fork(1) download
copy 
  1. #include <algorithm>
  2. #include <bits/stdc++.h>
  3. using namespace std;
  4. #define int long long
  5. const int MOD = 998244353;
  6. const int MAXVAL = 1e12;
  7.  
  8. int add(int x, int y) {
  9.     return (x + y) % MOD;
  10. }
  11.  
  12. int sub(int x, int y) {
  13.     return (x - y + MOD) % MOD;
  14. }
  15.  
  16. int mul(int x, int y) {
  17.     return (x % MOD * y % MOD) % MOD;
  18. }
  19.  
  20. int n;
  21. int a[200001];
  22. int s[200001], s2[200001];
  23.  
  24. int rechecker() {
  25.     int ans = 0;
  26.     for (int i = 1; i <= n; i++) {
  27.         for (int j = 1; j <= n; j++) {
  28.             int tmp = (a[i] % a[j]) % MOD;
  29.             ans = add(ans, mul(tmp, tmp));
  30.         }
  31.     }
  32.     return ans;
  33. }
  34.  
  35. void solve() {
  36.     cin >> n;
  37.     for (int i = 1; i <= n; i++) {
  38.         cin >> a[i];
  39.     }
  40.  
  41.     // Remove zeros and sort
  42.     int new_n = 0;
  43.     for (int i = 1; i <= n; i++) {
  44.         if (a[i] > 0) {
  45.             a[++new_n] = a[i];
  46.         }
  47.     }
  48.     n = new_n;
  49.  
  50.     if (n == 0) {
  51.         cout << 0 << endl;
  52.         return;
  53.     }
  54.  
  55.     sort(a + 1, a + n + 1);
  56.  
  57.     // Build prefix sums
  58.     for (int i = 1; i <= n; i++) {
  59.         s[i] = add(s[i-1], a[i] % MOD);
  60.         int tmp = a[i] % MOD;
  61.         s2[i] = add(s2[i-1], mul(tmp, tmp));
  62.     }
  63.  
  64.     int ans = 0;
  65.  
  66.     for (int i = 1; i <= n; i++) {
  67.         // For each a[i], find contribution as divisor
  68.         int divisor = a[i];
  69.  
  70.         // Handle different ranges of q where a[j] = q * divisor + r
  71.         for (int q = 0; ; q++) {
  72.             // Find range [l, r] where q * divisor <= a[j] < (q+1) * divisor
  73.             int left_bound = q * divisor;
  74.             int right_bound = (q + 1) * divisor;
  75.  
  76.             // Handle overflow check
  77.             if (q > 0 && left_bound / q != divisor) break; // overflow
  78.             if (right_bound < left_bound) break; // overflow
  79.  
  80.             int l = lower_bound(a + 1, a + n + 1, left_bound) - a;
  81.             int r = lower_bound(a + 1, a + n + 1, right_bound) - a - 1;
  82.  
  83.             if (l > n || r < 1 || l > r) {
  84.                 if (left_bound > a[n]) break;
  85.                 continue;
  86.             }
  87.  
  88.             // Clamp to valid range
  89.             l = max(l, 1LL);
  90.             r = min(r, n);
  91.  
  92.             if (l > r) continue;
  93.  
  94.             // Calculate contribution for this range
  95.             // For a[j] in [l, r]: a[j] % divisor = a[j] - q * divisor
  96.             // So (a[j] % divisor)^2 = (a[j] - q * divisor)^2
  97.             //                        = a[j]^2 - 2*q*divisor*a[j] + q^2*divisor^2
  98.  
  99.             int count = r - l + 1;
  100.             int sum_range = sub(s[r], s[l-1]);
  101.             int sum2_range = sub(s2[r], s2[l-1]);
  102.  
  103.             int term1 = sum2_range;
  104.             int term2 = mul(mul(2 * q % MOD, divisor % MOD), sum_range);
  105.             int term3 = mul(mul(mul(q % MOD, q % MOD), mul(divisor % MOD, divisor % MOD)), count % MOD);
  106.  
  107.             int contribution = add(sub(term1, term2), term3);
  108.             ans = add(ans, contribution);
  109.  
  110.             // Break if we've covered all elements
  111.             if (right_bound > a[n]) break;
  112.         }
  113.     }
  114.  
  115.     cout << ans << endl;
  116.  
  117.     // Uncomment for debugging
  118.     // if (n <= 1000) {
  119.     //     int check = rechecker();
  120.     //     if (ans != check) {
  121.     //         cout << "Recheck FAILED! Expected: " << check << ", Got: " << ans << endl;
  122.     //     } else {
  123.     //         cout << "Recheck: Passed" << endl;
  124.     //     }
  125.     // }
  126. }
  127.  
  128. int32_t main() {
  129.     ios_base::sync_with_stdio(false);
  130.     cin.tie(NULL);
  131.  
  132.     int t;
  133.     cin >> t;
  134.     while (t--) {
  135.         solve();
  136.     }
  137.     return 0;
  138. }
Success #stdin #stdout 2.14s 5728KB
comments (?)
stdin
copy 
1
10
1241111 3512121 224587487 4353453453 34534115345 34111534 5345 32919 12871289 234
stdout
copy 
757207889
https://ideone.com/F2NFWW
language:
C++14 (gcc 8.3)
created:
2 days ago
visibility:
public

Share or Embed source code

Discover > Sphere Engine API

The brand new service which powers Ideone!

Discover > IDE Widget

Widget for compiling and running the source code in a web browser!