結果
| 問題 | No.3046 yukicoderの過去問 |
| ユーザー |
 namakoiscat
|
| 提出日時 | 2023-06-15 17:51:53 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 483 ms / 2,000 ms |
| コード長 | 33,752 bytes |
| コンパイル時間 | 4,117 ms |
| コンパイル使用メモリ | 256,548 KB |
| 実行使用メモリ | 29,564 KB |
| 最終ジャッジ日時 | 2023-09-05 21:28:47 |
| 合計ジャッジ時間 | 10,244 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge15 |
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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 | 469 ms
28,724 KB |
| testcase_01 | AC | 471 ms
29,508 KB |
| testcase_02 | AC | 469 ms
29,512 KB |
| testcase_03 | AC | 473 ms
28,852 KB |
| testcase_04 | AC | 472 ms
28,736 KB |
| testcase_05 | AC | 467 ms
29,564 KB |
| testcase_06 | AC | 483 ms
28,748 KB |
| testcase_07 | AC | 481 ms
28,832 KB |
| testcase_08 | AC | 483 ms
28,732 KB |
ソースコード
/*
#include <bits/stdc++.h>
using namespace std;
int main(){
*/
// __builtin_popcountll() ;
// multiset ;
// unordered_set ;
// unordered_map ;
// reverse ;
/*
#include <atcoder/all>
using namespace atcoder ;
// using mint = modint;
// using mint = modint998244353 ;
// using mint = modint1000000007 ;
*/
#include <bits/stdc++.h>
using namespace std;
/*
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
typedef cpp_int cp ;
*/
//-------型-------
typedef long long ll;
typedef string st ;
typedef long double ld ;
typedef unsigned long long ull ;
using P = pair<ll,ll> ;
using run = pair<char,ll> ;
using Edge = tuple<ll,ll,ll> ;
using AAA = tuple<ll,ll,ll,ll> ;
//-------型-------
//-------定数-------
const ll mod0 = 1000000007;
const ll mod1 = 998244353 ;
const ll LINF = 1000000000000000000+2 ; //(10^18)
const ld pai = acos(-1) ;
const ld EPS = 1e-10 ;
//-------定数-------
//-------マクロ-------
#define pb push_back
#define ppb pop_back
#define pf push_front
#define ppf pop_front
#define all(x) x.begin(), x.end()
#define rep(i,a,n) for (ll i = a; i <= (n); ++i)
#define rrep(i,a,b,c) for (ll i = a ; i <= (b) ; i += c)
#define ketu(i,a,n) for (ll i = a; i >= (n); --i)
#define re return 0;
#define fore(i,a) for(auto &i:a)
#define V vector
#define fi first
#define se second
#define C cout
#define E "\n";
#define EE endl;
//-------マクロ-------
//-------テンプレ文字列-------
st zz = "abcdefghijklmnopqrstuvwxyz" ;
st ZZ = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" ;
st tintin = "%" ;
st Y = "Yes" ;
st YY = "No" ;
st KU = " " ;
//-------テンプレ文字列-------
void chmin(ll& x ,ll y){x = min(x,y) ;}
void chmax(ll& x ,ll y){x = max(x,y) ;}
ll max_element(V<ll> &A){
ll res = *max_element(all(A)) ;
return res ;
}
ll max_element_index(V<ll> &A){
ll res = max_element(all(A)) - A.begin() ;
return res ;
}
ll min_element(V<ll> &A){
ll res = *min_element(all(A)) ;
return res ;
}
ll min_element_index(V<ll> &A){
ll res = min_element(all(A)) - A.begin() ;
return res ;
}
vector<ll> Y4 = {0,1,0,-1} ;
vector<ll> X4 = {1,0,-1,0} ;
vector<ll> Y8 = {0,1,1,1,0,-1,-1,-1} ;
vector<ll> X8 = {1,1,0,-1,-1,-1,0,1} ;
template<class T> T pow_mod(T A, T N, T M) {
T res = 1 % M;
A %= M;
while (N) {
if (N & 1) res = (res * A) % M;
A = (A * A) % M;
N >>= 1;
}
return res;
}
// Miller-Rabin 素数判定
bool nis(ll N) {
if (N <= 1) return false;
if (N == 2) return true;
if (N == 3) return true ;
if (N == 5) return true ;
if (N == 7) return true ;
if (N == 11) return true ;
if (N % 2 == 0 || N % 3 == 0 || N % 5 == 0 || N % 7 == 0 || N % 11 == 0 ) return false ;
vector<ll> A = {2, 325, 9375, 28178, 450775,9780504, 1795265022};
ll s = 0, d = N - 1;
while (d % 2 == 0) {
++s;
d >>= 1;
}
fore(a,A) {
if (a % N == 0) return true;
ll t, x = pow_mod<__int128_t>(a, d, N);
if (x != 1) {
for (t = 0; t < s; ++t) {
if (x == N - 1) break;
x = __int128_t(x) * x % N;
}
if (t == s) return false;
}
}
return true;
}
// UF.initはいっかいだけならいいけど、二回目以降はrepで初期化
vector<ll> par;
class UnionFind {
public:
// サイズをＧＥＴ！
void init(ll sz) {
par.resize(sz,-1);
}
// 各連結成分の一番上を返す
ll root(ll x) {
if (par[x] < 0) return x;
return par[x] = root(par[x]);
}
// 結合作業
bool unite(ll x, ll y) {
x = root(x); y = root(y);
if (x == y) return false;
if (par[x] > par[y]) swap(x,y);
par[x] += par[y];
par[y] = x;
return true;
}
// 同じグループか判定
bool same(ll x, ll y) { return root(x) == root(y);}
// グループのサイズをＧＥＴ！
ll size(ll x) { return -par[root(x)];}
};
UnionFind UF ;
vector<ll> enumdiv(ll n) {
vector<ll> S;
for (ll i = 1; i*i <= n; i++) if (n%i == 0) { S.pb(i); if (i*i != n) S.pb(n / i); }
sort(S.begin(), S.end());
return S;
}
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_priority_queue = priority_queue<T, vector<T>, less<T>> ;
// 使用例 min_priority_queue<ll (ここは型)> Q ;
vector<pair<long long, long long>> prime_factorize(long long N){
vector<pair<long long, long long>> res;
for(long long a = 2; a * a <= N; ++a){
if(N % a != 0) continue;
long long ex = 0;
while(N % a == 0) ++ex, N /= a;
res.push_back({a,ex});
}
if(N != 1) res.push_back({N,1});
return res;
}
ll binpower(ll a, ll b,ll c) {
if(!b) return 1 ;
a %= c ;
ll d = binpower(a,b/2,c) ;
(d *= d) %= c ;
if(b%2) (d *= a) %= c ;
return d ;
}
template<typename T>
V<T> sr(V<T> A){
sort(all(A)) ;
reverse(all(A)) ;
return A ;
}
map<ll,ll> Compression(V<ll> A){
sort(all(A)) ;
A.erase(unique(all(A)),A.end()) ;
map<ll,ll> res ;
ll index = 0 ;
fore(u,A){
res[u] = index ;
index ++ ;
}
return res ;
}
V<ll> sort_erase_unique(V<ll> &A){
sort(all(A)) ;
A.erase(unique(all(A)),A.end()) ;
return A ;
}
struct sqrt_machine{
V<ll> A ;
const ll M = 1000000 ;
void init(){
A.pb(-1) ;
rep(i,1,M){
A.pb(i*i) ;
}
A.pb(LINF) ;
}
bool scan(ll a){
ll pos = lower_bound(all(A),a) - A.begin() ;
if(A[pos] == -1 || A[pos] == LINF || A[pos] != a)return false ;
return true ;
}
};
sqrt_machine SM ;
ll a_b(V<ll> A,ll a,ll b){
ll res = 0 ;
res += upper_bound(all(A),b) - lower_bound(all(A),a) ;
return res ;
}
struct era{
ll check[10000010] ;
void init(){
rep(i,2,10000000){
if(check[i] == 0){
for(ll j = i + i ;j <= 10000000 ; j += i){
check[j] ++ ;
}
}
}
}
bool look(ll x){
if(x == 1)return false ;
if(check[x] == 0)return true ;
else return false ;
}
ll enu_count(ll x){
if(x == 1)return 1 ;
if(check[x] == 0)return 1 ;
return check[x] ;
}
};
era era ;
st _10_to_2(ll x){
st abc = "" ;
if(x == 0){
return "0" ;
}
while(x > 0){
abc = char(x%2 + '0') + abc ;
x /= 2 ;
}
return abc ;
}
ll _2_to_10(st op){
ll abc = 0 ;
ll K = op.size() ;
for(ll i = 0 ;i < K ;i++){
abc = abc * 2 + ll(op[i] - '0') ;
}
return abc ;
}
ll powpow(ll A , ll B){
ll res = 1 ;
rep(i,1,B){
res *= A ;
}
return res ;
}
V<run> Run_Length_Encoding(st S){
ll N = S.size() ;
V<pair<char,ll>> A ;
ll count = 0 ;
char cc ;
bool RLEflag = false ;
if(N == 1){
A.pb({S[0],1}) ;
RLEflag = true ;
}
rep(i,0,N-1){
if(RLEflag == true)break ;
if(i == 0){
cc = S[i] ;
count = 1 ;
continue ;
}
if(i == N-1){
if(S[i] == cc){
A.pb({cc,count + 1}) ;
}else{
A.pb({cc,count}) ;
A.pb({S[i],1}) ;
}
break ;
}
if(S[i] == cc){
count ++ ;
}else{
A.pb({cc,count}) ;
cc = S[i] ;
count = 1 ;
}
}
return A ;
}
ll kiriage(ll a , ll b){
return (a + b - 1) / b ;
}
ll a_up(V<ll> &A , ll x){
if(A[A.size()-1] < x)return -1 ;
ll res = lower_bound(all(A),x) - A.begin() ;
return A[res] ;
}
ll b_down(V<ll> &B , ll x){
if(B[0] > x)return -1 ;
ll res = upper_bound(all(B),x) - B.begin() ;
return B[res-1] ;
}
ll Permutation(ll N){
ll res = 1 ;
rep(i,1,N)res *= i ;
return res ;
}
V<V<ll>> Next_permutation(ll N){
ll Size = Permutation(N) ;
V<V<ll>> res(Size) ;
V<ll> per(N) ;
rep(i,0,N-1)per[i] = i ;
ll count = 0 ;
do{
fore(u,per){
res[count].pb(u) ;
}
count ++ ;
}while(next_permutation(per.begin(),per.end()));
return res ;
}
/*
st Regex(st S, st A ,st B){
return regex_replace(S,regex(A),B) ;
}
st erase_string(st S , st T){
st ans = S.erase(S.find(T),T.length()) ;
return ans ;
}
*/
ll pow_daisyou(ll a , ll b , ll c){
ll d = c%2==1 ? 1 : 2 ;
ll ans = -1 ;
if(powpow(a,d) == powpow(b,d))ans = 0 ;
if(powpow(a,d) > powpow(b,d))ans = 1 ;
else if(powpow(a,d) < powpow(b,d))ans = 2 ;
return ans ;
}
template<typename T>
void debag_1V_kaigyou(V<T> A){
ll N = A.size() ;
rep(i,0,N-1){
C << A[i] << E
}
}
template<typename T>
void debag_1V_space(V<T> A){
ll N = A.size() ;
rep(i,0,N-1){
C << A[i] << KU ;
}
C << E
}
template<typename T>
void debag_2V(V<V<T>> A){
ll N = A.size() ;
ll M = A[0].size() ;
rep(i,0,N-1){
rep(j,0,M-1){
if(A[i][j] == LINF || A[i][j] == LINF)C << "L" << KU ;
else C << A[i][j] << KU ;
}
C << E
}
}
void debag_pair(V<P> A){
ll N = A.size() ;
rep(i,0,N-1){
auto [a,b] = A[i] ;
C << a << KU << b << E
}
}
void debag_Edge(V<Edge> A){
ll N = A.size() ;
rep(i,0,N-1){
auto [a,b,c] = A[i] ;
C << a << KU << b << KU << c << E
}
}
V<P> sort_Args(int len, ...)
{
V<ll> arr;
va_list args;
va_start(args, len);
for (int i = 0; i < len; ++i)
{
ll arg = va_arg(args, ll);
arr.push_back(arg);
}
va_end(args);
sort(arr.begin(), arr.end());
V<P> pos ;
pos.pb({0,-LINF}) ;
ll index = 1 ;
rep(i,0,len-1){
pos.pb({index,arr[i]}) ;
index ++ ;
}
return pos ;
}
ll c_c(char s){
ll x = s - 'a' ;
return x ;
}
ll C_C(char S){
ll X = S - 'A' ;
return X ;
}
// FPS (けんちょんさん)
/*
解説 https://drken1215.hatenablog.com/archive/category/%E5%A4%9A%E9%A0%85%E5%BC%8F%E3%83%BB%E5%BD%A2%E5%BC%8F%E7%9A%84%E5%86%AA%E7%B4%9A%E6%95%B0
f *= g
問題 https://atcoder.jp/contests/tdpc/tasks/tdpc_contest
提出 https://atcoder.jp/contests/tdpc/submissions/42229178
f /= g
係数そのままだしたかったら、 mod998なら1000000 >= なら -= MODする
問題 https://atcoder.jp/contests/abc245/tasks/abc245_d
提出 https://atcoder.jp/contests/abc245/submissions/42229617
こっちはACL特に必要ない
初期化 FPS f(N) ;
掛け算 f * g
FPS<mint> g(MAX) ;
g[0] = 1 ; g[a] = 1 ;
f *= g ;
pow f = (x+1) で (x+1)^2がほしいなら
FPS<mint> ff = pow(f,2,N) ; // Nは項数
か FPS<mint> ff = pow(f,2) ;
log , exp , inv も同じ感じ
inv = 1/f
inv やるときは余分にサイズとっておかないとREでる
FPS<mint> f(N+10) ; みたいにしないとだめ
BiCoefできること
初期化 Bicoef<mint> bc(N) ;
bc.fact(i) ===> i!
bc.finv(i) ===> (1/i!)
bc.com(n,k) ===> nCk
bc.inv(i) ===> 1/i
Bostan-Mori [x^N]P(x) / Q(x) を P(x)のサイズKとしたら、O(KlogKlogN)でだすアルゴリズム
P(x) はK次以下の多項式 , Q(x)は
BostanMori()
*/
// --------------------------code----------------------------
// modint
template<int MOD> struct Fp {
long long val;
constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
if (val < 0) val += MOD;
}
constexpr int getmod() const { return MOD; }
constexpr Fp operator - () const noexcept {
return val ? MOD - val : 0;
}
constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp& r) noexcept {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp& r) noexcept {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp& r) noexcept {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp& r) noexcept {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr bool operator == (const Fp& r) const noexcept {
return this->val == r.val;
}
constexpr bool operator != (const Fp& r) const noexcept {
return this->val != r.val;
}
friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
return os << x.val;
}
friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept {
if (n == 0) return 1;
if (n < 0) return modpow(modinv(r), -n);
auto t = modpow(r, n / 2);
t = t * t;
if (n & 1) t = t * r;
return t;
}
friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
return Fp<MOD>(u);
}
};
namespace NTT {
long long modpow(long long a, long long n, int mod) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
long long modinv(long long a, int mod) {
long long b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
int calc_primitive_root(int mod) {
if (mod == 2) return 1;
if (mod == 167772161) return 3;
if (mod == 469762049) return 3;
if (mod == 754974721) return 11;
if (mod == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (mod - 1) / 2;
while (x % 2 == 0) x /= 2;
for (long long i = 3; 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 (modpow(g, (mod - 1) / divs[i], mod) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return max(size_a, size_b) << 1;
}
// number-theoretic transform
template<class mint> void trans(vector<mint>& v, bool inv = false) {
if (v.empty()) return;
int N = (int)v.size();
int MOD = v[0].getmod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static vector<long long> vbw(30), vibw(30);
if (first) {
first = false;
for (int k = 0; k < 30; ++k) {
vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
vibw[k] = modinv(vbw[k], MOD);
}
}
for (int i = 0, j = 1; j < N - 1; j++) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (i > j) swap(v[i], v[j]);
}
for (int k = 0, t = 2; t <= N; ++k, t <<= 1) {
long long bw = vbw[k];
if (inv) bw = vibw[k];
for (int i = 0; i < N; i += t) {
mint w = 1;
for (int j = 0; j < t/2; ++j) {
int j1 = i + j, j2 = i + j + t/2;
mint c1 = v[j1], c2 = v[j2] * w;
v[j1] = c1 + c2;
v[j2] = c1 - c2;
w *= bw;
}
}
}
if (inv) {
long long invN = modinv(N, MOD);
for (int i = 0; i < N; ++i) v[i] = v[i] * invN;
}
}
// for garner
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Fp<MOD0>;
using mint1 = Fp<MOD1>;
using mint2 = Fp<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
// small case (T = mint, long long)
template<class T> vector<T> naive_mul
(const vector<T>& A, const vector<T>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
vector<T> res(N + M - 1);
for (int i = 0; i < N; ++i)
for (int j = 0; j < M; ++j)
res[i + j] += A[i] * B[j];
return res;
}
// mint
template<class mint> vector<mint> mul
(const vector<mint>& A, const vector<mint>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int MOD = A[0].getmod();
int size_fft = get_fft_size(N, M);
if (MOD == 998244353) {
vector<mint> a(size_fft), b(size_fft), c(size_fft);
for (int i = 0; i < N; ++i) a[i] = A[i];
for (int i = 0; i < M; ++i) b[i] = B[i];
trans(a), trans(b);
vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
trans(res, true);
res.resize(N + M - 1);
return res;
}
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++i)
a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
for (int i = 0; i < M; ++i)
b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
trans(c0, true), trans(c1, true), trans(c2, true);
static const mint mod0 = MOD0, mod01 = mod0 * MOD1;
vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
// long long
vector<long long> mul_ll
(const vector<long long>& A, const vector<long long>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int size_fft = get_fft_size(N, M);
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++i)
a0[i] = A[i], a1[i] = A[i], a2[i] = A[i];
for (int i = 0; i < M; ++i)
b0[i] = B[i], b1[i] = B[i], b2[i] = B[i];
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
trans(c0, true), trans(c1, true), trans(c2, true);
static const long long mod0 = MOD0, mod01 = mod0 * MOD1;
vector<long long> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
};
// Binomial coefficient
template<class T> struct BiCoef {
vector<T> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].getmod();
for(int i = 2; i < n; i++){
fact_[i] = fact_[i-1] * i;
inv_[i] = -inv_[MOD%i] * (MOD/i);
finv_[i] = finv_[i-1] * inv_[i];
}
}
constexpr T com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr T fact(int n) const noexcept {
if (n < 0) return 0;
return fact_[n];
}
constexpr T inv(int n) const noexcept {
if (n < 0) return 0;
return inv_[n];
}
constexpr T finv(int n) const noexcept {
if (n < 0) return 0;
return finv_[n];
}
};
// Formal Power Series
template <typename mint> struct FPS : vector<mint> {
using vector<mint>::vector;
// constructor
FPS(const vector<mint>& r) : vector<mint>(r) {}
// core operator
inline FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
inline FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
inline FPS& normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
inline FPS operator - () const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
inline FPS operator + (const mint& v) const { return FPS(*this) += v; }
inline FPS operator + (const FPS& r) const { return FPS(*this) += r; }
inline FPS operator - (const mint& v) const { return FPS(*this) -= v; }
inline FPS operator - (const FPS& r) const { return FPS(*this) -= r; }
inline FPS operator * (const mint& v) const { return FPS(*this) *= v; }
inline FPS operator * (const FPS& r) const { return FPS(*this) *= r; }
inline FPS operator / (const mint& v) const { return FPS(*this) /= v; }
inline FPS operator << (int x) const { return FPS(*this) <<= x; }
inline FPS operator >> (int x) const { return FPS(*this) >>= x; }
inline FPS& operator += (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
inline FPS& operator += (const FPS& 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->normalize();
}
inline FPS& operator -= (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
inline FPS& operator -= (const FPS& 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->normalize();
}
inline FPS& operator *= (const mint& v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
inline FPS& operator *= (const FPS& r) {
return *this = NTT::mul((*this), r);
}
inline FPS& operator /= (const mint& v) {
assert(v != 0);
mint iv = modinv(v);
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv;
return *this;
}
inline FPS& operator <<= (int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
inline FPS& operator >>= (int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
inline mint eval(const mint& v){
mint res = 0;
for (int i = (int)this->size()-1; i >= 0; --i) {
res *= v;
res += (*this)[i];
}
return res;
}
inline friend FPS gcd(const FPS& f, const FPS& g) {
if (g.empty()) return f;
return gcd(g, f % g);
}
// advanced operation
// df/dx
inline friend FPS diff(const FPS& f) {
int n = (int)f.size();
FPS res(n-1);
for (int i = 1; i < n; ++i) res[i-1] = f[i] * i;
return res;
}
// \int f dx
inline friend FPS integral(const FPS& f) {
int n = (int)f.size();
FPS res(n+1, 0);
for (int i = 0; i < n; ++i) res[i+1] = f[i] / (i+1);
return res;
}
// inv(f), f[0] must not be 0
inline friend FPS inv(const FPS& f, int deg) {
assert(f[0] != 0);
if (deg < 0) deg = (int)f.size();
FPS res({mint(1) / f[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * f.pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
inline friend FPS inv(const FPS& f) {
return inv(f, f.size());
}
// division, r must be normalized (r.back() must not be 0)
inline FPS& operator /= (const FPS& r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
if (this->size() < r.size()) {
this->clear();
return *this;
}
int need = (int)this->size() - (int)r.size() + 1;
*this = ((*this).rev().pre(need) * inv(r.rev(), need)).pre(need).rev();
return *this;
}
inline FPS& operator %= (const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
inline FPS operator / (const FPS& r) const { return FPS(*this) /= r; }
inline FPS operator % (const FPS& r) const { return FPS(*this) %= r; }
// log(f) = \int f'/f dx, f[0] must be 1
inline friend FPS log(const FPS& f, int deg) {
assert(f[0] == 1);
FPS res = integral(diff(f) * inv(f, deg));
res.resize(deg);
return res;
}
inline friend FPS log(const FPS& f) {
return log(f, f.size());
}
// exp(f), f[0] must be 0
inline friend FPS exp(const FPS& f, int deg) {
assert(f[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1);
}
res.resize(deg);
return res;
}
inline friend FPS exp(const FPS& f) {
return exp(f, f.size());
}
// pow(f) = exp(e * log f)
inline friend FPS pow(const FPS& f, long long e, int deg) {
long long i = 0;
while (i < (int)f.size() && f[i] == 0) ++i;
if (i == (int)f.size()) return FPS(deg, 0);
if (i * e >= deg) return FPS(deg, 0);
mint k = f[i];
FPS res = exp(log((f >> i) / k, deg) * e, deg) * modpow(k, e) << (e * i);
res.resize(deg);
return res;
}
inline friend FPS pow(const FPS& f, long long e) {
return pow(f, e, f.size());
}
// sqrt(f), f[0] must be 1
inline friend FPS sqrt_base(const FPS& f, int deg) {
assert(f[0] == 1);
mint inv2 = mint(1) / 2;
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + f.pre(i << 1) * inv(res, i << 1)).pre(i << 1);
for (mint& x : res) x *= inv2;
}
res.resize(deg);
return res;
}
inline friend FPS sqrt_base(const FPS& f) {
return sqrt_base(f, f.size());
}
};
////////////////////////////////////////
// FPS algorithms
////////////////////////////////////////
// Bostan-Mori
// find [x^N] P(x)/Q(x), O(K log K log N)
// deg(Q(x)) = K, deg(P(x)) < K
template <typename mint> mint BostanMori(const FPS<mint> &P, const FPS<mint> &Q, long long N) {
assert(!P.empty() && !Q.empty());
if (N == 0 || Q.size() == 1) return P[0] / Q[0];
int qdeg = (int)Q.size();
FPS<mint> P2{P}, minusQ{Q};
P2.resize(qdeg - 1);
for (int i = 1; i < (int)Q.size(); i += 2) minusQ[i] = -minusQ[i];
P2 *= minusQ;
FPS<mint> Q2 = Q * minusQ;
FPS<mint> S(qdeg - 1), T(qdeg);
for (int i = 0; i < (int)S.size(); ++i) {
S[i] = (N % 2 == 0 ? P2[i * 2] : P2[i * 2 + 1]);
}
for (int i = 0; i < (int)T.size(); ++i) {
T[i] = Q2[i * 2];
}
return BostanMori(S, T, N >> 1);
}
const int MOD = mod0 ;
// const int MOD = mod1 ;
using mint = Fp<MOD> ;
// --------------------------code----------------------------
int main(void){
ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
// SM.init() ;
// era.init() ;
// max_element(V<ll> A) Aの最大値を返す
// max_element_index(V<ll> A) Aの最大値のindex
// min_element(V<ll> A) Aの最小値を返す
// min_element_index(V<ll> A) Aの最小値のindex
// gcd(ll a , ll b) gcd(a,b) ;
// lcm(ll a ,ll b ) lcm
// nis(ll a) 素数判定 素数ならtrue
// UF UF.init(ll N) ; UF.root(i) ; UF.unite(a,b) ; UF.same(a,b) ; UF.size(i) ;
// enumdiv(ll a )約数列挙
// prime_factorize(ll p) aのb乗のかたちででてくる 配列で受け取る
// binpower(a,b,c) aのb条 をｃでわったやつをO(logb) ぐらいでだしてくれるやつ
// sr(V<ll> A) 配列を入れたら、sort --→ reverse して返してくれる関数 受け取りは auto とかで
// sort_erase_unique(V<ll> A) sortしてeraseしてuniqueする関数
// Compression(V<ll> A) 座圧したmapを返す関数
// SM.scan(ll a) で 平方数ならtrue が返ってくる。 範囲は √10^6まで SM.init() 必ず起動する。
// a_b(A,a,b) [a,b]の個数 ---→ upper_bound(all(A),b) - lower_bound(all(A),a) ;
// era.look(ll a) --→ true 素数 / era.enu_count(ll a) --→ 素因数の個数 1は1 、素数も1 その他はそのまんま 範囲は10^7まで
// _10_to_2(ll x) 10進数を二進数にして返す。文字列で出力する事に注意 ll --→ st
// _2_to_10(st a) 2進数を10進数にして返す。 st --→ ll
// powpow(ll a,ll b) a^b を返す
// Run_Length_Encoding(st S) ランレングス圧縮して配列を返す pair<char,ll>
// Regex(st S, st A , st B) SのAをBに変えた文字列を返す 使う場合は消す
// erase_string(st S , st T) Sの中のTを消す
// kiriage(ll a , ll b) a 割られる数 b 割る数
// a_up(V<ll> A , ll x) sort済み配列でｘ以上の最小値を返す。ない場合、-1を返す.
// b_down(V<ll> B , ll x)sort済み配列でx以下で最大値を返す。ない場合 -1を返す。
// Permutation(ll N) N!の値を返す。20までならオーバーフローしない。
// V<V<ll>> Next_permutation(ll N) next_permutationした配列の集合を返す.
// pow_daisyou(ll a, ll b , ll c )a^cとb^cを比較する 0 => 同値 1 => a側 2=> ｂ側
// debag_1V_kaigyou(V<ll> A) 一次元配列の中身を改行区切りで出力する
// debag_1V_space(V<ll> A) 一次元配列Aの中身をspace区切りで出力する
// debag_2V(V<V<ll>> A) 2次元配列Aの中身を返す関数
// debag_pair(V<P> A) pair型配列の中身を出力する
// debag_Edge(V<Edge> A) Edge型配列の中身を出力する
// V<P> sort_Args(len,a,b,c) 個数を指定して、その個数だけ変数を渡し、昇順にして返す。1-indexになってる。
// c_c 小文字charを数字に変換
// C_C 大文字charを数字に変換
// (double)clock()/CLOCKS_PER_SEC>1.987
// multisetで1つだけ要素消したかったら、 A.erase(A.find(x)) ;とする。
// mod0 --→ 1000000007 mod1 --→ 998244353
// 座圧した後、size変わることに注意。二回やらかしてます
ll K ;
cin >> K ;
ll N ;
cin >> N ;
FPS<mint> f(100010) ;
rep(i,0,N-1){
ll x ;
cin >> x ;
f[x] = 1 ;
}
auto g = -f + 1 ;
auto res = inv(g) ;
C << res[K] << E
// if(dx < 0 || dy < 0 || dx >= W || dy >= H) continue ;
// C << fixed << setprecision(10) << // 勝手に四捨五入してくれてるから安心して
re
}