This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
ID: varunra2
LANG: C++
TASK: skycraper
*/
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#include "lib/debug.h"
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define debug_arr(...) \
cerr << "[" << #__VA_ARGS__ << "]:", debug_arr(__VA_ARGS__)
#pragma GCC diagnostic ignored "-Wsign-compare"
//#pragma GCC diagnostic ignored "-Wunused-parameter"
//#pragma GCC diagnostic ignored "-Wunused-variable"
#else
#define debug(...) 42
#endif
#define EPS 1e-9
#define IN(A, B, C) assert(B <= A && A <= C)
#define INF (int)1e9
#define MEM(a, b) memset(a, (b), sizeof(a))
#define MOD 1000000007
#define MP make_pair
#define PB push_back
#define all(cont) cont.begin(), cont.end()
#define rall(cont) cont.end(), cont.begin()
#define x first
#define y second
#define int long long
const double PI = acos(-1.0);
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef map<int, int> MPII;
typedef multiset<int> MSETI;
typedef set<int> SETI;
typedef set<string> SETS;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<string> VS;
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto& a : x)
#define sz(x) (int)(x).size()
typedef pair<int, int> pii;
typedef vector<int> vi;
#pragma GCC diagnostic ignored "-Wsign-compare"
// util functions
const int N = (int)1e2 + 5;
const int L = (int)1e3 + 5;
int dp[N][N][L][3];
int n, l;
VI vals;
int solve(int i, int cc, int sum, int bnds) {
if (i == n) {
if (cc != 1) return 0;
if (sum > l) return 0;
if (bnds != 2) return 0;
return 1;
}
if (cc == 0) return 0;
if (bnds == 3) return 0;
if (sum > l) return 0;
if (dp[i][cc][sum][bnds] != -1) return dp[i][cc][sum][bnds];
int nsum = sum + (2 * cc - bnds) * (vals[i] - vals[i - 1]);
int ret = 0;
ret += (cc + 1 - bnds) * solve(i + 1, cc + 1, nsum, bnds);
ret += (2 * cc - bnds) * solve(i + 1, cc, nsum, bnds);
ret += (cc - 1) * solve(i + 1, cc - 1, nsum, bnds);
ret += (2 - bnds) * solve(i + 1, cc + 1, nsum, bnds + 1);
ret += (2 - bnds) * solve(i + 1, cc, nsum, bnds + 1);
ret %= MOD;
dp[i][cc][sum][bnds] = ret;
return ret;
}
int32_t main() {
// #ifndef ONLINE_JUDGE
// freopen("skycraper.in", "r", stdin);
// freopen("skycraper.out", "w", stdout);
// #endif
cin.sync_with_stdio(0);
cin.tie(0);
cin >> n >> l;
MEM(dp, -1);
vals.resize(n);
for (int i = 0; i < n; i++) {
cin >> vals[i];
}
sort(all(vals));
cout << (solve(1, 1, 0, 0) + 2 * solve(1, 1, 0, 1)) % MOD << '\n';
return 0;
}
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