#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
int dp[105][105][1005][4];
int Add(int x, int y) {
return (x + y) % MOD;
}
void Increase(int& x, int y) {
x = Add(x, y);
}
int Multiply(int x, int y) {
return 1LL * x * y % MOD;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n, L;
cin >> n >> L;
vector<int> a(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
sort(a.begin() + 1, a.end());
dp[2][1][0][0] = (n > 2); // middle
dp[2][1][0][1] = 1; // left
dp[2][1][0][2] = 1; // right
dp[2][1][0][3] = (n == 1); // both
for (int i = 2; i <= n; ++i) {
int delta = a[i] - a[i - 1];
for (int components = 1; components < i; ++components) {
for (int balance = 0; balance <= L; ++balance) {
for (int flag = 0; flag <= 3; ++flag) {
if (dp[i][components][balance][flag] == 0) {
continue;
}
int totalBorders = components * 2 - (flag & 1) - ((flag & 2) > 0);
if ((flag & 1) == 0) {
// place at the left side of the first component
int newBalance = balance + totalBorders * delta;
if (newBalance <= L) {
Increase(dp[i + 1][components][newBalance][flag | 1], dp[i][components][balance][flag]);
}
// create a new component at the left side
newBalance = balance + totalBorders * delta;
if (newBalance <= L) {
Increase(dp[i + 1][components + 1][newBalance][flag | 1], dp[i][components][balance][flag]);
}
}
if ((flag & 2) == 0) {
// place at the right side of the last component
int newBalance = balance + totalBorders * delta;
if (newBalance <= L) {
Increase(dp[i + 1][components][newBalance][flag | 2], dp[i][components][balance][flag]);
}
// create a new component at the right side
newBalance = balance + totalBorders * delta;
if (newBalance <= L) {
Increase(dp[i + 1][components + 1][newBalance][flag | 2], dp[i][components][balance][flag]);
}
}
// create a new component
int newBalance = balance + totalBorders * delta;
int validPositions = (components + 1) - (flag & 1) - ((flag & 2) > 0);
if (newBalance <= L) {
Increase(dp[i + 1][components + 1][newBalance][flag], Multiply(validPositions, dp[i][components][balance][flag]));
}
// append to the left side of a component
newBalance = balance + totalBorders * delta;
validPositions = components - (flag & 1);
if (newBalance <= L) {
Increase(dp[i + 1][components][newBalance][flag], Multiply(validPositions, dp[i][components][balance][flag]));
}
// append to the right side of a component
newBalance = balance + totalBorders * delta;
validPositions = components - ((flag & 2) > 0);
if (newBalance <= L) {
Increase(dp[i + 1][components][newBalance][flag], Multiply(validPositions, dp[i][components][balance][flag]));
}
// merge two components
newBalance = balance + totalBorders * delta;
validPositions = components - 1;
if (newBalance <= L) {
Increase(dp[i + 1][components - 1][newBalance][flag], Multiply(validPositions, dp[i][components][balance][flag]));
}
}
}
}
}
int answer = 0;
for (int balance = 0; balance <= L; ++balance) {
Increase(answer, dp[n + 1][1][balance][3]);
}
cout << answer;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
1 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
332 KB |
Output is correct |
| 4 |
Correct |
1 ms |
332 KB |
Output is correct |
| 5 |
Correct |
1 ms |
588 KB |
Output is correct |
| 6 |
Correct |
1 ms |
588 KB |
Output is correct |
| 7 |
Correct |
1 ms |
460 KB |
Output is correct |
| 8 |
Correct |
1 ms |
460 KB |
Output is correct |
| 9 |
Correct |
2 ms |
588 KB |
Output is correct |
| 10 |
Correct |
1 ms |
460 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
716 KB |
Output is correct |
| 2 |
Correct |
1 ms |
588 KB |
Output is correct |
| 3 |
Correct |
1 ms |
716 KB |
Output is correct |
| 4 |
Correct |
1 ms |
588 KB |
Output is correct |
| 5 |
Correct |
1 ms |
588 KB |
Output is correct |
| 6 |
Correct |
1 ms |
716 KB |
Output is correct |
| 7 |
Correct |
1 ms |
588 KB |
Output is correct |
| 8 |
Correct |
1 ms |
716 KB |
Output is correct |
| 9 |
Correct |
1 ms |
716 KB |
Output is correct |
| 10 |
Correct |
1 ms |
588 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
1 ms |
332 KB |
Output is correct |
| 3 |
Correct |
1 ms |
332 KB |
Output is correct |
| 4 |
Correct |
1 ms |
332 KB |
Output is correct |
| 5 |
Correct |
1 ms |
588 KB |
Output is correct |
| 6 |
Correct |
1 ms |
588 KB |
Output is correct |
| 7 |
Correct |
1 ms |
460 KB |
Output is correct |
| 8 |
Correct |
1 ms |
460 KB |
Output is correct |
| 9 |
Correct |
2 ms |
588 KB |
Output is correct |
| 10 |
Correct |
1 ms |
460 KB |
Output is correct |
| 11 |
Correct |
1 ms |
716 KB |
Output is correct |
| 12 |
Correct |
1 ms |
588 KB |
Output is correct |
| 13 |
Correct |
1 ms |
716 KB |
Output is correct |
| 14 |
Correct |
1 ms |
588 KB |
Output is correct |
| 15 |
Correct |
1 ms |
588 KB |
Output is correct |
| 16 |
Correct |
1 ms |
716 KB |
Output is correct |
| 17 |
Correct |
1 ms |
588 KB |
Output is correct |
| 18 |
Correct |
1 ms |
716 KB |
Output is correct |
| 19 |
Correct |
1 ms |
716 KB |
Output is correct |
| 20 |
Correct |
1 ms |
588 KB |
Output is correct |
| 21 |
Correct |
2 ms |
1484 KB |
Output is correct |
| 22 |
Correct |
108 ms |
20268 KB |
Output is correct |
| 23 |
Correct |
64 ms |
8264 KB |
Output is correct |
| 24 |
Correct |
68 ms |
11568 KB |
Output is correct |
| 25 |
Correct |
70 ms |
9264 KB |
Output is correct |
| 26 |
Correct |
67 ms |
8644 KB |
Output is correct |
| 27 |
Correct |
39 ms |
9572 KB |
Output is correct |
| 28 |
Correct |
42 ms |
11460 KB |
Output is correct |
| 29 |
Correct |
74 ms |
15012 KB |
Output is correct |
| 30 |
Correct |
70 ms |
9360 KB |
Output is correct |
