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  1. #include <bits/stdc++.h>
  2. using namespace std;
  3.  
  4. const long long MOD = 998244353;
  5.  
  6. long long finv(long long x) {
  7.     long long p = MOD - 2;
  8.     long long inv = 1;
  9.     while (p) {
  10.         if (p & 1) inv = inv * x % MOD;
  11.         x = x * x % MOD;
  12.         p >>= 1;
  13.     }
  14.     return inv;
  15. }
  16.  
  17. int main() {
  18.     const int lim = 200000;
  19.     vector<long long> inv(lim + 1, 1);
  20.     for (int i = 2; i <= lim; i++) inv[i] = finv(i);
  21.  
  22.     int t;
  23.     cin >> t;
  24.     while (t) {
  25.         t--;
  26.         int n;
  27.         cin >> n;
  28.         vector<int> cnt(20);
  29.         for (int x = 1; x <= n; x++) {
  30.           int bits = 32 - __builtin_clz(x);
  31.           cnt[bits]++;
  32.         }
  33.  
  34.         vector<vector<long long>> combs(20, vector<long long>(1, 1));
  35.         for (int b = 0; b < 20; b++) {
  36.             int mx = cnt[b];
  37.             long long ncr = 1, cur = 1;
  38.             for (int k = 1; k <= mx; k++) {
  39.                 ncr = (mx - k + 1) * ncr % MOD;
  40.                 ncr = inv[k] * ncr % MOD;
  41.                 cur = (cur + ncr) % MOD;
  42.                 combs[b].push_back(cur);
  43.             }
  44.         }
  45.  
  46.         long long ans = 0;
  47.         for (int b = 0; b < 20; b++) {
  48.             int mx = cnt[b];
  49.             for (int v = 1; v <= mx; v++) {
  50.                 long long c = (combs[b][v] - combs[b][v - 1] + MOD) % MOD;
  51.                 for (int bb = 0; bb < 20; bb++) {
  52.                     if (bb == b) continue;
  53.                     if (bb < b) c *= combs[bb][min(cnt[bb], v - 1)];
  54.                     else c *= combs[bb][min(cnt[bb], v)];
  55.                     c %= MOD;
  56.                 }
  57.                 ans += c * v;
  58.                 ans %= MOD;
  59.             }
  60.         }
  61.         cout << ans << '\n';
  62.     }
  63.     return 0;
  64. }
  65.  
Success #stdin #stdout 0.03s 5320KB
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https://ideone.com/0QJJgz
language:
C++ (gcc 8.3)
created:
11 hours ago
visibility:
public

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