题意描述

思路

AC代码

#include<bits/stdc++.h>
#define x first
#define y second
#define PB push_back
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define rep(x,l,u) for(ll x=l;x<u;x++)
#define rrep(x,l,u) for(ll x=l;x>=u;x--)
#define sz(x) x.size()
#define IOS ios::sync_with_stdio(false);cin.tie(0);
using namespace std;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<char,char> PCC;
typedef long long ll;
typedef pair<ll,ll> PLL;
const int N=2*1e5+10;
const int M=1e5+10;
const int INF=0x3f3f3f3f;
const int mod=1e9+7;
void solve(){
    int n,x,pos;cin>>n>>x>>pos;
    int left=0,right=0;
    int l=0,r=n;
    while(l<r){
        int mid=l+r>>1;
        if(mid>pos) right++,r=mid;
        else left+=mid!=pos,l=mid+1;
    }
    if(x-1<left || n-x<right){
        cout<<0<<endl;
        return;
    }
    ll res1=1,res2=1,fact=1;
    rep(i,1,left+1) res1=(res1*(x-i))%mod;
    rep(i,1,right+1) res2=(res2*(n-x-i+1))%mod;
    rep(i,1,n-1-left-right+1) fact=(fact*i)%mod;
    cout<<res1%mod*res2%mod*fact%mod<<endl;
}
int main(){
    IOS;
    //freopen("test.txt", "r", stdin);
    //freopen("test.txt", "w", stdout);
    //int t;cin>>t;
    //while(t--)
        solve();
    return 0;
}