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;
const long long MX=2e3+10;
const long long MOD=1e9+7;
long long mas[MX][MX][4]={0};
int main()
{
cin.tie(0);
ios_base::sync_with_stdio(0);
long long n,s,f;
cin>>n>>s>>f;
mas[1][1][0]=1;
for(long long i=1;i<n;i++)
{
for(long long k=1;k<n;k++)
{
if((i+1)<=s)
{
mas[i+1][k][2]=(mas[i+1][k][2]+mas[i][k][0])%MOD;
mas[i+1][k][3]=(mas[i+1][k][1]+mas[i][k][1])%MOD;
}
if((i+1)<=f)
{
mas[i+1][k][1]=(mas[i+1][k][1]+mas[i][k][0])%MOD;
mas[i+1][k][3]=(mas[i+1][k][3]+mas[i][k][2])%MOD;
}
if((i+1)!=s && (i+1)!=f)
{
mas[i+1][k-1][0]=(mas[i+1][k-1][0]+mas[i][k][0]*(k-1))%MOD;
mas[i+1][k-1][1]=(mas[i+1][k-1][1]+mas[i][k][1]*(k-1))%MOD;
mas[i+1][k-1][2]=(mas[i+1][k-1][2]+mas[i][k][2]*(k-1))%MOD;
mas[i+1][k-1][3]=(mas[i+1][k-1][3]+mas[i][k][3]*(k-1))%MOD;
}
if((i+1)==s)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0])%MOD;
mas[i+1][k+1][1]=(mas[i+1][k+1][1]+mas[i][k][1])%MOD;
}
if((i+1)==f)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0])%MOD;
mas[i+1][k+1][2]=(mas[i+1][k+1][2]+mas[i][k][2])%MOD;
}
if((i+1)<s && (i+1)<f)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0]*(k+1))%MOD;
mas[i+1][k+1][1]=(mas[i+1][k+1][1]+mas[i][k][1]*(k))%MOD;
mas[i+1][k+1][2]=(mas[i+1][k+1][2]+mas[i][k][2]*(k))%MOD;
mas[i+1][k+1][3]=(mas[i+1][k+1][3]+mas[i][k][3]*(k-1))%MOD;
continue;
}
if((i+1)>s && (i+1)<f)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0]*(k))%MOD;
mas[i+1][k+1][1]=(mas[i+1][k+1][1]+mas[i][k][1]*(k-1))%MOD;
mas[i+1][k+1][2]=(mas[i+1][k+1][2]+mas[i][k][2]*(k))%MOD;
mas[i+1][k+1][3]=(mas[i+1][k+1][3]+mas[i][k][3]*(k-1))%MOD;
continue;
}
if((i+1)<s && (i+1)>f)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0]*(k))%MOD;
mas[i+1][k+1][1]=(mas[i+1][k+1][1]+mas[i][k][1]*(k))%MOD;
mas[i+1][k+1][2]=(mas[i+1][k+1][2]+mas[i][k][2]*(k-1))%MOD;
mas[i+1][k+1][3]=(mas[i+1][k+1][3]+mas[i][k][3]*(k-1))%MOD;
continue;
}
if((i+1)>s && (i+1)>f)
{
mas[i+1][k+1][0]=(mas[i+1][k+1][0]+mas[i][k][0]*(k-1))%MOD;
mas[i+1][k+1][1]=(mas[i+1][k+1][1]+mas[i][k][1]*(k-1))%MOD;
mas[i+1][k+1][2]=(mas[i+1][k+1][2]+mas[i][k][2]*(k-1))%MOD;
mas[i+1][k+1][3]=(mas[i+1][k+1][3]+mas[i][k][3]*(k-1))%MOD;
continue;
}
}
}
cout<<(mas[n][1][0]+mas[n][1][1]+mas[n][1][2]+mas[n][1][3])%MOD<<"\n";
return 0;
}
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