結果
| 問題 | No.8046 yukicoderの過去問 |
| ユーザー |
 kyon2326
|
| 提出日時 | 2020-10-15 22:30:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 23,019 bytes |
| コンパイル時間 | 2,305 ms |
| コンパイル使用メモリ | 224,888 KB |
| 実行使用メモリ | 12,668 KB |
| 最終ジャッジ日時 | 2024-07-20 20:03:12 |
| 合計ジャッジ時間 | 6,043 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
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 | 2 ms
10,624 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 6 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 4 ms
5,376 KB |
| testcase_06 | TLE | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
ソースコード
#include <bits/stdc++.h>
using namespace std;
/*
#include <atcoder/all>
using namespace atcoder;
*/
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using bll = boost::multiprecision::cpp_int;
using bdouble = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>>;
using namespace boost::multiprecision;
*/
#ifdef LOCAL_TEST
#define BOOST_STACKTRACE_USE_ADDR2LINE
#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
#define _GNU_SOURCE 1
#include <boost/stacktrace.hpp>
namespace std {
template<typename T> class dvector : public std::vector<T> {
public:
dvector() : std::vector<T>() {}
explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
dvector(const std::vector<T>& v) : std::vector<T>(v) {}
dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
dvector(const typename std::vector<T>::reverse_iterator first, const typename std::vector<T>::reverse_iterator last) : std::vector<T>(first, last) {}
dvector(const typename std::vector<T>::const_iterator first, const typename std::vector<T>::const_iterator last) : std::vector<T>(first, last) {}
dvector(const typename std::vector<T>::const_reverse_iterator first, const typename std::vector<T>::const_reverse_iterator last) : std::vector<T>(first, last) {}
T& operator[](size_t n) {
try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); }
}
const T& operator[](size_t n) const {
try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); }
}
};
}
class dbool {
private:
bool boolvalue;
public:
dbool() : boolvalue(false) {}
dbool(bool b) : boolvalue(b) {}
operator bool&() { return boolvalue; }
operator const bool&() const { return boolvalue; }
};
#define vector dvector
#define bool dbool
class SIGFPE_exception : std::exception {};
class SIGSEGV_exception : std::exception {};
void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); }
void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
signed convertedmain();
signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
#define main() convertedmain()
#endif
#ifdef LOCAL_DEV
template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
return s << "(" << p.first << ", " << p.second << ")"; }
template <typename T, size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
template<typename T> std::ostream& operator<<(std::ostream& s, const std::deque<T>& v) {
for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
template<typename T> std::ostream& operator<<(std::ostream& s, const std::vector<T>& v) {
for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
template<typename T> std::ostream& operator<<(std::ostream& s, const std::vector<std::vector<T>>& vv) {
s << "\\\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
void debug_impl() { std::cerr << '\n'; }
template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
#define debug(...) do { std::cerr << ":" << __LINE__ << " (" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
#else
#define debug(...) do {} while (false)
#endif
//#define int long long
using ll = long long;
//constexpr int INF = (ll)1e9 + 7; //INT_MAX = (1<<31)-1 = 2147483647
constexpr ll INF = (ll)1e18; //INT64_MAX = (1LL<<63)-1 = 9223372036854775807
constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5
//constexpr ll MOD = 998244353; //primitive root = 3
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1, 0, -1, 0};
constexpr ll dy[4] = {0, 1, 0, -1};
constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define rep(i, n) for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define rrep(i, n) for(ll i=(n)-1; i>=0; --i)
#define rrepeq(i, n) for(ll i=(n) ; i>=1; --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
void p() { std::cout << '\n'; }
template<typename Head, typename... Tail> void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template<typename T> inline void pv(std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template<typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template<typename T> inline void uniq(std::vector<T>& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); }
/*-----8<-----template-----8<-----*/
inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y){ ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; }
inline constexpr ll invmod(ll a, ll m = MOD){ ll x = 0, y = 0; extgcd(a, m, x, y); return (x + m) % m; }
class Modint{
public:
ll _num;
constexpr Modint() : _num() { _num = 0; }
constexpr Modint(ll x) : _num() { _num = x % MOD; if(_num < 0) _num += MOD; }
inline constexpr Modint operator= (int x){ _num = x % MOD; if(_num<0) _num += MOD; return *this; }
inline constexpr Modint operator= (ll x){ _num = x % MOD; if(_num<0) _num += MOD; return *this; }
//inline constexpr Modint operator= (Modint x){ _num = x._num; return *this; }
inline constexpr Modint operator+ (int x){ return Modint(_num + x); }
inline constexpr Modint operator+ (ll x){ return Modint(_num + x); }
inline constexpr Modint operator+ (Modint x){ ll a = _num + x._num; if(a >= MOD) a -= MOD; return Modint{a}; }
inline constexpr Modint operator+=(int x){ _num += x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
inline constexpr Modint operator+=(ll x){ _num += x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
inline constexpr Modint operator+=(Modint x){ _num += x._num; if(_num >= MOD) _num -= MOD; return *this; }
inline constexpr Modint operator++(){ _num++; if(_num == MOD) _num = 0; return *this; }
inline constexpr Modint operator- (int x){ return Modint(_num - x); }
inline constexpr Modint operator- (ll x){ return Modint(_num - x); }
inline constexpr Modint operator- (Modint x){ ll a = _num - x._num; if(a < 0) a += MOD; return Modint{a}; }
inline constexpr Modint operator-=(int x){ _num -= x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
inline constexpr Modint operator-=(ll x){ _num -= x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
inline constexpr Modint operator-=(Modint x){ _num -= x._num; if(_num < 0) _num += MOD; return *this; }
inline constexpr Modint operator--(){ _num--; if(_num == -1) _num = MOD - 1; return *this; }
inline constexpr Modint operator* (int x){ return Modint(_num * (x % MOD)); }
inline constexpr Modint operator* (ll x){ return Modint(_num * (x % MOD)); }
inline constexpr Modint operator* (Modint x){ return Modint{_num * x._num % MOD}; }
inline constexpr Modint operator*=(int x){ _num *= Modint(x); _num %= MOD; return *this; }
inline constexpr Modint operator*=(ll x){ _num *= Modint(x); _num %= MOD; return *this; }
inline constexpr Modint operator*=(Modint x){ _num *= x._num; _num %= MOD; return *this; }
inline constexpr Modint operator/ (int x){ return Modint(_num * invmod(Modint(x), MOD)); }
inline constexpr Modint operator/ (ll x){ return Modint(_num * invmod(Modint(x), MOD)); }
inline constexpr Modint operator/ (Modint x){ return Modint{_num * invmod(x._num, MOD) % MOD}; }
inline constexpr Modint operator/=(int x){ _num *= invmod(Modint(x), MOD); _num %= MOD; return *this; }
inline constexpr Modint operator/=(ll x){ _num *= invmod(Modint(x), MOD); _num %= MOD; return *this; }
inline constexpr Modint operator/=(Modint x){ _num *= invmod(x._num, MOD); _num %= MOD; return *this; }
inline constexpr Modint pow(ll n){ ll i = 1, x = n>=0 ? n : -n; Modint ans = 1, cnt = n>=0 ? *this : Modint(1) / *this; while(i <= x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *= 2; } return ans; }
inline constexpr operator ll() const { return _num; }
inline constexpr static ll get_mod() { return MOD; }
};
inline std::istream& operator>>(std::istream &s, Modint &x){ ll t; s>>t; x=t; return s; }
vector<Modint> fac(1, 1), inv(1, 1);
inline void reserve(size_t a){
if(fac.size() >= a) return;
if(a < fac.size() * 2) a = fac.size() * 2;
if(a >= MOD) a = MOD;
while(fac.size() < a) fac.push_back(fac.back() * ll(fac.size()));
inv.resize(fac.size());
inv.back() = Modint(1) / fac.back();
for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i;
}
inline Modint factorial(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; }
inline Modint nPk_loop(ll n, ll k){ if(n<k) return 0; Modint val(1); for(ll i=n;i>(n-k);i--)val*=i; return val; }
inline Modint nCk_loop(ll n, ll k){ if(n<k) return 0; Modint val(1); k=min(k,n-k); for(ll i=n;i>(n-k);i--)val*=i; for(ll i=k;i>1;i--)val/=i; return val; };
inline Modint nPk(ll n, ll k){ if(k < 0 || n < k) return 0; if(n>=(ll)1e7) return nPk_loop(n, k); reserve(n + 1); return fac[n] * inv[n - k]; }
inline Modint nCk(ll n, ll k){ if(k < 0 || n < k) return 0; if(n>=(ll)1e7) return nCk_loop(n, k); reserve(n + 1); return fac[n] * inv[k] * inv[n - k]; }
inline Modint nHk(ll n, ll k){ return nCk(n + k - 1, k); } //n種類のものから重複を許してk個選ぶ=玉k個と仕切りn-1個
/*
nCk：n!が間に合わないくらい巨大でkが小さいとき、素直に計算すると間に合う のは1e7以上に組み込んであります
auto f = [](ll n, ll k){
if(n<k)return Modint(0);
Modint val(1);
k=min(k,n-k);
for(ll i=n;i>(n-k);i--)val*=i;
for(ll i=k;i>1;i--)val/=i;
return val;
};
*/
////
//高速フーリエ変換
//計算量 O((n+m)log(n+m))
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); }
};
int base = 1;
vector< C > rts = {{0, 0},
{1, 0}};
vector< int > rev = {0, 1};
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while(base < nbase) {
real angle = M_PI * 2.0 / (1 << (base + 1));
for(int 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< C > &a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int 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;
}
}
}
}
template<typename T>
vector< ll > multiply(vector< T > &a, vector< T > &b) {
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < sz; i++) {
real x = (i < (int) a.size() ? a[i] : 0);
real y = (i < (int) 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(int i = 0; i <= (sz >> 1); i++) {
int 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(int 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< ll > ret(need);
for(int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
};
//任意mod畳み込み(Arbitrary-Mod-Convolution)
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
if(need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < (int)a.size(); i++) {
fa[i] = C(a[i]._num & ((1 << 15) - 1), a[i]._num >> 15);
}
fft(fa, sz);
vector< C > fb(sz);
if(a == b) {
fb = fa;
} else {
for(int i = 0; i < (int)b.size(); i++) {
fb[i] = C(b[i]._num & ((1 << 15) - 1), b[i]._num >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for(int i = 0; i <= (sz >> 1); i++) {
int 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< T > ret(need);
for(int i = 0; i < need; i++) {
ll aa = llround(fa[i].x);
ll bb = llround(fb[i].x);
ll cc = llround(fa[i].y);
aa = T(aa)._num, bb = T(bb)._num, cc = T(cc)._num;
ret[i] = T(aa + (bb << 15) + (cc << 30));
}
return ret;
}
};
//形式的冪級数
//https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html
template< typename T >
struct FormalPowerSeries : vector< T > {
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) 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 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 < (int)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 < (int)(this->size()); i++) ret[i] = -(*this)[i];
return 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 pre(int sz) const {
return P(begin(*this), begin(*this) + min((int) this->size(), sz));
}
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;
}
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(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;
}
// 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() * (*this)[i].pow(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;
}
//sparse
P mul(vector<pair<ll, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
if (d == 0) g.erase(g.begin());
else c = 0;
for(int i=n-1; i>=0; i--){
(*this)[i] *= c;
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] += (*this)[i-j] * b;
}
}
return *this;
}
//sparse, required: "g[0] == (0, c)" and "c != 0"
P div(vector<pair<ll, T>> g) {
int n = (*this).size();
auto [d, c] = g.front();
assert(d == 0 && c != T(0));
g.erase(g.begin());
for(int i=0; i<n; i++) {
for (auto &[j, b] : g) {
if (j > i) break;
(*this)[i] -= (*this)[i-j] * b;
}
(*this)[i] /= c;
}
return *this;
}
};
//partition(N): [0,N] の分割数を返す。
//分割数：自然数 n を 自然数の和で表す組み合わせの数 (順序は考慮しない）
//計算量：O(NlogN)
template< typename T >
FormalPowerSeries< T > partition(int N) {
ArbitraryModConvolution< Modint > fft;
using FPS = FormalPowerSeries< Modint >;
auto mult = [&](const FPS::P &a, const FPS::P &b) { return fft.multiply(a, b); };
FPS::set_fft(mult);
FormalPowerSeries< T > po(N + 1);
po[0] = 1;
for(int k = 1; k <= N; k++) {
if(1LL * k * (3 * k + 1) / 2 <= N) po[k * (3 * k + 1) / 2] += (k % 2 ? -1 : 1);
if(1LL * k * (3 * k - 1) / 2 <= N) po[k * (3 * k - 1) / 2] += (k % 2 ? -1 : 1);
}
return po.inv();
}
/*-----8<-----library-----8<-----*/
void solve() {
ArbitraryModConvolution< Modint > fft;
using FPS = FormalPowerSeries< Modint >;
auto mult = [&](const FPS::P &a, const FPS::P &b) { return fft.multiply(a, b); };
FPS::set_fft(mult);
ll K, N;
cin >> K >> N;
/*
//f(T)=(T^(進める歩数1) + T^(進める歩数2) + ... )とすると、
//求めたいのは 1 + f(T) + f(T)^2 + ... = 1/(1-f(T))
//まず X に 1-f(T) をつくる
ll size = K+1;
FormalPowerSeries<Modint> X(size);
X[0] = 1;
for(ll i = 0; i < N; i++) {
ll t;
cin >> t;
if(t <= K) X[t] = -1;
}
//1/(1-f(T))
FormalPowerSeries<Modint> v = X.inv(size);
//x^Kの係数が解となる
Modint ans = v[K];
cout << ans << endl;
*/
FormalPowerSeries<Modint> X(K+1);
X[0]=1;
vector<pair<ll,Modint>> Y{{0,1}};
rep(i,N){
ll t;cin>>t;
Y.push_back({t,-1});
}
FormalPowerSeries<Modint> ans=X.div(Y);
p(ans[K]);
}
signed main() {
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
//ll Q; cin >> Q; while(Q--)solve();
solve();
return 0;
}