#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using ll = long long; using namespace std; using namespace __gnu_pbds; template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; const double pi = acos(-1); const int N = 1e2 + 5, K = 1e3 + 5, SQ = 500, M = 1e9 + 7; //#define TESTS //#define INTERACTIVE //#define COMMUNICATION /* * Remember who you are. */ void pre() { } void solve() { int n, L; cin >> n >> L; vector<int> a(n); if (n == 1) { cout << 1; return; } for (int i = 0; i < n; ++i) cin >> a[i]; ranges::sort(a); vector<vector<vector<vector<int>>>> dp(2, vector<vector<vector<int>>>(n + 1, vector<vector<int>>(L + 1, vector<int>(3)))); for (int i = n; i >= 0; --i) for (int j = 0; j <= n; ++j) for (int k = 0; k <= L; ++k) for (int l = 0; l <= 2; ++l) { auto &ret = dp[i & 1][j][k][l]; ret = 0; if (j > i) continue; if (i == n) { ret = j == 1 && l == 2; continue; } int nk = k + (i ? a[i] - a[i - 1] : 0) * (2 * j - l); if (nk > L || nk < 0) continue; if (j + 1 <= n) ret = 1ll * dp[~i & 1][j + 1][nk][l] * (j + 1 - l) % M; if (l != 2 && j + 1 <= n) ret = (ret + 1ll * dp[~i & 1][j + 1][nk][l + 1] * (2 - l) % M) % M; if (j) ret = (ret + 1ll * dp[~i & 1][j][nk][l] * (2 * j - l) % M) % M; if (j && l != 2) ret = (ret + 1ll * dp[~i & 1][j][nk][l + 1] * (2 - l) % M) % M; if (j > 1) ret = (ret + 1ll * dp[~i & 1][j - 1][nk][l] * (j - 1) % M) % M; } cout << dp[0][0][0][0]; } void solve2() { } signed main() { ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); #ifdef CAROOT #ifndef INTERACTIVE freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); #endif #else #endif int tt = 1; pre(); #ifdef COMMUNICATION string run; cin >> run; #endif #ifdef TESTS cin >> tt; #endif for (int tc = 1; tc <= tt; ++tc) { #ifdef COMMUNICATION if (run == "first") solve(); else solve2(); #else solve(); #endif cout << '\n'; } }