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// Q = # of queries, bucket sort is sometimes faster
vector<int> low(Q, 0), high(Q, MAX_OPERATIONS + 1);
while (true) {
vector<pair<int, int>> focus;
for (int i = 0; i < Q; i++) {
if (low[i] + 1 < high[i]) {
focus.emplace_back((low[i] + high[i]) / 2, i);
}}
if (focus.empty()) break;
sort(all(focus));
// reset simulation
for (int step = 0; auto [mid, i] : focus) {
for (; step <= mid; step++) {
// simulation step
}
if (/* requirement already fulfilled */) high[i] = mid;
else low[i] = mid;
}} // answer in low (and high)
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