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  1. //...START BY DOING WHAT IS NECESSARY, THEN WHAT IS POSSIBLE AND SUDDENLY YOU ARE DOING THE IMPOSSIBLE... 
  2. #include <bits/stdc++.h>
  3. using namespace std;
  4. #define FAST_FURIER ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
  5. #define pb push_back
  6. #define mk make_pair
  7. #define rep(i,a,N) for(ll i=a;i<N;i++)
  8. #define rrep(i,a,N) for(ll i=a;i>N;i--)
  9. typedef long long ll;
  10. #define M 1000000007
  11. bool comp(int x,int y)
  12. {
  13.     return x > y;
  14. }
  15.  
  16.  
  17. /*..............................code starts here........................*/
  18. // S is the courage to continue that counts.
  19. ll m,n,k,x,post,s,t;
  20. ll factorial[1002];
  21. void fac(){
  22.     factorial[1] = 1;
  23.     factorial[0] = 1;
  24.     rep(i,2,1002){
  25.         factorial[i] = (factorial[i-1] * i)%M;
  26.     }
  27. }
  28. ll power(ll no,ll p)
  29. {
  30.     if(p == 1)
  31.     return no;
  32.     if(p == 0)
  33.     return 1;
  34.     ll q = power(no,p/2);
  35.     q = (q*q)%M;
  36.     if(p % 2 != 0)
  37.     q = (q*no)%M;
  38.     return q;
  39. }
  40. vector<int>vec;
  41. void binsearch(){
  42.     int left = 0,right = n;
  43.     while(left < right){
  44.         int middle = int((left+right)/2);
  45.         if(middle <= post){
  46.             left = middle+1;
  47.         }
  48.         else right = middle;
  49.         if(middle != n) vec.pb(middle);
  50.     }
  51.     rep(i,0,vec.size()){
  52.         if(vec[i] < post) ++s;
  53.         else if(vec[i] > post) ++t;
  54.     }
  55. }
  56. int main() {
  57.     FAST_FURIER;
  58.     int t=1;
  59.     //cin >> t;
  60.    // string a,b;
  61.     fac();
  62.     while(t--)
  63.     {
  64.         cin >> n >> x >> post;
  65.         binsearch();
  66.         //formula = (n-(1+t+s))! *((x-1)! * (n-x)!)/(x-1-s)!*(n-x-t)!
  67.         if(s > x-1 or t > n-x) cout << 0 << endl;
  68.         else{
  69.             ll a = factorial[n-1-t-s], b = factorial[x-1], c = factorial[n-x];
  70.             ll d = power(factorial[x-1-s],M-2)%M, e = power(factorial[n-x-t],M-2)%M;
  71.             a = ((a*b)%M*c)%M;
  72.             d = (d*e)%M;
  73.             a = (a*d)%M;
  74.             cout << a << endl;
  75.         }
  76.     }
  77. }
  78.  
  79.  
  80.  
  81. // Author : shivam_123
  82.  
  83. // g++ -std=c++17
Success #stdin #stdout 0s 4272KB
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https://ideone.com/gRTOIo
language:
C++ (gcc 8.3)
created:
3 years ago
visibility:
secret

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