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  1. //#pragma GCC optimize("Ofast,unroll-loops")
  2. //#pragma GCC target("avx2,tune=native")
  3. #include <bits/stdc++.h>
  4. using namespace std;
  5.  
  6. #define file "permutations"
  7. #define ff(i,a,b) for(auto i=(a); i<=(b); ++i)
  8. #define ffr(i,b,a) for(auto i=(b); i>=(a); --i)
  9. #define nl "\n"
  10. #define pb emplace_back
  11. #define all(s) (s).begin(), (s).end()
  12.  
  13. using ll = long long;
  14.  
  15. inline void rf(){
  16.     ios::sync_with_stdio(false);
  17.     cin.tie(nullptr);
  18.     if (fopen(file".inp","r")){
  19.         freopen(file".inp","r",stdin);
  20.         freopen(file".out","w",stdout);
  21.     }
  22. }
  23.  
  24. const ll BASE = 22071997LL;
  25. const ll MODH = 1000000000LL + 19972207LL;
  26.  
  27. ll C[40][40];
  28.  
  29. ll comb(int n, int k){
  30.     if(k<0 || k>n) return 0;
  31.     return C[n][k];
  32. }
  33.  
  34. ll S(int m, int V){
  35.     if(V<m) return 0;
  36.     if(V>2*m) V=2*m;
  37.     return comb(V,m) - comb(V,m+1);
  38. }
  39.  
  40. ll catalan(int n){
  41.     return comb(2*n, n) / (n+1);
  42. }
  43.  
  44. int main(){
  45.     rf();
  46.     // precompute C up to 36
  47.     ff(i,0,36){
  48.         C[i][0]=C[i][i]=1;
  49.         ff(j,1,i-1) C[i][j]=C[i-1][j-1]+C[i-1][j];
  50.     }
  51.  
  52.     int T; 
  53.     if(!(cin>>T)) return 0;
  54.     while(T--){
  55.         int n; ll k;
  56.         cin>>n>>k;                 // n <= 18
  57.  
  58.         ll cat = catalan(n);
  59.         if(k>cat){ cout<<-1<<nl; continue; }
  60.  
  61.         vector<int> leftVals;
  62.         int upper = 2*n-1;
  63.         for(int m=n; m>=1; --m){
  64.             int lo=m, hi=min(upper, 2*m-1);
  65.             while(lo<hi){
  66.                 int mid=(lo+hi)>>1;
  67.                 if(S(m,mid) >= k) hi=mid;
  68.                 else lo=mid+1;
  69.             }
  70.             int v=lo;
  71.             k -= S(m, v-1);
  72.             leftVals.pb(v);
  73.             upper = v-1;
  74.         }
  75.         sort(all(leftVals));
  76.  
  77.         vector<int> perm; perm.reserve(2*n);
  78.         for(int i=(int)leftVals.size()-1;i>=0;--i) perm.pb(leftVals[i]);
  79.  
  80.         vector<int> mark(2*n+1,0);
  81.         for(int x:leftVals) mark[x]=1;
  82.         for(int x=2*n; x>=1; --x) if(!mark[x]) perm.pb(x);
  83.  
  84.         ll ans=0, pw=1;
  85.         ff(i,1,2*n){
  86.             pw = (pw * BASE) % MODH;
  87.             ans = (ans + (ll)perm[i-1] * pw) % MODH;
  88.         }
  89.         cout<<ans<<nl;
  90.     }
  91.     return 0;
  92. }
  93.  
Success #stdin #stdout 0.01s 5296KB
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stdin
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stdout
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827482776
815013008
426921014
https://ideone.com/zOP5WJ
language:
C++14 (gcc 8.3)
created:
9 days ago
visibility:
public

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