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>
#define pb push_back
#define pf push_front
using namespace std;
#define F first
#define S second
typedef long long ll;
#define pii pair <int, int>
#define pll pair <ll, ll>
typedef long double ld;
const ll N = 2000 + 10;
const ll mod = 1e9 + 7;
ll um(ll a, ll b){
return ((1LL * a * b) % mod + mod) % mod;
}
ll subr(ll a, ll b){
return ((1LL * a - b) % mod + mod) % mod;
}
ll add(ll a, ll b){
return ((1LL * a + b) % mod + mod) % mod;
}
ll binpow(ll x, ll step){
ll res = 1LL;
while(step){
if(step & 1) res = um(res, x);
x = um(x, x);
step /= 2;
}
return res;
}
bool was[N];
ll cnt, n, f, h[N];
map <pair <ll, pll>, pair <ll, bool>> mp;
ll calc(ll index, ll dir, ll hsh){
//cout << index << " "<< dir << endl;
pair <ll, bool> cur = mp[{hsh, {index, dir}}];
//cout << index << " " << dir << " "<< hsh << endl;
if(cur.S) return cur.F;
if(cnt == n){
if(index == f) return 1LL;
return 0LL;
}
ll local = 0LL;
if(dir <= 0){
for(ll i = index + 1; i <= n; i++){
if(was[i]) continue;
was[i] = true;
cnt++;
local = add(local, calc(i, 1, add(hsh, h[i])));
cnt--;
was[i] = false;
}
}
if(dir >= 0){
for(ll i = index - 1; i >= 1; i--){
if(was[i]) continue;
was[i] = true;
cnt++;
local = add(local, calc(i, -1, add(hsh, h[i])));
cnt--;
was[i] = false;
}
}
mp[{hsh, {index, dir}}] = {local, true};
return local;
}
int main() {
// freopen("kangaroo.txt", "r", stdin);
// freopen("kangaroo.txt", "w", stdout);
ios::sync_with_stdio(false);
cin.tie(NULL);
ll s;
cin >> n >> s >> f;
h[1] = 1LL;
for(ll i = 2; i <= n; i++){
h[i] = um(h[i - 1], 2LL);
}
was[s] = true;
cnt = 1;
cout << calc(s, 0, 0LL);
return 0;
}
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