#include <algorithm>
#include <iostream>
#include <vector>
const long long MOD = 1e9 + 7;
inline long long add(long long a, long long b) {
return ((a + b) % MOD + MOD) % MOD;
}
inline long long mul(long long a, long long b) {
return (((a * b) % MOD) + MOD) % MOD;
}
inline void addto(long long& dest, long long x) {
dest = add(dest, x);
}
int main() {
int n, l;
std::cin >> n >> l;
std::vector<int> h(n);
for (int& i : h) std::cin >> i;
std::sort(h.begin(), h.end());
if (n == 1) {
std::cout << "1\n";
return 0;
}
/*
dp[i][comp][ends][k] is the number of ways to create `comp` components
using `ends` ends, with total sum of EXACTLY `k` using first `i` shortest
buildings
Note that components are ORDERED, this just makes merging way easier
dp[0][0][0][0] = 1
dp[0][!0][or !0][or !0] = 0
When inserting i, we can insert...
... As a new component (not an end), this can go into any of prev(`comp`+1-`ends`)
= cur(`comp`-`ends`) locations
It will increase the `k` value by (h[i] - h[i-1]) * prev((2*`comp` - `ends`))
... As a new component (on an end), this can go into any of prev(2-`ends`) =
cur(3-`ends`) locations. Note that cur(`ends`) cannot be 0
It will increase the `k` value by (h[i]-h[i-1]) * prev((2*`comp`-`ends`))
... At the edge of an existing component (not on an end), this can be done in
prev(2*`comp`-`ends`) ways
It will increase the `k` value by (h[i]-h[i-1]) * prev(2*`comp`-`ends`)
... At the edge of an existing component (on an end), this can be done in prev(2-`ends`)
ways
It will increase the `k` value by (h[i]-h[i-1]) * prev(2*`comp`-`ends`)
... In between two components, to merge them. This can be done in prev(`comp`-1) ways
It will increase the `k` value by (h[i]-h[i-1]) * prev(2*`comp`-`ends`)
Note: we will proceed to do this using a forward dp, cus the logic is much simpler that way
*/
std::vector<std::vector<std::vector<std::vector<long long>>>> dp(n + 1, std::vector<std::vector<std::vector<long long>>>(n + 1, std::vector<std::vector<long long>>(3, std::vector<long long>(l + 1))));
dp[0][0][0][0] = 1;
for (int i = 0; i < n; ++i) {
int heightdiff = (i == 0 ? h[0] : h[i] - h[i - 1]);
for (int comp = 0; comp <= n; ++comp) {
for (int ends = 0; ends < 3; ++ends) {
if (2 * comp - ends < 0) break;
for (int k = 0; k <= l; ++k) {
int newk = k + heightdiff * (2 * comp - ends);
if (newk > l) continue;
long long cur = dp[i][comp][ends][k];
if (comp + 1 <= n) {
addto(dp[i + 1][comp + 1][ends][newk], mul(comp + 1 - ends, cur));
}
if (comp + 1 <= n && ends < 2) {
addto(dp[i + 1][comp + 1][ends + 1][newk], mul(2 - ends, cur));
}
addto(dp[i + 1][comp][ends][newk], mul(2 * comp - ends, cur));
if (ends < 2) {
addto(dp[i + 1][comp][ends + 1][newk], mul(2 - ends, cur));
}
if (comp > 0) {
addto(dp[i + 1][comp - 1][ends][newk], mul(comp - 1, cur));
}
}
}
}
}
long long ans = 0;
for (int k = 0; k <= l; ++k) {
addto(ans, dp[n][1][2][k]);
}
std::cout << ans << '\n';
return 0;
}
