#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
#define FOR(i,a,b) for(int i = (a) , _b = (b); i <= _b; ++i)
#define MASK(x) ((LL)(1)<<(x))
#define BIT(mask , x) (((mask)>>(x))&(1))
template<class X , class Y>
bool maximize(X &x , Y y){
if (x<y) return x=y,true; else return false;
}
template<class X,class Y>
bool minimize(X &x, Y y){
if (x>y) return x=y,true; else return false;
}
template<class T>
void compress(vector<T>&data){
sort(data.begin() , data.end()) ;
data.resize(unique(data.begin() , data.end()) - data.begin());
return;
}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
int Rand(int l,int r){
return uniform_int_distribution<int>(l,r)(rng);
}
const int N = (int)2000;
const int MOD = (int)1e9+7;
int add(int a,int b){
return a + b >= MOD ?a + b - MOD : a + b;
}
int mul(int a,int b){
return (LL)a*b % MOD;
}
int start , finish , n;
int dp[N+2][N+2][2][2][2] = {};
int main(){
ios::sync_with_stdio(false);
cin.tie(0) ; cout.tie(0);
#define name "main"
if (fopen(name".inp","r")){
freopen(name".inp","r",stdin);
freopen(name".out","w",stdout);
}
cin >> n >> start >> finish;
dp[0][0][0][0][0] = 1;
FOR(i,0,n-1){
FOR(cur_comp , 0 , i) FOR(have_start , 0 , 1) FOR(have_end , 0 , 1) FOR(connect , 0 , 1){
if (connect) continue;
bool nxt_start = have_start | (i + 1 == start);
bool nxt_end = have_end | (i + 1 == finish);
//... create a new component
dp[i + 1][cur_comp + 1][nxt_start][nxt_end][0] = add(dp[i+1][cur_comp + 1][nxt_start][nxt_end][0] , dp[i][cur_comp][have_start][have_end][0]);
//... insert start and finish positions
if (i + 1 == start && have_end && cur_comp==1) {
dp[i+1][cur_comp][nxt_start][nxt_end][1] = add(dp[i+1][cur_comp][nxt_start][nxt_end][1] , dp[i][cur_comp][have_start][have_end][0]);
}
else
if (i + 1 == finish && have_start && cur_comp==1){
dp[i+1][cur_comp][nxt_start][nxt_end][1] = add(dp[i+1][cur_comp][nxt_start][nxt_end][1] , dp[i][cur_comp][have_start][have_end][0]);
}
else
if (i + 1 == start && have_start == 0){
dp[i+1][cur_comp][1][nxt_end][0] = add(dp[i+1][cur_comp][1][nxt_end][0] , (LL)dp[i][cur_comp][0][nxt_end][0] * (cur_comp - nxt_end) % MOD);
}
else
if (i + 1 == finish && have_end == 0){
dp[i+1][cur_comp][nxt_start][1][0] = add(dp[i+1][cur_comp][nxt_start][1][0] , (LL)dp[i][cur_comp][nxt_start][0][0] * (cur_comp - nxt_start) % MOD);
}
//... merging two components together
if (cur_comp > 1 && i + 1 != start && i + 1 != finish){
int rest_comp = cur_comp - have_start - have_end;
LL t = dp[i][cur_comp][have_start][have_end][0];
int &t1 = dp[i+1][cur_comp-1][have_start][have_end][0];
int &t2 = dp[i+1][cur_comp-1][have_start][have_end][1];
dp[i+1][cur_comp-1][have_start][have_end][0] = add(dp[i+1][cur_comp-1][have_start][have_end][0] , (LL)t * rest_comp * (rest_comp - 1) % MOD);
t1 = add(t1 , (LL)t * rest_comp * (rest_comp - 1) % MOD);
if (have_start) {
t1 = add(t1 , (LL)t * rest_comp % MOD);
}
if (have_end){
t1 = add(t1 , (LL)t * rest_comp % MOD);
}
if (have_start && have_end) {
t2 = add(t2 , t);
}
}
}
}
cout<<dp[n][1][1][1][1];
}
Compilation message (stderr)
kangaroo.cpp: In function 'int main()':
kangaroo.cpp:47:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
47 | freopen(name".inp","r",stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
kangaroo.cpp:48:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
48 | freopen(name".out","w",stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
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