// gemini code #include <iostream> #include <vector> #include <numeric> #include <algorithm> using namespace std; // Maximum number of groups N (or B) is 100 in Subtask 4 const int MAXN = 105; const int MAX_GROUPS = 105; // DP table for feasibility check: dp[i][j] is true if the first i sculptures can be partitioned // into j groups such that the OR-sum of all groups respects the 'target_or' prefix. bool dp[MAXN][MAX_GROUPS]; // Check function for the feasibility of an OR-sum. // current_prefix: the required upper bound for the final OR-sum. bool check(int N, int A, int B, const vector<long long>& Y, long long current_prefix) { // 1. Calculate prefix sums for O(1) range sum calculation vector<long long> prefix_sum(N + 1, 0); for (int i = 0; i < N; ++i) { prefix_sum[i + 1] = prefix_sum[i] + Y[i]; } // 2. Initialize DP table: dp[i][j] = false (cannot reach state i with j groups) for (int i = 0; i <= N; ++i) { for (int j = 0; j <= B; ++j) { dp[i][j] = false; } } // Base case: 0 sculptures, 0 groups is possible. dp[0][0] = true; // 3. Dynamic Programming // i: end position of the overall partition (1 to N) for (int i = 1; i <= N; ++i) { // j: number of groups used so far (1 to B) for (int j = 1; j <= B; ++j) { // k: end position of the *previous* group (0 to i-1) for (int k = 0; k < i; ++k) { if (dp[k][j - 1]) { // Current group is from k+1 to i long long group_sum = prefix_sum[i] - prefix_sum[k]; // Condition Check: (S OR P) = P // This is equivalent to: (S & ~P) == 0 // Ensures that group_sum S does not have any bit set that we have committed // to be 0 (i.e., bits in the region ~current_prefix) if ((group_sum | current_prefix) == current_prefix) { dp[i][j] = true; // Optimization: once dp[i][j] is true, break inner loops break; } } } } } // 4. Feasibility Result // Check if the full partition (N sculptures) is possible with A <= groups <= B for (int j = A; j <= B; ++j) { if (dp[N][j]) { return true; } } return false; } void solve() { int N, A, B; if (!(cin >> N >> A >> B)) return; vector<long long> Y(N); long long total_sum = 0; for (int i = 0; i < N; ++i) { cin >> Y[i]; total_sum += Y[i]; } // The maximum possible OR-sum is bounded by total_sum. // We search from the MSB of total_sum down to bit 0. int max_bits = 0; if (total_sum > 0) { max_bits = 63 - __builtin_clzll(total_sum); // Find the position of the MSB } long long min_or_sum = 0; // Greedy Bit-by-Bit Search for (int k = max_bits; k >= 0; --k) { // Current guaranteed prefix of the answer is min_or_sum. // 1. Try to set the k-th bit to 0. // The check function must ensure that all group sums S are submasks of min_or_sum // (for bits > k) AND all bits < k (which we don't care about yet). // Since min_or_sum is the committed answer so far, passing it to check ensures that // no group sum violates the "0" bits we have already fixed in higher positions. if (check(N, A, B, Y, min_or_sum)) { // Case 1: Possible to achieve the current OR-sum prefix (with bit k as 0). // min_or_sum remains unchanged (k-th bit is 0). continue; } else { // Case 2: IMPOSSIBLE to achieve the current OR-sum prefix (with bit k as 0). // The k-th bit MUST be 1. We commit to 1 and update the prefix. min_or_sum |= (1LL << k); } } cout << min_or_sum << endl; } // int main() { // // For testing with Sample Input: 6 1 3 | 8 1 2 1 5 4 -> Output: 11 // solve(); // return 0; // }

/usr/bin/ld: /usr/lib/gcc/x86_64-linux-gnu/13/../../../x86_64-linux-gnu/crt1.o: in function `_start':
(.text+0x1b): undefined reference to `main'
collect2: error: ld returned 1 exit status