結果
| 問題 | No.1856 Mex Sum 2 |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2022-02-25 23:23:21 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 20,359 bytes |
| コンパイル時間 | 3,561 ms |
| コンパイル使用メモリ | 233,152 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-07-03 18:24:52 |
| 合計ジャッジ時間 | 13,288 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
| testcase_03 | RE | - |
| testcase_04 | RE | - |
| testcase_05 | RE | - |
| testcase_06 | RE | - |
| testcase_07 | RE | - |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | RE | - |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | RE | - |
| testcase_24 | RE | - |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
| testcase_34 | RE | - |
| testcase_35 | RE | - |
| testcase_36 | RE | - |
| testcase_37 | RE | - |
| testcase_38 | RE | - |
| testcase_39 | RE | - |
| testcase_40 | RE | - |
| testcase_41 | RE | - |
| testcase_42 | RE | - |
| testcase_43 | RE | - |
| testcase_44 | RE | - |
| testcase_45 | RE | - |
| testcase_46 | RE | - |
| testcase_47 | RE | - |
| testcase_48 | RE | - |
| testcase_49 | RE | - |
| testcase_50 | RE | - |
| testcase_51 | RE | - |
| testcase_52 | RE | - |
| testcase_53 | RE | - |
| testcase_54 | RE | - |
| testcase_55 | RE | - |
| testcase_56 | RE | - |
| testcase_57 | RE | - |
| testcase_58 | RE | - |
| testcase_59 | RE | - |
| testcase_60 | RE | - |
| testcase_61 | RE | - |
| testcase_62 | RE | - |
| testcase_63 | RE | - |
| testcase_64 | RE | - |
| testcase_65 | RE | - |
| testcase_66 | RE | - |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <int M>
struct MInt {
unsigned int v;
MInt() : v(0) {}
MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr int get_mod() { return M; }
static void set_mod(const int divisor) { assert(divisor == M); }
static void init(const int x = 10000000) {
inv(x, true);
fact(x);
fact_inv(x);
}
static MInt inv(const int n, const bool init = false) {
// assert(0 <= n && n < M && std::__gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) {
return inverse[n];
} else if (init) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * (M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
const int prev = factorial.size();
if (n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
const int prev = f_inv.size();
if (n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) return 0;
inv(k, true);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
MInt& operator+=(const MInt& x) {
if ((v += x.v) >= M) v -= M;
return *this;
}
MInt& operator-=(const MInt& x) {
if ((v += M - x.v) >= M) v -= M;
return *this;
}
MInt& operator*=(const MInt& x) {
v = static_cast<unsigned long long>(v) * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
bool operator==(const MInt& x) const { return v == x.v; }
bool operator!=(const MInt& x) const { return v != x.v; }
bool operator<(const MInt& x) const { return v < x.v; }
bool operator<=(const MInt& x) const { return v <= x.v; }
bool operator>(const MInt& x) const { return v > x.v; }
bool operator>=(const MInt& x) const { return v >= x.v; }
MInt& operator++() {
if (++v == M) v = 0;
return *this;
}
MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
MInt operator+() const { return *this; }
MInt operator-() const { return MInt(v ? M - v : 0); }
MInt operator+(const MInt& x) const { return MInt(*this) += x; }
MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
using ModInt = MInt<MOD>;
template <int T>
struct NumberTheoreticTransform {
using ModInt = MInt<T>;
NumberTheoreticTransform() {
for (int i = 0; i < 23; ++i) {
if (primes[i][0] == ModInt::get_mod()) {
n_max = 1 << primes[i][2];
root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]);
return;
}
}
assert(false);
}
template <typename U>
std::vector<ModInt> dft(const std::vector<U>& a) {
const int n = a.size();
int lg = 1;
while ((1 << lg) < n) ++lg;
std::vector<ModInt> b(1 << lg, 0);
std::copy(a.begin(), a.end(), b.begin());
calc(&b);
return b;
}
void idft(std::vector<ModInt>* a) {
const int n = a->size();
assert(__builtin_popcount(n) == 1);
calc(a);
std::reverse(std::next(a->begin()), a->end());
const ModInt inv_n = ModInt::inv(n);
for (int i = 0; i < n; ++i) {
(*a)[i] *= inv_n;
}
}
template <typename U>
std::vector<ModInt> convolution(const std::vector<U>& a,
const std::vector<U>& b) {
const int a_size = a.size(), b_size = b.size();
const int c_size = a_size + b_size - 1;
int lg = 1;
while ((1 << lg) < c_size) ++lg;
const int n = 1 << lg;
std::vector<ModInt> c(n, 0), d(n, 0);
std::copy(a.begin(), a.end(), c.begin());
calc(&c);
std::copy(b.begin(), b.end(), d.begin());
calc(&d);
for (int i = 0; i < n; ++i) {
c[i] *= d[i];
}
idft(&c);
c.resize(c_size);
return c;
}
private:
const int primes[23][3]{
{16957441, 329, 14},
{17006593, 26, 15},
{19529729, 770, 17},
{167772161, 3, 25},
{469762049, 3, 26},
{645922817, 3, 23},
{897581057, 3, 23},
{924844033, 5, 21},
{935329793, 3, 22},
{943718401, 7, 22},
{950009857, 7, 21},
{962592769, 7, 21},
{975175681, 17, 21},
{976224257, 3, 20},
{985661441, 3, 22},
{998244353, 3, 23},
{1004535809, 3, 21},
{1007681537, 3, 20},
{1012924417, 5, 21},
{1045430273, 3, 20},
{1051721729, 6, 20},
{1053818881, 7, 20},
{1224736769, 3, 24}
};
int n_max;
ModInt root;
std::vector<int> butterfly{0};
std::vector<std::vector<ModInt>> omega{{1}};
void calc(std::vector<ModInt>* a) {
const int n = a->size(), prev_n = butterfly.size();
if (n > prev_n) {
assert(n <= n_max);
butterfly.resize(n);
const int prev_lg = omega.size(), lg = __builtin_ctz(n);
for (int i = 1; i < prev_n; ++i) {
butterfly[i] <<= lg - prev_lg;
}
for (int i = prev_n; i < n; ++i) {
butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));
}
omega.resize(lg);
for (int i = prev_lg; i < lg; ++i) {
omega[i].resize(1 << i);
const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1));
for (int j = 0; j < (1 << (i - 1)); ++j) {
omega[i][j << 1] = omega[i - 1][j];
omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp;
}
}
}
const int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
for (int i = 0; i < n; ++i) {
const int j = butterfly[i] >> shift;
if (i < j) std::swap((*a)[i], (*a)[j]);
}
for (int block = 1, den = 0; block < n; block <<= 1, ++den) {
for (int i = 0; i < n; i += (block << 1)) {
for (int j = 0; j < block; ++j) {
const ModInt tmp = (*a)[i + j + block] * omega[den][j];
(*a)[i + j + block] = (*a)[i + j] - tmp;
(*a)[i + j] += tmp;
}
}
}
}
};
template <typename T>
struct FormalPowerSeries {
std::vector<T> coef;
explicit FormalPowerSeries(const int deg = 0) : coef(deg + 1, 0) {}
explicit FormalPowerSeries(const std::vector<T>& coef) : coef(coef) {}
FormalPowerSeries(const std::initializer_list<T> init)
: coef(init.begin(), init.end()) {}
template <typename InputIter>
explicit FormalPowerSeries(const InputIter first, const InputIter last)
: coef(first, last) {}
inline const T& operator[](const int term) const { return coef[term]; }
inline T& operator[](const int term) { return coef[term]; }
using MULT = std::function<std::vector<T>(const std::vector<T>&,
const std::vector<T>&)>;
using SQRT = std::function<bool(const T&, T*)>;
static void set_mult(const MULT mult) { get_mult() = mult; }
static void set_sqrt(const SQRT sqrt) { get_sqrt() = sqrt; }
void resize(const int deg) { coef.resize(deg + 1, 0); }
void shrink() {
while (coef.size() > 1 && coef.back() == 0) coef.pop_back();
}
int degree() const { return static_cast<int>(coef.size()) - 1; }
FormalPowerSeries& operator=(const std::vector<T>& coef_) {
coef = coef_;
return *this;
}
FormalPowerSeries& operator=(const FormalPowerSeries& x) = default;
FormalPowerSeries& operator+=(const FormalPowerSeries& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] += x[i];
}
return *this;
}
FormalPowerSeries& operator-=(const FormalPowerSeries& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] -= x[i];
}
return *this;
}
FormalPowerSeries& operator*=(const T x) {
for (T& e : coef) e *= x;
return *this;
}
FormalPowerSeries& operator*=(const FormalPowerSeries& x) {
return *this = get_mult()(coef, x.coef);
}
FormalPowerSeries& operator/=(const T x) {
assert(x != 0);
return *this *= static_cast<T>(1) / x;
}
FormalPowerSeries& operator/=(const FormalPowerSeries& x) {
const int n = degree() - x.degree() + 1;
if (n <= 0) return *this = FormalPowerSeries();
const std::vector<T> tmp = get_mult()(
std::vector<T>(coef.rbegin(), std::next(coef.rbegin(), n)),
FormalPowerSeries(
x.coef.rbegin(),
std::next(x.coef.rbegin(), std::min(x.degree() + 1, n)))
.inv(n - 1).coef);
return *this = FormalPowerSeries(std::prev(tmp.rend(), n), tmp.rend());
}
FormalPowerSeries& operator%=(const FormalPowerSeries& x) {
if (x.degree() == 0) return *this = FormalPowerSeries{0};
*this -= *this / x * x;
resize(x.degree() - 1);
return *this;
}
FormalPowerSeries& operator<<=(const int n) {
coef.insert(coef.begin(), n, 0);
return *this;
}
FormalPowerSeries& operator>>=(const int n) {
if (degree() < n) return *this = FormalPowerSeries();
coef.erase(coef.begin(), coef.begin() + n);
return *this;
}
bool operator==(FormalPowerSeries x) const {
x.shrink();
FormalPowerSeries y = *this;
y.shrink();
return x.coef == y.coef;
}
bool operator!=(const FormalPowerSeries& x) const { return !(*this == x); }
FormalPowerSeries operator+() const { return *this; }
FormalPowerSeries operator-() const {
FormalPowerSeries res = *this;
for (T& e : res.coef) e = -e;
return res;
}
FormalPowerSeries operator+(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) += x;
}
FormalPowerSeries operator-(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) -= x;
}
FormalPowerSeries operator*(const T x) const {
return FormalPowerSeries(*this) *= x;
}
FormalPowerSeries operator*(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) *= x;
}
FormalPowerSeries operator/(const T x) const {
return FormalPowerSeries(*this) /= x;
}
FormalPowerSeries operator/(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) /= x;
}
FormalPowerSeries operator%(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) %= x;
}
FormalPowerSeries operator<<(const int n) const {
return FormalPowerSeries(*this) <<= n;
}
FormalPowerSeries operator>>(const int n) const {
return FormalPowerSeries(*this) >>= n;
}
T horner(const T x) const {
T res = 0;
for (int i = degree(); i >= 0; --i) {
res = res * x + coef[i];
}
return res;
}
FormalPowerSeries differential() const {
const int deg = degree();
assert(deg >= 0);
FormalPowerSeries res(std::max(deg - 1, 0));
for (int i = 1; i <= deg; ++i) {
res[i - 1] = coef[i] * i;
}
return res;
}
FormalPowerSeries exp(int deg = -1) const {
assert(coef[0] == 0);
const int n = coef.size();
if (deg == -1) deg = n - 1;
const FormalPowerSeries one{1};
FormalPowerSeries res = one;
for (int i = 1; i <= deg; i <<= 1) {
res *= FormalPowerSeries(coef.begin(),
std::next(coef.begin(), std::min(n, i << 1)))
- res.log((i << 1) - 1) + one;
res.coef.resize(i << 1);
}
res.resize(deg);
return res;
}
FormalPowerSeries inv(int deg = -1) const {
assert(coef[0] != 0);
const int n = coef.size();
if (deg == -1) deg = n - 1;
FormalPowerSeries res{static_cast<T>(1) / coef[0]};
for (int i = 1; i <= deg; i <<= 1) {
res = res + res - res * res * FormalPowerSeries(
coef.begin(), std::next(coef.begin(), std::min(n, i << 1)));
res.coef.resize(i << 1);
}
res.resize(deg);
return res;
}
FormalPowerSeries log(int deg = -1) const {
assert(coef[0] == 1);
if (deg == -1) deg = degree();
FormalPowerSeries integrand = differential() * inv(deg - 1);
integrand.resize(deg);
for (int i = deg; i > 0; --i) {
integrand[i] = integrand[i - 1] / i;
}
integrand[0] = 0;
return integrand;
}
FormalPowerSeries pow(long long exponent, int deg = -1) const {
const int n = coef.size();
if (deg == -1) deg = n - 1;
for (int i = 0; i < n; ++i) {
if (coef[i] == 0) continue;
const long long shift = exponent * i;
if (shift > deg) break;
T tmp = 1, base = coef[i];
for (long long e = exponent; e > 0; e >>= 1) {
if (e & 1) tmp *= base;
base *= base;
}
const FormalPowerSeries res = ((*this >> i) / coef[i]).log(deg - shift);
return ((res * exponent).exp(deg - shift) * tmp) << shift;
}
return FormalPowerSeries(deg);
}
FormalPowerSeries mod_pow(long long exponent,
const FormalPowerSeries& md) const {
const int deg = md.degree() - 1;
if (deg < 0) return FormalPowerSeries(-1);
const FormalPowerSeries inv_rev_md =
FormalPowerSeries(md.coef.rbegin(), md.coef.rend()).inv();
const auto mod_mult = [&md, &inv_rev_md, deg](
FormalPowerSeries* multiplicand, const FormalPowerSeries& multiplier)
-> void {
*multiplicand *= multiplier;
if (deg < multiplicand->degree()) {
const int n = multiplicand->degree() - deg;
const FormalPowerSeries quotient =
FormalPowerSeries(multiplicand->coef.rbegin(),
std::next(multiplicand->coef.rbegin(), n))
* FormalPowerSeries(
inv_rev_md.coef.begin(),
std::next(inv_rev_md.coef.begin(), std::min(deg + 2, n)));
*multiplicand -=
FormalPowerSeries(std::prev(quotient.coef.rend(), n),
quotient.coef.rend()) * md;
multiplicand->resize(deg);
}
multiplicand->shrink();
};
FormalPowerSeries res{1}, base = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) mod_mult(&res, base);
mod_mult(&base, base);
}
return res;
}
FormalPowerSeries sqrt(int deg = -1) const {
const int n = coef.size();
if (deg == -1) deg = n - 1;
if (coef[0] == 0) {
for (int i = 1; i < n; ++i) {
if (coef[i] == 0) continue;
if (i & 1) return FormalPowerSeries(-1);
const int shift = i >> 1;
if (deg < shift) break;
FormalPowerSeries res = (*this >> i).sqrt(deg - shift);
if (res.coef.empty()) return FormalPowerSeries(-1);
res <<= shift;
res.resize(deg);
return res;
}
return FormalPowerSeries(deg);
}
T s;
if (!get_sqrt()(coef.front(), &s)) return FormalPowerSeries(-1);
FormalPowerSeries res{s};
const T half = static_cast<T>(1) / 2;
for (int i = 1; i <= deg; i <<= 1) {
res = (FormalPowerSeries(coef.begin(),
std::next(coef.begin(), std::min(n, i << 1)))
* res.inv((i << 1) - 1) + res) * half;
}
res.resize(deg);
return res;
}
FormalPowerSeries translate(const T c) const {
const int n = coef.size();
std::vector<T> fact(n, 1), inv_fact(n, 1);
for (int i = 1; i < n; ++i) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) {
inv_fact[i - 1] = inv_fact[i] * i;
}
std::vector<T> g(n), ex(n);
for (int i = 0; i < n; ++i) {
g[i] = coef[i] * fact[i];
}
std::reverse(g.begin(), g.end());
T pow_c = 1;
for (int i = 0; i < n; ++i) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
const std::vector<T> conv = get_mult()(g, ex);
FormalPowerSeries res(n - 1);
for (int i = 0; i < n; ++i) {
res[i] = conv[n - 1 - i] * inv_fact[i];
}
return res;
}
private:
static MULT& get_mult() {
static MULT mult = [](const std::vector<T>& a, const std::vector<T>& b)
-> std::vector<T> {
const int n = a.size(), m = b.size();
std::vector<T> res(n + m - 1, 0);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
res[i + j] += a[i] * b[j];
}
}
return res;
};
return mult;
}
static SQRT& get_sqrt() {
static SQRT sqrt = [](const T& a, T* res) -> bool { return false; };
return sqrt;
}
};
template <template <typename> class C, typename T>
struct MultipointEvaluation {
std::vector<T> f_x;
std::vector<C<T>> subproduct_tree;
explicit MultipointEvaluation(const std::vector<T> &xs)
: n(xs.size()), f_x(xs.size()), subproduct_tree(xs.size() << 1) {
for (int i = 0; i < n; ++i) {
subproduct_tree[i + n] = C<T>{-xs[i], 1};
}
for (int i = n - 1; i > 0; --i) {
subproduct_tree[i] =
subproduct_tree[i << 1] * subproduct_tree[(i << 1) + 1];
}
}
void build(const C<T>& f) { dfs(f, 1); }
private:
const int n;
void dfs(C<T> f, int node) {
f %= subproduct_tree[node];
if (node < n) {
dfs(f, node << 1);
dfs(f, (node << 1) + 1);
} else {
f_x[node - n] = f[0];
}
}
};
int main() {
FormalPowerSeries<ModInt>::set_mult([](const vector<ModInt>& a, const vector<ModInt>& b) -> vector<ModInt> {
static NumberTheoreticTransform<MOD> ntt;
return ntt.convolution(a, b);
});
int n, s; cin >> n >> s;
vector<ModInt> p(n);
REP(i, n) {
cin >> p[i];
p[i] /= s;
}
vector<ModInt> cs(n);
REP(i, n) cs[i] = -ModInt::inv(p[i].v);
FormalPowerSeries<ModInt> f = MultipointEvaluation<FormalPowerSeries, ModInt>(cs).subproduct_tree[1];
assert(f.degree() == n);
ModInt c = 1;
REP(i, n) c *= p[i];
f *= c;
REP(i, n + 1) f[i] *= ModInt::fact(i);
REP(i, n) f[i + 1] += f[i];
ModInt ans = 0;
REP(i, n) {
ans += p[i] * p[i] * (f / FormalPowerSeries<ModInt>{1, p[i]})[n - 1];
}
cout << ans << '\n';
return 0;
}