void exclusive_scan_iterative(int* start, int* end, int* output)
{
    int N = end - start;
    memmove(output, start, N*sizeof(int));
    // upsweep phase.
    for (int twod = 1; twod < N; twod*=2)
    {
     int twod1 = twod*2;
     parallel_for (int i = 0; i < N; i += twod1)
     {
         output[i+twod1-1] += output[i+twod-1];
     }
    }

    output[N-1] = 0;

    // downsweep phase.
    for (int twod = N/2; twod >= 1; twod /= 2)
    {
     int twod1 = twod*2;
     parallel_for (int i = 0; i < N; i += twod1)
     {
         int t = output[i+twod-1];
         output[i+twod-1] = output[i+twod1-1];
         output[i+twod1-1] += t; // change twod1 to twod to reverse prefix sum.
     }
    }
}