#include <bits/stdc++.h>
using namespace std;
//#define DEBUG
void setIO(const string &name) {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin.exceptions(istream::failbit);
#ifdef LOCAL
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
freopen((name + ".out").c_str(), "w", stderr);
#endif
}
template<typename T>
T mod_inv_in_range(T a, T m) {
// assert(0 <= a && a < m);
T x = a, y = m;
T vx = 1, vy = 0;
while (x) {
T k = y / x;
y %= x;
vy -= k * vx;
std::swap(x, y);
std::swap(vx, vy);
}
assert(y == 1);
return vy < 0 ? m + vy : vy;
}
template<int MOD_>
struct modnum {
static constexpr int MOD = MOD_;
static_assert(MOD_ > 0, "MOD must be positive");
private:
using ll = long long;
int v;
public:
modnum() : v(0) {}
modnum(ll v_) : v(int(v_ % MOD)) {
if (v < 0) v += MOD;
}
explicit operator int() const { return v; }
friend std::ostream &operator<<(std::ostream &out, const modnum &n) { return out << int(n); }
friend std::istream &operator>>(std::istream &in, modnum &n) {
ll v_;
in >> v_;
n = modnum(v_);
return in;
}
friend bool operator==(const modnum &a, const modnum &b) { return a.v == b.v; }
friend bool operator!=(const modnum &a, const modnum &b) { return a.v != b.v; }
modnum inv() const {
modnum res;
res.v = mod_inv_in_range(v, MOD);
return res;
}
friend modnum inv(const modnum &m) { return m.inv(); }
modnum neg() const {
modnum res;
res.v = v ? MOD - v : 0;
return res;
}
friend modnum neg(const modnum &m) { return m.neg(); }
modnum operator-() const {
return neg();
}
modnum operator+() const {
return modnum(*this);
}
modnum &operator++() {
v++;
if (v == MOD) v = 0;
return *this;
}
modnum &operator--() {
if (v == 0) v = MOD;
v--;
return *this;
}
modnum &operator+=(const modnum &o) {
v -= MOD - o.v;
v = (v < 0) ? v + MOD : v;
return *this;
}
modnum &operator-=(const modnum &o) {
v -= o.v;
v = (v < 0) ? v + MOD : v;
return *this;
}
modnum &operator*=(const modnum &o) {
v = int(ll(v) * ll(o.v) % MOD);
return *this;
}
modnum &operator/=(const modnum &o) {
return *this *= o.inv();
}
friend modnum operator++(modnum &a, int) {
modnum r = a;
++a;
return r;
}
friend modnum operator--(modnum &a, int) {
modnum r = a;
--a;
return r;
}
friend modnum operator+(const modnum &a, const modnum &b) { return modnum(a) += b; }
friend modnum operator-(const modnum &a, const modnum &b) { return modnum(a) -= b; }
friend modnum operator*(const modnum &a, const modnum &b) { return modnum(a) *= b; }
friend modnum operator/(const modnum &a, const modnum &b) { return modnum(a) /= b; }
};
const int inf = 0x3f3f3f3f, mod = 1e9 + 7, maxn = 105, maxl = 1005;
const long long INFL = 0x3f3f3f3f3f3f3f3f;
modnum<mod> dp[maxn][maxn][maxl][3];
/*
dp[i][j][k][l] :
i - number of numbers placed
j - number of connected components
k - total sum currently (filling empty spaces with a_{i} (0-indexed)
l - number of endpoints that are filled
*/
int main() {
setIO("1");
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());
a.push_back(10000); // inf
dp[0][0][0][0] = 1;
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= i; ++j) {
for (int k = 0; k <= l; ++k) {
for (int m = 0; m < 3; ++m) {
int diff = (2 * j - m) * (a[i] - a[i - 1]), pre_cost = k - diff;
if (pre_cost < 0 || i + j + 1 - m > n) {
continue;
}
modnum<mod> &cur = dp[i][j][k][m];
// create a new CC that is not an endpoint
cur += dp[i - 1][j - 1][pre_cost][m];
// create a new CC that is an endpoint
if (m >= 1) {
cur += (3 - m) * dp[i - 1][j - 1][pre_cost][m - 1];
}
// add to an existing CC such that new element is not an endpoint
cur += (2 * j - m) * dp[i - 1][j][pre_cost][m];
// add to an existing CC such that new element is an endpoint
if (m == 1) {
cur += 2 * j * dp[i - 1][j][pre_cost][m - 1];
} else if (m == 2) {
if (i == n) {
// special case because the connected component contains both endpoints
cur += dp[i - 1][j][pre_cost][m - 1];
} else {
cur += (j - 1) * dp[i - 1][j][pre_cost][m - 1];
}
}
// merge two existing CCs
if (m == 2) {
if (i == n) {
cur += dp[i - 1][j + 1][pre_cost][m];
} else {
cur += j * (j - 1) * dp[i - 1][j + 1][pre_cost][m];
}
} else if (m == 1) {
cur += j * j * dp[i - 1][j + 1][pre_cost][m];
} else {
cur += j * (j + 1) * dp[i - 1][j + 1][pre_cost][m];
}
}
}
}
}
modnum<mod> answer = 0;
for (int i = 0; i <= l; i++) {
answer += dp[n][1][i][2]; //sum the dp values for all possible sums
}
cout << answer << '\n';
return 0;
}
