This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
#define lb lower_bound
#define ub upper_bound
#define owo ios_base::sync_with_stdio(0);cin.tie(0);
#define MOD (ll)(1e9+7)
#define INF (ll)(1e18)
#define debug(...) fprintf(stderr, __VA_ARGS__),fflush(stderr)
#define time__(d) for(long blockTime = 0; (blockTime == 0 ? (blockTime=clock()) != 0 : false);\
debug("%s time : %.4fs\n", d, (double)(clock() - blockTime) / CLOCKS_PER_SEC))
typedef long long int ll;
typedef long double ld;
typedef pair<ll,ll> PII;
typedef pair<int,int> pii;
typedef vector<vector<int>> vii;
typedef vector<vector<ll>> VII;
typedef pair<int,pii> P;
ll gcd(ll a,ll b){if(!b)return a;else return gcd(b,a%b);}
ll dp[101][101][1001][2][2];
ll n,L;
vector<ll>a;
//go in reverse direction,treat dp states like a tree
// 0,0,0,0,0 is the root
ll solve(int i,int comp,int cur,int l,int r){
int ncur = cur;
if(i)ncur+=(2*comp + l + r) * (a[i]-a[i-1]);
if(ncur>L)return 0;
if(comp < 0)return 0;
if(dp[i][comp][cur][l][r] != -1)return dp[i][comp][cur][l][r];
if(i == n-1)return comp==0?1:0;
ll res = 0;
res+=solve(i+1,comp,ncur,1,r);
res+=solve(i+1,comp-1,ncur,1,r) * comp;
res+=solve(i+1,comp,ncur,l,1);
res+=solve(i+1,comp-1,ncur,l,1) * comp;
res+=solve(i+1,comp+1,ncur,l,r);
res+=solve(i+1,comp,ncur,l,r) * comp * 2;
res+=solve(i+1,comp-1,ncur,l,r) * (comp)*(comp-1);
return dp[i][comp][cur][l][r] = res%MOD;
}
int main()
{
cin>>n>>L;
a.resize(n);
for(int i=0;i<n;i++)cin>>a[i];
sort(all(a));
memset(dp,-1,sizeof(dp));
cout<< solve(0,0,0,0,0);
}
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