).x; int y2 = (im0m1 * (l2[i] - y0) - im1 * y1).x; this->a[i] = m0m1 * y2 + y0 + m0 * y1; } return *this; } } P &operator*=(const long long v) { for (int i = 0; i < this->a.size(); i++) this->a[i] *= v; return *this; } P &operator/=(const P &a) { *this *= a.inverse(); return *this; } //逆数 P inverse(int deg = -1) const { assert(this->a.size() != 0 && this->a[0].x != 0); const int n = (int)this->a.size(); if (deg == -1) deg = n; P ret(1); ret[0] = mint< MOD >(1) / a[0]; for (int i = 1; i < deg; i <<= 1) { ret = pre((ret + ret - ret * ret * pre(*this, i << 1)), i << 1); } return pre(ret, deg); } //微分 P differential() const { const int n = (int)this->a.size(); P ret(max(0, n - 1)); for (int i = 1; i < n; i++) ret[i - 1] = this->a[i] * i; return ret; } //不定積分 P integral() const { const int n = (int)this->a.size(); P ret(n + 1); for (int i = 0; i < n; i++) ret[i + 1] = this->a[i] / (i + 1); return ret; } P log(int deg = -1) const { assert(this->a.size() != 0 && this->a[0] == 1); const int n = (int)this->a.size(); if (deg == -1) deg = n; return pre((this->differential() * this->inverse(deg)), deg - 1).integral(); } P exp(int deg = -1) const { if (this->a.size() == 0) return P(0); assert(this->a[0] == 0); const int n = (int)this->a.size(); if (deg == -1) deg = n; P ret(1); ret.a[0] = 1; for (int i = 1; i < deg; i <<= 1) { ret = pre((ret * (pre(*this, i << 1) + 1 - ret.log(i << 1))), i << 1); } return pre(ret, deg); } P pow(long long k, int deg = -1) const { const int n = (int)this->a.size(); if (deg == -1) deg = n; for (int i = 0; i < n; i++) { if (this->a[i].x != 0) { long long rev = (mint< MOD >(1) / this->a[i]).x; 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() * power(this->a[i], k).x; 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; } mint< MOD > &operator[](int x) { assert(0 <= x && x < (int)this->a.size()); return a[x]; } friend std::ostream &operator<<(std::ostream &os, const P &p) { os << "[ "; for (int i = 0; i < p.size(); ++i) { os << p.a[i] << " "; } os << "]"; return os; } }; //[x^k] p(x)/q(x) template < int MOD, bool any = false > mint< MOD > Bostan_Mori(FormalPowerSeries< MOD, any > p, FormalPowerSeries< MOD, any > q, ll k) { if(k<0)return 0; p.a.resize(max(p.size(), q.size())); q.a.resize(max(p.size(), q.size())); typedef FormalPowerSeries< MOD, any > FPS; while (k) { FPS _q = q; for (int i = 1; i < _q.size(); i += 2) _q[i] = -_q[i]; FPS v = q, u = p; v *= _q; u *= _q; for (int i = k % 2; i < u.size(); i += 2) p[i / 2] = u[i]; for (int i = 0; i < v.size(); i += 2) q[i / 2] = v[i]; k /= 2; } return p[0] / q[0]; } typedef FormalPowerSeries<mod,true> FPS; int main(){ ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); int k;cin>>k; int n;cin>>n; int x[n]; FPS f(100001); rep(i,0,n){ cin>>x[i]; f[x[i]]+=1; } f=FPS{1}-f; f=FPS{1}/f; cout<<f[k]<<endl; }