1436C-Binary_Search.cpp

/*
    written by Pankaj Kumar.
    country:-INDIA
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll ;
typedef vector<ll> vl;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef map<ll,ll> ml;
typedef set<char>sc;
typedef set<ll> sl;
#define pan cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);
// define values.
// #define mod 1000000007
#define phi 1.618
/* Bit-Stuff */
#define get_set_bits(a) (__builtin_popcount(a))
#define get_set_bitsll(a) ( __builtin_popcountll(a))
#define get_trail_zero(a) (__builtin_ctz(a))
#define get_lead_zero(a) (__builtin_clz(a))
#define get_parity(a) (__builtin_parity(a))
/*  Abbrevations  */
#define ff first
#define ss second
#define mp make_pair
#define line cout<<endl;
#define pb push_back
#define Endl "\n"
// loops
#define forin(arr,n) for(ll i=0;i<n;i++) cin>>arr[i];
// Some print
#define no cout<<"NO"<<endl;
#define yes cout<<"YES"<<endl;
#define cc ll test;cin>>test;while(test--)
// sort
#define all(V) (V).begin(),(V).end()
#define srt(V) sort(all(V))
#define srtGreat(V) sort(all(V),greater<ll>())
// function

ll power(ll x,ll y,ll mod)
{
    ll res=1;
    // x=x%mod;
    while(y>0)
    {
        if(y%2==1)
        {
            res*=x;
            // res=res%mod;
        }
        y/=2; x*=x; // x=x%mod;
    }
    return res;
}
/* ascii value 
A=65,Z=90,a=97,z=122
*/
/*  -----------------------------------------------------------------------------------*/


ll solve()
{
    ll n,x,pos;
    cin>>n>>x>>pos;
    ll greater=n-x;
    ll lower=x-1;
    ll start=0,end=n;
    ll mod=1000000007;
    ll ans=1;
    while(end>start)
    {
        ll mid=(start+end)/2;
        if(mid<pos)
        {
            ans=(ans*lower)%mod;
            lower--;
            start=mid+1;
        }
        else if(mid==pos)
        {
            ans=ans;
            start=mid+1;
        }
        else
        {
            ans=(ans*greater)%mod;
            greater--;
            end=mid;
        }
    }
    lower+=greater;
    while(lower>0)
    {
        ans=(ans*lower)%mod;
        lower--;
    }
    cout<<ans<<Endl;
    return 0;
}

int main()
{
    //freopen("input.txt"a, "r", stdin);
    pan;
    solve();
    // cc
    // {
    //     solve();
    // }
}