結果
| 問題 |
No.8046 yukicoderの過去問
|
| コンテスト | |
| ユーザー |
 glreto
|
| 提出日時 | 2021-04-06 17:52:24 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 495 ms / 2,000 ms |
| コード長 | 10,556 bytes |
| コンパイル時間 | 2,041 ms |
| コンパイル使用メモリ | 194,744 KB |
| 実行使用メモリ | 22,184 KB |
| 最終ジャッジ日時 | 2024-06-11 15:39:26 |
| 合計ジャッジ時間 | 5,191 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 9 |
ソースコード
#include <bits//stdc++.h>
using namespace std;
#define rep(i,n) for(ll i = 0;i<n;i++)
#define req(i,n) for(ll i = 1;i<=n;i++)
#define rrep(i,n) for(int i = n-1;i>=0;i--)
#define ALL(a) a.begin(),a.end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
void chmin(int& a, int b){if(a>b)a=b;}
typedef long long ll;
typedef long double ld;
template<int MOD> struct ModInt {
static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
int get() const { return (int)x; }
ModInt& operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
ModInt& operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
ModInt& operator/=(ModInt that) { return *this *= that.inverse(); }
ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
ModInt inverse() const {
long long a = x, b = MOD, u = 1, v = 0;
while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
return ModInt(u);
}
bool operator==(ModInt that) const { return x == that.x; }
bool operator!=(ModInt that) const { return x != that.x; }
ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; };
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r;
}
typedef ModInt<1000000007> mint;
///
template<typename T>
struct FormalPowerSeries {
using Poly = vector<T>;
using Conv = function<Poly(Poly, Poly)>;//定義するときにFFTを定義する
Conv conv;
FormalPowerSeries(Conv conv) :conv(conv) {}
Poly pre(const Poly& as, int deg) {
return Poly(as.begin(), as.begin() + min((int)as.size(), deg));
}
Poly add(Poly as, Poly bs) {
int sz = max(as.size(), bs.size());
Poly cs(sz, T(0));
for (int i = 0; i < (int)as.size(); i++) cs[i] += as[i];
for (int i = 0; i < (int)bs.size(); i++) cs[i] += bs[i];
return cs;
}
Poly sub(Poly as, Poly bs) {
int sz = max(as.size(), bs.size());
Poly cs(sz, T(0));
for (int i = 0; i < (int)as.size(); i++) cs[i] += as[i];
for (int i = 0; i < (int)bs.size(); i++) cs[i] -= bs[i];
return cs;
}
Poly mul(Poly as, Poly bs) {
return conv(as, bs);
}
Poly mul(Poly as, T k) {
for (auto& a : as) a *= k;
return as;
}
// F(0) must not be 0
Poly inv(Poly as, int deg) {
assert(as[0] != T(0));
Poly rs({ T(1) / as[0] });
for (int i = 1; i < deg; i <<= 1)
rs = pre(sub(add(rs, rs), mul(mul(rs, rs), pre(as, i << 1))), i << 1);
return rs;
}
// not zero
Poly div(Poly as, Poly bs) {
while (as.back() == T(0)) as.pop_back();
while (bs.back() == T(0)) bs.pop_back();
if (bs.size() > as.size()) return Poly();
reverse(as.begin(), as.end());
reverse(bs.begin(), bs.end());
int need = as.size() - bs.size() + 1;
Poly ds = pre(mul(as, inv(bs, need)), need);
reverse(ALL(ds));
return ds;
}
// F(0) must be 1
Poly sqrt(Poly as, int deg) {
assert(as[0] == T(1));
T inv2 = T(1) / T(2);
Poly ss({ T(1) });
for (int i = 1; i < deg; i <<= 1) {
ss = pre(add(ss, mul(pre(as, i << 1), inv(ss, i << 1))), i << 1);
for (T& x : ss) x *= inv2;
}return ss;
}
Poly diff(Poly as) {
int n = as.size();
Poly res(n - 1);
req(i,n-1) res[i - 1] = as[i] * T(i);
return res;
}
Poly integral(Poly as) {
int n = as.size();
Poly res(n + 1);
res[0] = T(0);
rep(i,n) res[i + 1] = as[i] / T(i + 1);
return res;
}
// F(0) must be 1
Poly log(Poly as, int deg) {
return pre(integral(mul(diff(as), inv(as, deg))), deg);
}
// F(0) must be 0
Poly exp(Poly as, int deg) {
Poly f({ T(1) });
as[0] += T(1);
for (int i = 1; i < deg; i <<= 1)
f = pre(mul(f, sub(pre(as, i << 1), log(f, i << 1))), i << 1);
return f;
}
Poly partition(int n) {
Poly rs(n + 1);
rs[0] = T(1);
for (int k = 1; k <= n; k++) {
if (1LL * k * (3 * k + 1) / 2 <= n) rs[k * (3 * k + 1) / 2] += T(k % 2 ? -1LL : 1LL);
if (1LL * k * (3 * k - 1) / 2 <= n) rs[k * (3 * k - 1) / 2] += T(k % 2 ? -1LL : 1LL);
}return inv(rs, n + 1);
}
};
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) {
ll ret = 1; ll p = a % mod;
while (n) {
if (n & 1) ret = ret * p % mod;
p = p * p % mod; n >>= 1;
} return ret;
}
struct MathsNTTModAny {
template<int mod, int primitive_root>
class NTT {
public:
int get_mod() const { return mod; }
void _ntt(vector<ll>& a, int sign) {
const int n = a.size();
assert((n ^ (n & -n)) == 0); //n = 2^k
const int g = 3; //g is primitive root of mod
int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod
//bit reverse
int i = 0;
for (int j = 1; j < n - 1; ++j) {
for (int k = n >> 1; k > (i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}for (int m = 1; m < n; m *= 2) {
const int m2 = 2 * m;
const ll base = mod_pow(h, n / m2, mod);
ll w = 1;
rep(x, m) {
for (int s = x; s < n; s += m2) {
ll u = a[s];
ll d = a[s + m] * w % mod;
a[s] = u + d;
if (a[s] >= mod) a[s] -= mod;
a[s + m] = u - d;
if (a[s + m] < 0) a[s + m] += mod;
}w = w * base % mod;
}
}for (auto& x : a) if (x < 0) x += mod;
}void ntt(vector<ll>& input) {
_ntt(input, 1);
}
void intt(vector<ll>& input) {
_ntt(input, -1); int sz = input.size();
const int n_inv = mod_inv(sz, mod);
for (auto& x : input) x = x * n_inv % mod;
}
vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {
int ntt_size = 1; int sa = a.size(), sb = b.size();
while (ntt_size < sa + sb) ntt_size *= 2;
vector<ll> _a = a, _b = b;
_a.resize(ntt_size); _b.resize(ntt_size);
ntt(_a);
ntt(_b);
rep(i, ntt_size) (_a[i] *= _b[i]) %= mod;
intt(_a);
return _a;
}
};
ll garner(vector<pair<int, int>> mr, int mod) {
mr.emplace_back(mod, 0);
int mrs = mr.size();
vector<ll> coffs(mrs, 1),constants(mrs, 0);
rep(i, mrs - 1) {
// coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first)
ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;
if (v < 0) v += mr[i].first;
for (int j = i + 1; j < mrs; j++) {
(constants[j] += coffs[j] * v) %= mr[j].first;
(coffs[j] *= mr[i].first) %= mr[j].first;
}
}return constants[mrs - 1];
}
typedef NTT<167772161, 3> NTT_1;
typedef NTT<469762049, 3> NTT_2;
typedef NTT<1224736769, 3> NTT_3;
// 上から順に 64bit 32bit modint対応
vector<ll> solve(vector<ll> a, vector<ll> b, int mod = 1000000007) {
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod());
auto x = ntt1.convolution(a, b);
auto y = ntt2.convolution(a, b);
auto z = ntt3.convolution(a, b);
const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();
const ll m1_inv_m2 = mod_inv<ll>(m1, m2);
const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);
const ll m12_mod = m1 * m2 % mod; int sx = x.size();
vector<ll> ret(sx);
rep(i, sx) {
ll v1 = (y[i] - x[i]) * m1_inv_m2 % m2;
if (v1 < 0) v1 += m2;
ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;
if (v2 < 0) v2 += m3;
ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;
if (constants3 < 0) constants3 += mod;
ret[i] = constants3;
}return ret;
}
vector<int> solve(vector<int> a, vector<int> b, int mod = 1000000007) {
vector<ll> x(ALL(a)),y(ALL(b));
auto z = solve(x, y, mod);
vector<int> res;
for(auto &aa:z) res.push_back(aa % mod);
return res;
}
vector<mint> solve(vector<mint> a, vector<mint> b, int mod = 1000000007) {
int n = a.size();
vector<ll> x(n);
rep(i, n) x[i] = a[i].get();
n = b.size();
vector<ll> y(n);
rep(i, n) y[i] = b[i].get();
auto z = solve(x, y, mod);
vector<int> res;
for(auto &aa:z) res.push_back(aa % mod);
vector<mint> res2;
for(auto &x: res) res2.push_back(x);
return res2;
}
};
int main() {
int k, n; cin >> k >> n;
FormalPowerSeries<mint> fps([&](auto a, auto b) {
MathsNTTModAny ntt;
return ntt.solve(a, b);
});// convolutionの定義
vector<int> x(n);
rep(i, n) cin >> x[i];
vector<mint> fy(k + 1); fy[0] = 1;
rep(i, n) fy[x[i]] = -1;
fy = fps.inv(fy, k + 1);
cout << fy[k] << endl;
}