/**
* author: NimaAryan
* created: 2024-06-26 20:39:48
**/
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "algo/debug.h"
#endif
using i64 = long long;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type & operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type & operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if < !is_integral<typename Modular<U>::Type>::value, Modular >::type & operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U>
friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T, typename U> Modular<T> operator^(const Modular<T>& lhs, U rhs) { return power(lhs, rhs); };
template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
return stream << number();
}
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = (int) 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, L;
cin >> N >> L;
vector<int> A(N);
for (int i = 0; i < N; ++i) {
cin >> A[i];
}
if (N == 1) {
cout << 1 << "\n";
return 0;
}
sort(A.begin(), A.end());
int M = max(accumulate(A.begin(), A.end(), 0) / 2 + 100, 2 * A[0] + 5);
int T = M + 1 + L;
vector f(3, vector(N + 1, vector<Mint>(T + 1)));
f[0][1][0] = 1;
f[1][1][-A[0] + M] = 2;
f[2][1][2 * -A[0] + M] = 1;
for (int i = 1; i < N; ++i) {
vector g(3, vector(N + 1, vector<Mint>(T + 1)));
for (int c = 1; c <= N; ++c) {
for (int s = 0; s <= T; ++s) {
{
if (c + 1 <= N && s - 2 * A[i] >= 0) {
g[0][c + 1][s - 2 * A[i]] += f[0][c][s] * max(0, c - 1);
}
g[0][c][s] += f[0][c][s] * max(0, 2 * c - 2);
if (c - 1 >= 0 && s + 2 * A[i] <= T) {
g[0][c - 1][s + 2 * A[i]] += f[0][c][s] * max(0, c - 1);
}
}
{
if (c + 1 <= N && s - 2 * A[i] >= 0) {
g[1][c + 1][s - 2 * A[i]] += f[1][c][s] * c;
}
if (c + 1 <= N && s - A[i] >= 0) {
g[0][c + 1][s - A[i]] += f[1][c][s];
}
g[1][c][s] += f[1][c][s] * max(0, 2 * c - 1);
if (s + A[i] <= T) {
g[0][c][s + A[i]] += f[1][c][s];
}
if (c - 1 >= 0 && s + 2 * A[i] <= T) {
g[1][c - 1][s + 2 * A[i]] += f[1][c][s] * max(0, c - 1);
}
}
{
if (c + 1 <= N && s - 2 * A[i] >= 0) {
g[2][c + 1][s - 2 * A[i]] += f[2][c][s] * (c + 1);
}
if (c + 1 <= N && s - A[i] >= 0) {
g[1][c + 1][s - A[i]] += f[2][c][s] * 2;
}
g[2][c][s] += f[2][c][s] * 2 * c;
if (s + A[i] <= T) {
g[1][c][s + A[i]] += f[2][c][s] * 2;
}
if (c - 1 >= 0 && s + 2 * A[i] <= T) {
g[2][c - 1][s + 2 * A[i]] += f[2][c][s] * max(0, c - 1);
}
}
}
}
f.swap(g);
}
Mint ans = 0;
for (int l = 0; l <= L; ++l) {
ans += f[0][1][l + M];
}
cout << ans << "\n";
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
4 ms |
1116 KB |
Output is correct |
| 6 |
Correct |
3 ms |
860 KB |
Output is correct |
| 7 |
Correct |
1 ms |
604 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
3 ms |
860 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
2 ms |
676 KB |
Output is correct |
| 3 |
Correct |
1 ms |
348 KB |
Output is correct |
| 4 |
Correct |
2 ms |
604 KB |
Output is correct |
| 5 |
Correct |
2 ms |
604 KB |
Output is correct |
| 6 |
Correct |
2 ms |
604 KB |
Output is correct |
| 7 |
Correct |
1 ms |
348 KB |
Output is correct |
| 8 |
Correct |
1 ms |
348 KB |
Output is correct |
| 9 |
Correct |
1 ms |
348 KB |
Output is correct |
| 10 |
Correct |
2 ms |
604 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
1 ms |
344 KB |
Output is correct |
| 5 |
Correct |
4 ms |
1116 KB |
Output is correct |
| 6 |
Correct |
3 ms |
860 KB |
Output is correct |
| 7 |
Correct |
1 ms |
604 KB |
Output is correct |
| 8 |
Correct |
0 ms |
348 KB |
Output is correct |
| 9 |
Correct |
3 ms |
860 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| 11 |
Correct |
1 ms |
348 KB |
Output is correct |
| 12 |
Correct |
2 ms |
676 KB |
Output is correct |
| 13 |
Correct |
1 ms |
348 KB |
Output is correct |
| 14 |
Correct |
2 ms |
604 KB |
Output is correct |
| 15 |
Correct |
2 ms |
604 KB |
Output is correct |
| 16 |
Correct |
2 ms |
604 KB |
Output is correct |
| 17 |
Correct |
1 ms |
348 KB |
Output is correct |
| 18 |
Correct |
1 ms |
348 KB |
Output is correct |
| 19 |
Correct |
1 ms |
348 KB |
Output is correct |
| 20 |
Correct |
2 ms |
604 KB |
Output is correct |
| 21 |
Correct |
22 ms |
856 KB |
Output is correct |
| 22 |
Correct |
431 ms |
6472 KB |
Output is correct |
| 23 |
Execution timed out |
2070 ms |
77440 KB |
Time limit exceeded |
| 24 |
Halted |
0 ms |
0 KB |
- |
