Submission #19713590

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Source Code Expand

//*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/
 
#include <bits/stdc++.h>
 
// #include <atcoder/all>
 
using namespace std;
// using namespace atcoder;
 
#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl;
#define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;}
typedef long long ll;
// #define int ll
 
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(int)(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
void YES(bool t=true) {cout<<(t?"YES":"NO")<<endl;}
void Yes(bool t=true) {cout<<(t?"Yes":"No")<<endl;}
void yes(bool t=true) {cout<<(t?"yes":"no")<<endl;}
void NO(bool t=true) {cout<<(t?"NO":"YES")<<endl;}
void No(bool t=true) {cout<<(t?"No":"Yes")<<endl;}
void no(bool t=true) {cout<<(t?"no":"yes")<<endl;}
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 1, 0, -1}, dy = {-1, 0, 1, 0};
// vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 };
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
    }
} setup_io;
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'

const int MAXN = 555555;

vl fact(MAXN);
vl rfact(MAXN);

ll mod_pow(ll x, ll p, ll M = MOD) {
  if (p < 0) {
    x = mod_pow(x, M - 2, M);
    p = -p;
  }
  ll a = 1;
  while (p) {
    if (p % 2)
      a = a*x%M;
    x = x*x%M;
    p /= 2;
  }
  return a;
}

ll mod_inverse(ll a, ll M = MOD) {
  return mod_pow(a, M - 2, M);
}

void set_fact(ll n, ll M = MOD) {
  fact[0] = 1;
  for (ll i = 1; i <= n; i++) {
    fact[i] = i * fact[i - 1] % M;
  }
  rfact[n] = mod_inverse(fact[n], M);
  for (ll i = n - 1; i >= 0; i--) {
      rfact[i] = (i + 1) * rfact[i + 1] % M;
  }
}

//http://drken1215.hatenablog.com/entry/2018/06/08/210000
//n���傫��fact���v�Z�ł��Ȃ��Ƃ��̂ق��̌v�Z���@�ɂ‚��ď����Ă���
ll nCr(ll n, ll r, ll M = MOD) {
  if (r > n) return 0;
  assert(fact[2] == 2);
  ll ret = fact[n];
  if (rfact[r] == 0) {
    rfact[r] = mod_inverse(fact[r], M);
  }
  ret = (ret*rfact[r]) % M;
  if (rfact[n - r] == 0) {
    rfact[n - r] = mod_inverse(fact[n - r], M);
  }
  ret = (ret*rfact[n - r]) % M;
  return ret;
}

ll nHr(ll n, ll r) {
  return nCr(n+r-1, r);
}

ll solve(int n, int k, int idx) {
    int left = idx, right = n - 1 - left;
    vector<vll> dp(k, vll(left + 1, vl(right + 1)));
    vll free(left + 1, vl(right + 1));
    auto free2 = free;
    free[left][right] = 1;
    rep (_, left) {
        rep (i, left + 1) rep (j, right + 1) free2[i][j] = 0;

        rep (i, left + 1) rep (j, right + 1) {
            if (free[i][j] == 0) continue;
            ll rem = k - (left - i) - (right - j);
            ll suc = rem * mod_inverse(k) % MOD;
            if (suc != 0) {
                (free2[i - 1][j] += free[i][j] * suc % MOD) %= MOD;
            }
            (free2[i][j] += free[i][j] * (1 - suc) % MOD) %= MOD;
        }
        swap(free, free2);
    }
    rep (i, left + 1) rep (j, right + 1) {
        if (free[i][j] == 0) continue;
        assert(j == right);
        dp[0][i][right] = free[i][j];
    }
    
    ll ans = 0;
    rep (i, k) {
        // DEBUG(i);
        rep (i, left + 1) rep (j, right + 1) {
            free[i][j] = free2[i][j] = 0;
        }

        // DEBUG("dp");
        // rep (l, left + 1) {
        //     rep (r, right + 1) {
        //         cout << dp[i][l][r] << " ";
        //     }
        //     cout << endl;
        // }

        rep (l, left + 1) rep (r, right + 1) {
            if (dp[i][l][r] == 0) continue;
            ll rem = k - (left - l) - (right - r);
            ll suc = rem * mod_inverse(k - i) % MOD;
            (ans += suc * dp[i][l][r]) %= MOD;

            if (i == k - 1) continue;
            (free[l][r] += dp[i][l][r] * (1 - suc + MOD) % MOD) %= MOD;
        }
        if (i == k - 1) continue;

        // DEBUG_MAT(free);

        for (int u = idx + 1; u < n; u++) {
            rep (i, left + 1) rep (j, right + 1) {
                free2[i][j] = 0;
            }
            int rr = n - u - 1;
            rep (l, left + 1) rep (r, right + 1) {
                if (free[l][r] == 0) continue;
                if (rr >= r) {
                    (free2[l][r] += free[l][r]) %= MOD;
                }
                else {
                    ll rem = k - (left - l) - (right - r);
                    ll suc = rem * mod_inverse(k - i) % MOD;
                    if (rem != 0) {
                        (free2[l][r - 1] += free[l][r] * suc) %= MOD;
                    }
                    (free2[l][r] += free[l][r] * (1 - suc)) %= MOD;
                }
            }
            swap(free, free2);
        }
        // DEBUG_MAT(free);

        for (int u = 0; u < idx; u++) {
            rep (i, left + 1) rep (j, right + 1) {
                free2[i][j] = 0;
            }
            int rr = idx - u - 1;
            rep (l, left + 1) rep (r, right + 1) {
                if (free[l][r] == 0) continue;
                if (rr >= l) {
                    (free2[l][r] += free[l][r]) %= MOD;
                }
                else {
                    ll rem = k - (left - l) - (right - r);
                    ll suc = rem * mod_inverse(k - i - 1) % MOD;
                    if (rem != 0) {
                        (free2[l - 1][r] += free[l][r] * suc) %= MOD;
                    }
                    (free2[l][r] += free[l][r] * (1 - suc)) %= MOD;
                }
            }
            swap(free, free2);
        }

        // DEBUG_MAT(free);
        rep (l, left + 1) rep (r, right + 1) {
            if (free[l][r] == 0) continue;
            dp[i + 1][l][r] = free[l][r];
        }
    }
    return (ans + MOD) % MOD;
}

signed main() {
    int n, k;
    cin >> n >> k;
    ll sum = 0;
    rep (i, n) {
        ll ans = solve(n, k, i);
        cout << ans << endl;
        sum += ans;
    }
    // cout << sum % MOD << endl;
}

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