#include <bits/stdc++.h>
using namespace std;
#define MASK(x) (1LL << (x))
#define BIT(x, i) (((x) >> (i)) & 1)
#define ALL(x) (x).begin(), (x).end()
#define REP(i, n) for (int i = 0, _n = n; i < _n; ++i)
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; --i)
#define FORE(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define debug(...) "[" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
template <class A, class B> bool minimize(A &a, B b) { if (a > b) { a = b; return true; } return false; }
template <class A, class B> bool maximize(A &a, B b) { if (a < b) { a = b; return true; } return false; }
template <int Mod>
struct Modular {
private :
int val;
static int inverse(int a, int b) {
a %= b;
assert(a);
if(a == 1) return 1;
return int(b - (long long) inverse(b, a) * (long long) b / a);
}
public :
Modular(long long x = 0) : val(x % Mod) { if(val < 0) val += Mod; }
friend bool operator == (const Modular &a, const Modular &b) { return a.val == b.val; }
friend bool operator != (const Modular &a, const Modular &b) { return a.val != b.val; }
Modular& operator = (const long long &x) { val = x % Mod; if(val < 0) val += Mod; return *this; }
Modular& operator = (const Modular &x) { val = x.val; return *this; }
friend istream & operator >> (istream &in, Modular &a) { long long x; in >> x; a = Modular(x); return in; }
friend ostream & operator << (ostream &out, const Modular &a) { return out << a.val; }
explicit operator int() const { return val; }
explicit operator bool() const { return val > 0; }
Modular inv() const {
Modular res;
res.val = inverse(val, Mod);
return res;
}
Modular operator ++() { (*this) += 1; return *this; }
Modular operator --() { (*this) -= 1; return *this; }
Modular operator ++(int) { (*this) += 1; return *this - 1; }
Modular operator --(int) { (*this) -= 1; return *this + 1; }
Modular operator + () const { return *this; }
Modular operator - () const {
Modular res;
res.val = (val ? Mod - val : 0);
return res;
}
Modular& operator += (const Modular &a) {
val += a.val;
if(val >= Mod) val -= Mod;
return *this;
}
Modular& operator -= (const Modular &a) {
val -= a.val;
if(val < 0) val += Mod;
return *this;
}
Modular& operator *= (const Modular &a) {
val = 1LL * val * a.val % Mod;
return *this;
}
Modular& operator /= (const Modular &a) {
(*this) *= a.inv();
return *this;
}
friend Modular operator + (const Modular &a, const Modular &b) { return Modular(a) += b; }
friend Modular operator - (const Modular &a, const Modular &b) { return Modular(a) -= b; }
friend Modular operator * (const Modular &a, const Modular &b) { return Modular(a) *= b; }
friend Modular operator / (const Modular &a, const Modular &b) { return Modular(a) /= b; }
};
// const int Mod = 998244353;
// const int Mod = 1e9 + 9; // 1000000009
const int Mod = 1e9 + 7; // 1000000007
using Modint = Modular <Mod>;
template <class T> T pow(T a, long long b) {
T ans = 1, mul = a;
for (; b; b >>= 1) {
if(b & 1LL) ans *= mul;
mul *= mul;
}
return ans;
}
const int MAXN = 105, MAXL = 1005;
int N, L, a[MAXN];
Modint dp[MAXN][MAXN][MAXL][3];
void you_make_it(void) {
cin >> N >> L;
FOR(i, 1, N) cin >> a[i];
sort(a + 1, a + N + 1);
if(N == 1) {
cout << 1;
return;
}
dp[1][1][0][0] = 1;
dp[1][1][0][1] = 2;
FOR(i, 2, N) FORE(j, 1, i) FOR(cost, 0, L) FOR(e, 0, 2) {
int new_cost = cost + (a[i] - a[i - 1]) * (2 * j - e);
if(new_cost > L) continue;
dp[i][j + 1][new_cost][e] += dp[i - 1][j][cost][e] * (j + 1 - e);
if(e < 2) {
dp[i][j + 1][new_cost][e + 1] += dp[i - 1][j][cost][e] * (2 - e);
dp[i][j][new_cost][e + 1] += dp[i - 1][j][cost][e] * (2 - e);
}
dp[i][j][new_cost][e] += dp[i - 1][j][cost][e] * (2 * j - e);
dp[i][j - 1][new_cost][e] += dp[i - 1][j][cost][e] * (j - 1);
}
Modint ans = 0;
FOR(i, 0, L) ans += dp[N][1][i][2];
cout << ans;
}
signed main() {
#ifdef LOCAL
freopen("TASK.inp", "r", stdin);
freopen("TASK.out", "w", stdout);
#endif
auto start_time = chrono::steady_clock::now();
cin.tie(0), cout.tie(0) -> sync_with_stdio(0);
you_make_it();
auto end_time = chrono::steady_clock::now();
cerr << "\nExecution time : " << chrono::duration_cast <chrono::milliseconds> (end_time - start_time).count() << "[ms]" << endl;
return (0 ^ 0);
}
// Dream it. Wish it. Do it.
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 2 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 3 |
Correct |
23 ms |
130412 KB |
Output is correct |
| 4 |
Correct |
23 ms |
130388 KB |
Output is correct |
| 5 |
Correct |
24 ms |
130392 KB |
Output is correct |
| 6 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 7 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 8 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 9 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 10 |
Correct |
24 ms |
130392 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 2 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 3 |
Correct |
24 ms |
130456 KB |
Output is correct |
| 4 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 5 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 6 |
Correct |
24 ms |
130392 KB |
Output is correct |
| 7 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 8 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 9 |
Correct |
24 ms |
130396 KB |
Output is correct |
| 10 |
Correct |
24 ms |
130384 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 2 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 3 |
Correct |
23 ms |
130412 KB |
Output is correct |
| 4 |
Correct |
23 ms |
130388 KB |
Output is correct |
| 5 |
Correct |
24 ms |
130392 KB |
Output is correct |
| 6 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 7 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 8 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 9 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 10 |
Correct |
24 ms |
130392 KB |
Output is correct |
| 11 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 12 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 13 |
Correct |
24 ms |
130456 KB |
Output is correct |
| 14 |
Correct |
23 ms |
130392 KB |
Output is correct |
| 15 |
Correct |
23 ms |
130384 KB |
Output is correct |
| 16 |
Correct |
24 ms |
130392 KB |
Output is correct |
| 17 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 18 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 19 |
Correct |
24 ms |
130396 KB |
Output is correct |
| 20 |
Correct |
24 ms |
130384 KB |
Output is correct |
| 21 |
Correct |
25 ms |
130384 KB |
Output is correct |
| 22 |
Correct |
105 ms |
130392 KB |
Output is correct |
| 23 |
Correct |
121 ms |
130532 KB |
Output is correct |
| 24 |
Correct |
110 ms |
130492 KB |
Output is correct |
| 25 |
Correct |
121 ms |
130536 KB |
Output is correct |
| 26 |
Correct |
108 ms |
130532 KB |
Output is correct |
| 27 |
Correct |
56 ms |
130388 KB |
Output is correct |
| 28 |
Correct |
68 ms |
130528 KB |
Output is correct |
| 29 |
Correct |
102 ms |
130532 KB |
Output is correct |
| 30 |
Correct |
123 ms |
130528 KB |
Output is correct |
