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bool next(string& s, int n, char mi = '0', char ma = '1') {
for (int i = sz(s), j = sz(s); i < n; i++)
s.push_back(s[i % j]);
while(!s.empty() && s.back() == ma) s.pop_back();
if (s.empty()) {
s = mi;
return false;
} else {
s.back()++;
return true;
}}
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