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> // Tomasz Nowak
using namespace std; // XIII LO Szczecin
using LL = long long; // Poland
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define REP(i, n) FOR(i, 0, (n) - 1)
template<class T> int size(T &&x) {
return int(x.size());
}
template<class A, class B> ostream& operator<<(ostream &out, const pair<A, B> &p) {
return out << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &out, T &&x) -> decltype(x.begin(), out) {
out << '{';
for(auto it = x.begin(); it != x.end(); ++it)
out << *it << (it == prev(x.end()) ? "" : ", ");
return out << '}';
}
void dump() {}
template<class T, class... Args> void dump(T &&x, Args... args) {
cerr << x << "; ";
dump(args...);
}
#ifdef DEBUG
struct Nl{~Nl(){cerr << '\n';}};
# define debug(x...) cerr << (strcmp(#x, "") ? #x ": " : ""), dump(x), Nl(), cerr << ""
#else
# define debug(...) 0 && cerr
#endif
mt19937_64 rng(0);
int rd(int l, int r) {
return uniform_int_distribution<int>(l, r)(rng);
}
// end of templates
constexpr int mod = int(1e9) + 7;
int add(int a, int b) {
a += b;
if(a >= mod)
a -= mod;
return a;
}
int mul(int a, int b) {
return int(a * LL(b) % mod);
}
int& add_to(int &a, int b) {
return a = add(a, b);
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, start, end;
cin >> n >> start >> end;
vector<vector<array<int, 3>>> dp(n + 1, vector<array<int, 3>>(n, array<int, 3>{{0, 0, 0}}));
dp[0][0][0] = 1;
auto choose2 = [&](int cnt) {
return int((cnt * LL(cnt - 1) / 2) % mod);
};
FOR(i, 1, n)
FOR(open, 0, n - 1) {
if(i == start or i == end) {
add_to(dp[i][open][1], dp[i - 1][open][0]);
add_to(dp[i][open][2], dp[i - 1][open][1]);
if(open + 1 < n) {
add_to(dp[i][open][1], dp[i - 1][open + 1][0]);
add_to(dp[i][open][2], dp[i - 1][open + 1][1]);
}
}
else {
if(open + 1 < n) {
add_to(dp[i][open][0], mul(dp[i - 1][open + 1][0], choose2(open + 1)));
add_to(dp[i][open][1], mul(dp[i - 1][open + 1][1], choose2(open + 1)));
add_to(dp[i][open][2], mul(dp[i - 1][open + 1][2], choose2(open + 1)));
add_to(dp[i][open][0], dp[i - 1][open][2]);
}
if(open >= 1) {
add_to(dp[i][open][0], dp[i - 1][open - 1][0]);
add_to(dp[i][open][1], dp[i - 1][open - 1][1]);
add_to(dp[i][open][2], dp[i - 1][open - 1][2]);
}
}
}
FOR(i, 1, n)
FOR(open, 0, n - 1)
debug(i, open, dp[i][open]);
cout << dp[n][0][0] << '\n';
}
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