How to use std::partial_sum and output to a std::map?

I want an output map that has { {0,1},{1,2},{2,3},{3,4},{4,5} }, c++11 only. Any ideas?

std::map<int, int> m, out;
for( auto i=0; i < 5; ++i ) 
    m[i] = 1;

std::partial_sum( m.begin(), m.end(), std::inserter( out, out.begin() ),
        []( const std::pair<int,int>& a, const std::pair<int,int>& b ) 
             { return std::pair<int,int>( a.first, a.second + b.second ); } 
);

This gives compile error:

/usr/include/c++/5/bits/stl_pair.h: In instantiation of ‘std::pair<_T1, _T2>& std::pair<_T1, _T2>::operator=(std::pair<_U1, _U2>&&) [with _U1 = int; _U2 = int; _T1 = const int; _T2 = int]’:
/usr/include/c++/5/bits/stl_numeric.h:295:12:   required from ‘_OutputIterator std::partial_sum(_InputIterator, _InputIterator, _OutputIterator, _BinaryOperation) [with _InputIterator = std::_Rb_tree_iterator<std::pair<const int, int> >; _OutputIterator = std::insert_iterator<std::map<int, int> >; _BinaryOperation = main()::<lambda(const std::pair<int, int>&, const std::pair<int, int>&)>]’
../src/test_cumsum.cpp:43:130:   required from here
/usr/include/c++/5/bits/stl_pair.h:188:10: error: assignment of read-only member ‘std::pair<const int, int>::first’
first = std::forward<_U1>(__p.first);