結果
| 問題 | No.2709 1975 Powers |
| ユーザー |
 drken1215
|
| 提出日時 | 2024-03-31 14:12:39 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 35,745 bytes |
| コンパイル時間 | 2,649 ms |
| コンパイル使用メモリ | 218,208 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-09-30 19:09:49 |
| 合計ジャッジ時間 | 3,497 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（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
6,816 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 2 ms
6,820 KB |
| testcase_03 | AC | 16 ms
6,816 KB |
| testcase_04 | AC | 24 ms
6,816 KB |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | AC | 2 ms
6,820 KB |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | AC | 2 ms
6,824 KB |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | AC | 5 ms
6,820 KB |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | AC | 27 ms
6,820 KB |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | AC | 27 ms
6,816 KB |
| testcase_26 | AC | 27 ms
6,820 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
// 4-neighbor (or 8-neighbor)
const vector<int> dx = {1, 0, -1, 0, 1, -1, 1, -1};
const vector<int> dy = {0, 1, 0, -1, 1, 1, -1, -1};
/*///////////////////////////////////////////////////////*/
// debug
/*///////////////////////////////////////////////////////*/
#define DEBUG 1
#define COUT(x) if (DEBUG) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, vector<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, deque<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, set<T> P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, multiset<T> P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
/*///////////////////////////////////////////////////////*/
// QCFium 法
/*///////////////////////////////////////////////////////*/
#pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
/*/////////////////////////////*/
// modint, FPS
/*/////////////////////////////*/
// modint
template<int MOD> struct Fp {
// inner value
long long val;
// constructor
constexpr Fp() : val(0) { }
constexpr Fp(long long v) : val(v % MOD) {
if (val < 0) val += MOD;
}
constexpr long long get() const { return val; }
constexpr int get_mod() const { return MOD; }
// arithmetic operators
constexpr Fp operator + () const { return Fp(*this); }
constexpr Fp operator - () const { return Fp(0) - Fp(*this); }
constexpr Fp operator + (const Fp &r) const { return Fp(*this) += r; }
constexpr Fp operator - (const Fp &r) const { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp &r) const { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp &r) const { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp &r) {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp &r) {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp &r) {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp &r) {
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 Fp pow(long long n) const {
Fp res(1), mul(*this);
while (n > 0) {
if (n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
constexpr Fp inv() const {
Fp res(1), div(*this);
return res / div;
}
// other operators
constexpr bool operator == (const Fp &r) const {
return this->val == r.val;
}
constexpr bool operator != (const Fp &r) const {
return this->val != r.val;
}
constexpr Fp& operator ++ () {
++val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -- () {
if (val == 0) val += MOD;
--val;
return *this;
}
constexpr Fp operator ++ (int) const {
Fp res = *this;
++*this;
return res;
}
constexpr Fp operator -- (int) const {
Fp res = *this;
--*this;
return res;
}
friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) {
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) {
return os << x.val;
}
friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
return r.pow(n);
}
friend constexpr Fp<MOD> inv(const Fp<MOD> &r) {
return r.inv();
}
};
// Binomial coefficient
template<class mint> struct BiCoef {
vector<mint> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].get_mod();
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 mint com(int n, int k) const {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr mint fact(int n) const {
if (n < 0) return 0;
return fact_[n];
}
constexpr mint inv(int n) const {
if (n < 0) return 0;
return inv_[n];
}
constexpr mint finv(int n) const {
if (n < 0) return 0;
return finv_[n];
}
};
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].get_mod();
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;
}
// mul by convolution
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].get_mod();
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);
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;
}
};
// Formal Power Series
template<typename mint> struct FPS : vector<mint> {
using vector<mint>::vector;
// constructor
constexpr FPS(const vector<mint> &r) : vector<mint>(r) {}
// core operator
constexpr FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
constexpr FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
constexpr FPS& normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
constexpr FPS operator - () const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
constexpr FPS operator + (const mint &v) const { return FPS(*this) += v; }
constexpr FPS operator + (const FPS &r) const { return FPS(*this) += r; }
constexpr FPS operator - (const mint &v) const { return FPS(*this) -= v; }
constexpr FPS operator - (const FPS &r) const { return FPS(*this) -= r; }
constexpr FPS operator * (const mint &v) const { return FPS(*this) *= v; }
constexpr FPS operator * (const FPS &r) const { return FPS(*this) *= r; }
constexpr FPS operator / (const mint &v) const { return FPS(*this) /= v; }
constexpr FPS operator / (const FPS &r) const { return FPS(*this) /= r; }
constexpr FPS operator % (const FPS &r) const { return FPS(*this) %= r; }
constexpr FPS operator << (int x) const { return FPS(*this) <<= x; }
constexpr FPS operator >> (int x) const { return FPS(*this) >>= x; }
constexpr FPS& operator += (const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
constexpr 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();
}
constexpr FPS& operator -= (const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
constexpr 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();
}
constexpr FPS& operator *= (const mint &v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
constexpr FPS& operator *= (const FPS &r) {
return *this = NTT::mul((*this), r);
}
constexpr 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;
}
// division, r must be normalized (r.back() must not be 0)
constexpr 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 = (rev().pre(need) * r.rev().inv(need)).pre(need).rev();
return *this;
}
constexpr FPS& operator %= (const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
constexpr FPS& operator <<= (int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
constexpr FPS& operator >>= (int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
constexpr 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;
}
// advanced operation
// df/dx
constexpr FPS diff() const {
int n = (int)this->size();
FPS res(n-1);
for (int i = 1; i < n; ++i) res[i-1] = (*this)[i] * i;
return res;
}
// \int f dx
constexpr FPS integral() const {
int n = (int)this->size();
FPS res(n+1, 0);
for (int i = 0; i < n; ++i) res[i+1] = (*this)[i] / (i+1);
return res;
}
// inv(f), f[0] must not be 0
constexpr FPS inv(int deg) const {
assert((*this)[0] != 0);
if (deg < 0) deg = (int)this->size();
FPS res({mint(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS inv() const {
return inv((int)this->size());
}
// log(f) = \int f'/f dx, f[0] must be 1
constexpr FPS log(int deg) const {
assert((*this)[0] == 1);
FPS res = (diff() * inv(deg)).integral();
res.resize(deg);
return res;
}
constexpr FPS log() const {
return log((int)this->size());
}
// exp(f), f[0] must be 0
constexpr FPS exp(int deg) const {
assert((*this)[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (pre(i << 1) - res.log(i << 1) + 1).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS exp() const {
return exp((int)this->size());
}
// pow(f) = exp(e * log f)
constexpr FPS pow(long long e, int deg) const {
if (e == 0) {
FPS res(deg, 0);
res[0] = 1;
return res;
}
long long i = 0;
while (i < (int)this->size() && (*this)[i] == 0) ++i;
if (i == (int)this->size() || i > (deg - 1) / e) return FPS(deg, 0);
mint k = (*this)[i];
FPS res = ((((*this) >> i) / k).log(deg) * e).exp(deg) * mint(k).pow(e) << (e * i);
res.resize(deg);
return res;
}
constexpr FPS pow(long long e) const {
return pow(e, (int)this->size());
}
// sqrt(f), f[0] must be 1
constexpr FPS sqrt_base(int deg) const {
assert((*this)[0] == 1);
mint inv2 = mint(1) / 2;
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + pre(i << 1) * res.inv(i << 1)).pre(i << 1);
for (mint &x : res) x *= inv2;
}
res.resize(deg);
return res;
}
constexpr FPS sqrt_base() const {
return sqrt_base((int)this->size());
}
// friend operators
friend constexpr FPS diff(const FPS &f) { return f.diff(); }
friend constexpr FPS integral(const FPS &f) { return f.integral(); }
friend constexpr FPS inv(const FPS &f, int deg) { return f.inv(deg); }
friend constexpr FPS inv(const FPS &f) { return f.inv((int)f.size()); }
friend constexpr FPS log(const FPS &f, int deg) { return f.log(deg); }
friend constexpr FPS log(const FPS &f) { return f.log((int)f.size()); }
friend constexpr FPS exp(const FPS &f, int deg) { return f.exp(deg); }
friend constexpr FPS exp(const FPS &f) { return f.exp((int)f.size()); }
friend constexpr FPS pow(const FPS &f, long long e, int deg) { return f.pow(e, deg); }
friend constexpr FPS pow(const FPS &f, long long e) { return f.pow(e, (int)f.size()); }
friend constexpr FPS sqrt_base(const FPS &f, int deg) { return f.sqrt_base(deg); }
friend constexpr FPS sqrt_base(const FPS &f) { return f.sqrt_base((int)f.size()); }
};
/*/////////////////////////////*/
// Union-Find
/*/////////////////////////////*/
// Union-Find
struct UnionFind {
// core member
vector<int> par, nex;
// constructor
UnionFind() { }
UnionFind(int N) : par(N, -1), nex(N) {
init(N);
}
void init(int N) {
par.assign(N, -1);
nex.resize(N);
for (int i = 0; i < N; ++i) nex[i] = i;
}
// core methods
int root(int x) {
if (par[x] < 0) return x;
else return par[x] = root(par[x]);
}
bool same(int x, int y) {
return root(x) == root(y);
}
bool merge(int x, int y) {
x = root(x), y = root(y);
if (x == y) return false;
if (par[x] > par[y]) swap(x, y); // merge technique
par[x] += par[y];
par[y] = x;
swap(nex[x], nex[y]);
return true;
}
int size(int x) {
return -par[root(x)];
}
// get group
vector<int> group(int x) {
vector<int> res({x});
while (nex[res.back()] != x) res.push_back(nex[res.back()]);
return res;
}
vector<vector<int>> groups() {
vector<vector<int>> member(par.size());
for (int v = 0; v < (int)par.size(); ++v) {
member[root(v)].push_back(v);
}
vector<vector<int>> res;
for (int v = 0; v < (int)par.size(); ++v) {
if (!member[v].empty()) res.push_back(member[v]);
}
return res;
}
// debug
friend ostream& operator << (ostream &s, UnionFind uf) {
const vector<vector<int>> &gs = uf.groups();
for (const vector<int> &g : gs) {
s << "group: ";
for (int v : g) s << v << " ";
s << endl;
}
return s;
}
};
/*/////////////////////////////*/
// Segment Tree
/*/////////////////////////////*/
// Segment Tree
template<class Monoid> struct SegmentTree {
using Func = function<Monoid(Monoid, Monoid)>;
// core member
int N;
Func OP;
Monoid IDENTITY;
// inner data
int log, offset;
vector<Monoid> dat;
// constructor
SegmentTree() {}
SegmentTree(int n, const Func &op, const Monoid &identity) {
init(n, op, identity);
}
SegmentTree(const vector<Monoid> &v, const Func &op, const Monoid &identity) {
init(v, op, identity);
}
void init(int n, const Func &op, const Monoid &identity) {
N = n;
OP = op;
IDENTITY = identity;
log = 0, offset = 1;
while (offset < N) ++log, offset <<= 1;
dat.assign(offset * 2, IDENTITY);
}
void init(const vector<Monoid> &v, const Func &op, const Monoid &identity) {
init((int)v.size(), op, identity);
build(v);
}
void pull(int k) {
dat[k] = OP(dat[k * 2], dat[k * 2 + 1]);
}
void build(const vector<Monoid> &v) {
assert(N == (int)v.size());
for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
for (int k = offset - 1; k > 0; --k) pull(k);
}
int size() const {
return N;
}
Monoid operator [] (int i) const {
return dat[i + offset];
}
// update A[i], i is 0-indexed, O(log N)
void set(int i, const Monoid &v) {
assert(0 <= i && i < N);
int k = i + offset;
dat[k] = v;
while (k >>= 1) pull(k);
}
// get [l, r), l and r are 0-indexed, O(log N)
Monoid prod(int l, int r) {
assert(0 <= l && l <= r && r <= N);
Monoid val_left = IDENTITY, val_right = IDENTITY;
l += offset, r += offset;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) val_left = OP(val_left, dat[l++]);
if (r & 1) val_right = OP(dat[--r], val_right);
}
return OP(val_left, val_right);
}
Monoid all_prod() {
return dat[1];
}
// get max r that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int max_right(const function<bool(Monoid)> f, int l = 0) {
if (l == N) return N;
l += offset;
Monoid sum = IDENTITY;
do {
while (l % 2 == 0) l >>= 1;
if (!f(OP(sum, dat[l]))) {
while (l < offset) {
l = l * 2;
if (f(OP(sum, dat[l]))) {
sum = OP(sum, dat[l]);
++l;
}
}
return l - offset;
}
sum = OP(sum, dat[l]);
++l;
} while ((l & -l) != l); // stop if l = 2^e
return N;
}
// get min l that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int min_left(const function<bool(Monoid)> f, int r = -1) {
if (r == 0) return 0;
if (r == -1) r = N;
r += offset;
Monoid sum = IDENTITY;
do {
--r;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(OP(dat[r], sum))) {
while (r < offset) {
r = r * 2 + 1;
if (f(OP(dat[r], sum))) {
sum = OP(dat[r], sum);
--r;
}
}
return r + 1 - offset;
}
sum = OP(dat[r], sum);
} while ((r & -r) != r);
return 0;
}
// debug
friend ostream& operator << (ostream &s, const SegmentTree &seg) {
for (int i = 0; i < (int)seg.size(); ++i) {
s << seg[i];
if (i != (int)seg.size() - 1) s << " ";
}
return s;
}
};
// Lazy Segment Tree
template<class Monoid, class Action> struct LazySegmentTree {
// various function types
using FuncMonoid = function<Monoid(Monoid, Monoid)>;
using FuncAction = function<Monoid(Action, Monoid)>;
using FuncComposition = function<Action(Action, Action)>;
// core member
int N;
FuncMonoid OP;
FuncAction ACT;
FuncComposition COMP;
Monoid IDENTITY_MONOID;
Action IDENTITY_ACTION;
// inner data
int log, offset;
vector<Monoid> dat;
vector<Action> lazy;
// constructor
LazySegmentTree() {}
LazySegmentTree(int n, const FuncMonoid op, const FuncAction act, const FuncComposition comp,
const Monoid &identity_monoid, const Action &identity_action) {
init(n, op, act, comp, identity_monoid, identity_action);
}
LazySegmentTree(const vector<Monoid> &v,
const FuncMonoid op, const FuncAction act, const FuncComposition comp,
const Monoid &identity_monoid, const Action &identity_action) {
init(v, op, act, comp, identity_monoid, identity_action);
}
void init(int n, const FuncMonoid op, const FuncAction act, const FuncComposition comp,
const Monoid &identity_monoid, const Action &identity_action) {
N = n, OP = op, ACT = act, COMP = comp;
IDENTITY_MONOID = identity_monoid, IDENTITY_ACTION = identity_action;
log = 0, offset = 1;
while (offset < N) ++log, offset <<= 1;
dat.assign(offset * 2, IDENTITY_MONOID);
lazy.assign(offset * 2, IDENTITY_ACTION);
}
void init(const vector<Monoid> &v,
const FuncMonoid op, const FuncAction act, const FuncComposition comp,
const Monoid &identity_monoid, const Action &identity_action) {
init((int)v.size(), op, act, comp, identity_monoid, identity_action);
build(v);
}
void build(const vector<Monoid> &v) {
assert(N == (int)v.size());
for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
for (int k = offset - 1; k > 0; --k) pull_dat(k);
}
int size() const {
return N;
}
// basic functions for lazy segment tree
void pull_dat(int k) {
dat[k] = OP(dat[k * 2], dat[k * 2 + 1]);
}
void apply_lazy(int k, const Action &f) {
dat[k] = ACT(f, dat[k]);
if (k < offset) lazy[k] = COMP(f, lazy[k]);
}
void push_lazy(int k) {
apply_lazy(k * 2, lazy[k]);
apply_lazy(k * 2 + 1, lazy[k]);
lazy[k] = IDENTITY_ACTION;
}
void pull_dat_deep(int k) {
for (int h = 1; h <= log; ++h) pull_dat(k >> h);
}
void push_lazy_deep(int k) {
for (int h = log; h >= 1; --h) push_lazy(k >> h);
}
// setter and getter, update A[i], i is 0-indexed, O(log N)
void set(int i, const Monoid &v) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
dat[k] = v;
pull_dat_deep(k);
}
Monoid get(int i) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
return dat[k];
}
Monoid operator [] (int i) {
return get(i);
}
// apply f for index i
void apply(int i, const Action &f) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
dat[k] = ACT(f, dat[k]);
pull_dat_deep(k);
}
// apply f for interval [l, r)
void apply(int l, int r, const Action &f) {
assert(0 <= l && l <= r && r <= N);
if (l == r) return;
l += offset, r += offset;
for (int h = log; h >= 1; --h) {
if (((l >> h) << h) != l) push_lazy(l >> h);
if (((r >> h) << h) != r) push_lazy((r - 1) >> h);
}
int original_l = l, original_r = r;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) apply_lazy(l++, f);
if (r & 1) apply_lazy(--r, f);
}
l = original_l, r = original_r;
for (int h = 1; h <= log; ++h) {
if (((l >> h) << h) != l) pull_dat(l >> h);
if (((r >> h) << h) != r) pull_dat((r - 1) >> h);
}
}
// get prod of interval [l, r)
Monoid prod(int l, int r) {
assert(0 <= l && l <= r && r <= N);
if (l == r) return IDENTITY_MONOID;
l += offset, r += offset;
for (int h = log; h >= 1; --h) {
if (((l >> h) << h) != l) push_lazy(l >> h);
if (((r >> h) << h) != r) push_lazy(r >> h);
}
Monoid val_left = IDENTITY_MONOID, val_right = IDENTITY_MONOID;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) val_left = OP(val_left, dat[l++]);
if (r & 1) val_right = OP(dat[--r], val_right);
}
return OP(val_left, val_right);
}
Monoid all_prod() {
return dat[1];
}
// get max r that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int max_right(const function<bool(Monoid)> f, int l = 0) {
if (l == N) return N;
l += offset;
push_lazy_deep(l);
Monoid sum = IDENTITY_MONOID;
do {
while (l % 2 == 0) l >>= 1;
if (!f(OP(sum, dat[l]))) {
while (l < offset) {
push_lazy(l);
l = l * 2;
if (f(OP(sum, dat[l]))) {
sum = OP(sum, dat[l]);
++l;
}
}
return l - offset;
}
sum = OP(sum, dat[l]);
++l;
} while ((l & -l) != l); // stop if l = 2^e
return N;
}
// get min l that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int min_left(const function<bool(Monoid)> f, int r = -1) {
if (r == 0) return 0;
if (r == -1) r = N;
r += offset;
push_lazy_deep(r - 1);
Monoid sum = IDENTITY_MONOID;
do {
--r;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(OP(dat[r], sum))) {
while (r < offset) {
push_lazy(r);
r = r * 2 + 1;
if (f(OP(dat[r], sum))) {
sum = OP(dat[r], sum);
--r;
}
}
return r + 1 - offset;
}
sum = OP(dat[r], sum);
} while ((r & -r) != r);
return 0;
}
// debug stream
friend ostream& operator << (ostream &s, LazySegmentTree seg) {
for (int i = 0; i < (int)seg.size(); ++i) {
s << seg[i];
if (i != (int)seg.size() - 1) s << " ";
}
return s;
}
// dump
void dump() {
for (int i = 0; i <= log; ++i) {
for (int j = (1 << i); j < (1 << (i + 1)); ++j) {
cout << "{" << dat[j] << "," << lazy[j] << "} ";
}
cout << endl;
}
}
};
/*/////////////////////////////*/
// Solver
/*/////////////////////////////*/
// dynamic modint
struct DynamicModint {
using mint = DynamicModint;
// static menber
static int MOD;
// inner value
long long val;
// constructor
DynamicModint() : val(0) { }
DynamicModint(long long v) : val(v % MOD) {
if (val < 0) val += MOD;
}
long long get() const { return val; }
static int get_mod() { return MOD; }
static void set_mod(int mod) { MOD = mod; }
// arithmetic operators
mint operator + () const { return mint(*this); }
mint operator - () const { return mint(0) - mint(*this); }
mint operator + (const mint &r) const { return mint(*this) += r; }
mint operator - (const mint &r) const { return mint(*this) -= r; }
mint operator * (const mint &r) const { return mint(*this) *= r; }
mint operator / (const mint &r) const { return mint(*this) /= r; }
mint& operator += (const mint &r) {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
mint& operator -= (const mint &r) {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
mint& operator *= (const mint &r) {
val = val * r.val % MOD;
return *this;
}
mint& operator /= (const mint &r) {
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;
}
mint pow(long long n) const {
mint res(1), mul(*this);
while (n > 0) {
if (n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
mint inv() const {
mint res(1), div(*this);
return res / div;
}
// other operators
bool operator == (const mint &r) const {
return this->val == r.val;
}
bool operator != (const mint &r) const {
return this->val != r.val;
}
mint& operator ++ () {
++val;
if (val >= MOD) val -= MOD;
return *this;
}
mint& operator -- () {
if (val == 0) val += MOD;
--val;
return *this;
}
mint operator ++ (int) {
mint res = *this;
++*this;
return res;
}
mint operator -- (int) {
mint res = *this;
--*this;
return res;
}
friend istream& operator >> (istream &is, mint &x) {
is >> x.val;
x.val %= x.get_mod();
if (x.val < 0) x.val += x.get_mod();
return is;
}
friend ostream& operator << (ostream &os, const mint &x) {
return os << x.val;
}
friend mint pow(const mint &r, long long n) {
return r.pow(n);
}
friend mint inv(const mint &r) {
return r.inv();
}
};
int DynamicModint::MOD;
int main() {
long long N, P, Q;
cin >> N >> P >> Q;
vector<long long> A(N);
for (int i = 0; i < N; ++i) cin >> A[i];
using mint = DynamicModint;
mint::set_mod(P);
vector<mint> ten(N), nine(N), seven(N), five(N);
for (int i = 0; i < N; ++i) {
ten[i] = mint(10).pow(A[i]);
nine[i] = mint(9).pow(A[i]);
seven[i] = mint(7).pow(A[i]);
five[i] = mint(5).pow(A[i]);
}
long long res = 0;
for (int a = 0; a < N; ++a) {
for (int b = a+1; b < N; ++b) {
for (int c = b+1; c < N; ++c) {
for (int d = c+1; d < N; ++d) {
if (ten[a] + nine[b] + seven[c] + five[d] == mint(Q)) {
++res;
}
}
}
}
}
cout << res << endl;
}