This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
* author: NeroZein
* created: 23.01.2023 11:07:10
*/
#include <bits/stdc++.h>
using namespace std;
#ifdef Nero
#include "Deb.h"
#else
#define deb(...)
#endif
const int md = 1e9+7;
inline void add(int& a, int b) {
a += b;
if(a >= md){
a -= md;
}
}
inline int mul(int a, int b) {
return (int)((long long) a * b % md);
}
signed main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
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());
vector<vector<array<int, 3>>>dp(n, vector<array<int, 3>>(m + 1));
//ncc, sum, used endpoints
dp[1][0][0] = 1;
dp[1][0][1] = 2;
for (int i = 1; i < n; ++i) {
vector<vector<array<int, 3>>>pd(n, vector<array<int, 3>>(m + 1));
for (int j = 1; j < n; ++j) {
for(int k = 0; k <= m; ++k) {
for(int e = 0; e < 3; ++e){
int diff = (2 * j - e) * (a[i] - a[i-1]);
if(k + diff > m){
continue;
}
//merge two cc
if(j > 1) {
add(pd[j - 1][k + diff][e], mul(j - 1, dp[j][k][e]));
}
//create a cc
if(j + 1 < n) {
add(pd[j + 1][k + diff][e], mul(j + 1 - e, dp[j][k][e]));
}
//create a cc on the endpoints
if(j + 1 < n && e < 2){
add(pd[j + 1][k + diff][e + 1], mul(2 - e, dp[j][k][e]));
}
//add to the left or right to an already existing component but not become an endpoint
add(pd[j][k + diff][e], mul(2 * j - e, dp[j][k][e]));
//add to the left or right to an already existing component but become an endpoint
if(e < 2){
add(pd[j][k + diff][e + 1], mul(2 - e, dp[j][k][e]));
}
}
}
}
swap(dp, pd);
}
int ans = 0;
for(int i = 0; i <= m; ++i){
add(ans, dp[1][i][2]);
}
cout << ans << '\n';
}
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