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  1. #include <bits/stdc++.h>
  2. using namespace std;
  3.  
  4. const int MOD = 1e9 + 7;
  5.  
  6. long long pow_mod(long long base, long long exp) {
  7.     long long result = 1;
  8.     base %= MOD;
  9.     while (exp > 0) {
  10.         if (exp % 2 == 1) {
  11.             result = (result * base) % MOD;
  12.         }
  13.         base = (base * base) % MOD;
  14.         exp /= 2;
  15.     }
  16.     return result;
  17. }
  18.  
  19. int main() {
  20.     ios::sync_with_stdio(false);
  21.     cin.tie(nullptr);
  22.  
  23.     int t;
  24.     cin >> t;
  25.     while (t--) {
  26.         int n;
  27.         cin >> n;
  28.         vector<int> a(n);
  29.         unordered_map<int, int> freq;
  30.         for (int i = 0; i < n; ++i) {
  31.             cin >> a[i];
  32.             freq[a[i]]++;
  33.         }
  34.  
  35.         int mex = 0;
  36.         while (freq.count(mex)) {
  37.             mex++;
  38.         }
  39.  
  40.         sort(a.begin(), a.end());
  41.  
  42.         vector<long long> left_product(mex + 1);
  43.         left_product[0] = 1;
  44.         for (int y = 0; y < mex; ++y) {
  45.             int cnt = freq[y];
  46.             long long term = (pow_mod(2, cnt) - 1 + MOD) % MOD;
  47.             left_product[y + 1] = (left_product[y] * term) % MOD;
  48.         }
  49.  
  50.         long long sum = 0;
  51.         for (int x = 1; x <= mex; ++x) {
  52.             int sum_leq_x = upper_bound(a.begin(), a.end(), x) - a.begin();
  53.             int sum_gt_x = n - sum_leq_x;
  54.             long long right_pow = pow_mod(2, sum_gt_x);
  55.             long long count_x = (left_product[x] * right_pow) % MOD;
  56.             sum = (sum + x * count_x) % MOD;
  57.         }
  58.  
  59.         cout << sum % MOD << '\n';
  60.     }
  61.  
  62.     return 0;
  63. }
Success #stdin #stdout 0s 5288KB
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https://ideone.com/2XCKfm
language:
C++ (gcc 8.3)
created:
11 days ago
visibility:
public

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