#include <bits/stdc++.h> #define ll long long #define int ll #define ld long double #define all(v) v.begin(),v.end() #define rall(v) v.rbegin(),v.rend() #define vi vector<int> #define vvi vector<vi> #define vvv vector<vvi> #define vpi vector<pair<int,int>> #define sz(v) (int)v.size() #define pb push_back #define ii pair<int,int> #define F first #define S second using namespace std; const int mod = 1e9+7, N = 100+5 ,M=1005; const ll inf = 1e18; int dx[] = {0, 0, 1, -1, 1, 1, -1, -1}; int dy[] = {-1, 1, 0, 0, 1, -1, 1, -1}; int n,l,a[N],dp[N][N][M][3]; // ith sorted element , #of components , #of ends in final answer int calc(int i,int comp,int sum,int ends){ if(sum>l) return 0; if(i>n) return comp==1&&ends==2; int&ret=dp[i][comp][sum][ends]; if(~ret) return ret; ret=0; int newSum=sum+(2*comp-ends)*(a[i]-a[i-1]); //// 1- no more ends // new comp ret=(ret+ 1ll*(comp+1-ends)*calc(i+1,comp+1,newSum,ends)%mod )%mod; // extend comp if(comp) ret=(ret+ 1ll*(2*comp-ends)*calc(i+1,comp,newSum,ends)%mod )%mod; // combine 2 comp if(comp>=2) ret=(ret+ 1ll*(comp-1)*calc(i+1,comp-1,newSum,ends)%mod )%mod; //// 2- add a new end if(ends<2){ // new comp ret=(ret+ 1ll*(2-ends)*calc(i+1,comp+1,newSum,ends+1)%mod )%mod; // extend comp if(comp) ret=(ret+ 1ll*(2-ends)*calc(i+1,comp,newSum,ends+1)%mod )%mod; } return ret; } void here_we_go_again() { cin>>n>>l; for (int i = 1; i <= n ; ++i) cin>>a[i]; if(n==1) { cout<<1; return; } sort(a+1,a+n+1); memset(dp,-1,sizeof dp); cout<<calc(1,0,0,0); } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0), cout.tie(0); int tc = 1; // cin >> tc; for(int i=1;i<=tc;++i) { // cout<<"Case #"<<i<<": "; here_we_go_again(); } return 0; }