This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MAXN = 105;
const ll COST = 1005;
const ll MOD = 1e9+7;
ll dp[MAXN][MAXN][COST][3];
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
ll N, L;
cin >> N >> L;
dp[0][0][0][0] = 1;
vector<ll> heights;
for (int i=0; i<N; i++){
ll x;
cin >> x;
heights.push_back(x);
}
heights.push_back(0);
sort(heights.begin(), heights.end());
for (int i=1; i<=N; i++){
ll C = heights[i] - heights[i-1];
if (i==1) C = 0;
for (int j=1; j<=N; j++){
for (int k=0; k<=L; k++){
for (int l=0; l<3; l++){
//adding a component without closing any end
if (k - (2*j-2-l)*C >= 0) dp[i][j][k][l] += dp[i-1][j-1][k - (2*j-2-l)*C][l];
//adding a component and closing one end
if (k - (2*j-1-l)*C >= 0 && l){
if (l==1) dp[i][j][k][l] += dp[i-1][j-1][k - (2*j-1-l)*C][l-1] * 2;
if (l==2) dp[i][j][k][l] += dp[i-1][j-1][k - (2*j-1-l)*C][l-1];
}
//adding to a component without closing any end
if (k - (2*j-l)*C >= 0) dp[i][j][k][l] += dp[i-1][j][k - (2*j-l)*C][l] * (2*j - l);
//adding to a component and closing one end
if (i==N && j==1 && k-C>=0 && l==2) dp[i][j][k][l] += dp[i-1][j][k - C][l-1];
else if (k - (2*j-l+1)*C >= 0){
if (l == 1) dp[i][j][k][l] += dp[i-1][j][k - (2*j-l+1)*C][l-1] * (2 * j);
if (l == 2) dp[i][j][k][l] += dp[i-1][j][k - (2*j-l+1)*C][l-1] * (j - 1);
}
//merging two components
if (i==N && j==1 && k-2*C>=0 && l==2) dp[i][j][k][l] += dp[i-1][j+1][k - 2*C][l];
else if (k - (2*j+2-l)*C >= 0) {
if (l==0) dp[i][j][k][l] += dp[i-1][j+1][k - (2*j+2-l)*C][l] * (j+1) * j;
if (l==1) dp[i][j][k][l] += dp[i-1][j+1][k - (2*j+2-l)*C][l] * j * j;
if (l==2) dp[i][j][k][l] += dp[i-1][j+1][k - (2*j+2-l)*C][l] * (j-1) * j;
}
dp[i][j][k][l] %= MOD;
}
}
}
}
ll ans=0;
for (int cost=0; cost<=L; cost++){
ans += dp[N][1][cost][2];
ans%=MOD;
}
cout << ans;
}
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