c++ - why std::max_element over std::map within some lower_bound not working? -

i not sure why following snippet not working: lower_bound call return key 7, expected. std::max_element between begin() , lower_bound() iterator should return 6, should search between key 4 , key 7 , max value 6 key 7. it's returning last pair(15, 12) reason can't figure out.

bool cmp(const std::pair<t, t>& p1, const std::pair<t, t>& p2)  {     return p1.second < p2.second; }  int main() {     std::map< t, t, std::greater<t> > store;     std::map< t, t, std::greater<t> >::iterator found_max, lower;      store[ 4 ] = 2;     store[ 7 ] = 6;     store[ 10 ] = 2;     store[ 15 ] = 12;     lower = store.lower_bound( 8 );      printf("%ld %ld\n", lower->first,lower->second);      found_max = std::max_element(store.begin(), lower, cmp);     printf("%ld %ld\n", found_max->first,found_max->second);      return 0; } 

std::map< t, t, std::greater<t> > store; 

store has key sorted in descending order. thus, [store.begin(), lower) contains (15, 22) , (10, 2). element maximum value (15, 22).