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  1. #include <bits/stdc++.h>
  2. //#include <ext/pb_ds/assoc_container.hpp>
  3.  
  4. //using namespace __gnu_pbds;
  5. using namespace std;
  6. //typedef tree<int,null_type,less_equal<int>,rb_tree_tag, tree_order_statistics_node_update> ordered_set;
  7. #define int            long long
  8. #define mem(a,x)       memset(a,x,sizeof(a))
  9. #define fast(s)        s.reserve(2000); s.max_load_factor(0.5);
  10. #define F              first
  11. #define S              second
  12. #define pii            pair <int, int>
  13. #define all(p)         p.begin(), p.end()
  14. template<typename T> bool maximum(T &A, const T &B) {return A<B? A=B, true: false;}
  15. template<typename T> bool minimum(T &A, const T &B) {return A>B? A=B, true: false;}
  16. const int mod=998244353;
  17. const int base=2999;
  18. const int INF=1e9;
  19. const int N=1e5+5, M=10;
  20. int n, k, dp[100][101];
  21. void file()
  22. {
  23.     #define task "diduduadi"
  24.     if(fopen(task".inp","r"))
  25.     {
  26.         freopen(task".inp","r",stdin);
  27.         freopen(task".out","w",stdout);
  28.     }
  29.     ios_base::sync_with_stdio(false);
  30.     cin.tie(0);
  31.     cout.tie(0);
  32. }
  33. struct Matrix
  34. {
  35.     int n, m;
  36.     vector<vector<int>> d;
  37.     Matrix(int n=0, int m=0): n(n), m(m) {d.resize(n,vector<int>(m,0));}
  38.     Matrix(const vector<vector<int>> &d): d(d)
  39.     {
  40.         n=(int)d.size();
  41.         m=(n? (int)d[0].size(): 0);
  42.     }
  43.     Matrix operator* (const Matrix &a) const
  44.     {
  45.         int x=n, y=m, z=a.m;
  46.         Matrix res(x,z);
  47.         for(int i=0; i<x; ++i) for(int j=0; j<y; ++j) for(int k=0; k<z; ++k)
  48.         {
  49.             res.d[i][j]+=d[i][k]*a.d[k][j];
  50.             res.d[i][j]%=mod;
  51.         }
  52.         return res;
  53.     }
  54.     Matrix operator^ (int k) const
  55.     {
  56.         Matrix res(n,n);
  57.         for(int i=0; i<n; ++i) res.d[i][i]=1;
  58.         Matrix tmp=*this;
  59.         while(k)
  60.         {
  61.             if(k&1) res=res*tmp;
  62.             tmp=tmp*tmp;
  63.             k>>=1;
  64.         }
  65.         return res;
  66.     }
  67. };
  68. vector<vector<int>> tmp;
  69. int pos(int i, int j)
  70. {
  71.     return i*11+j;
  72. }
  73. void Solve()
  74. {
  75.     cin>>n>>k;
  76.     n-=k*(k-1)/2;
  77.     if(n<k) return void(cout<<"0\n");
  78.     dp[0][0]=1;
  79.     for(int i=1; i<10; ++i)
  80.     {
  81.         for(int j=1; j<=10; ++j)
  82.         {
  83.             dp[i][j]+=dp[i-1][j-1];
  84.             if(i>=j) (dp[i][j]+=dp[i-j][j]);
  85.         }
  86.     }
  87.     if(n<10) return void(cout<<dp[n][k]<<"\n");
  88.     tmp.resize(1,vector<int>(110));
  89.     for(int i=0; i<10; ++i)
  90.         for(int j=0; j<=10; ++j)
  91.             tmp[0][pos(i,j)]=dp[i][j];
  92.     Matrix mt(tmp);
  93.     tmp.clear();
  94.     tmp.resize(110,vector<int>(110,0));
  95.     for(int i=0; i<10; ++i)
  96.     {
  97.         for(int j=1; j<=10; ++j)
  98.         {
  99.             if(i<9)
  100.             {
  101.                 tmp[pos(i+1,j)][pos(i,j)]=1;
  102.                 continue;
  103.             }
  104.             tmp[pos(i,j-1)][pos(i,j)]=1;
  105.             if(i-j+1>=0) tmp[pos(i-j+1,j)][pos(i,j)]=1;
  106.         }
  107.     }
  108.     Matrix kk(tmp);
  109.     kk=kk^(n-9);
  110.     mt=mt*kk;
  111.     cout<<mt.d[0][pos(9,k)]<<"\n";
  112. }
  113.  
  114. main()
  115. {
  116.     file();
  117.     Solve();
  118.     return 0;
  119. }
  120.  
  121.  
Success #stdin #stdout 0.01s 5288KB
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https://ideone.com/OtNO7Z
language:
C++14 (gcc 8.3)
created:
1 hour ago
visibility:
public

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