Как оптимизировать эту задачу ?

Question : We have been given two arrays of size N with each element as hi, ai the elements are positive integers and random. We are Also Given with Q queries of 2 type. 

In query type 1 : we will be given with 2 positive integers b k and we have to update a[b] to k.

In query Type 2 : we will be given with 2 positive integers b c and we need to find out whether moving from h[b] to h[c] possible and if yes then we have to find a sum.

Now, there are rules to move in array h[i]. 

Rule 1 : We can only move from i to j if A[i] < A[j]. 

Rule 2 : We can only move to just next greatest element. i.e if array [1,5,4,8] and we want to move from 1 to 8, then path taken will be 1-->5-->8. we cannot take 1-->4-->8 as 4 is not the next greater element of 1.

Constraints :

1≤N,Q≤2⋅10^5 

1≤hi≤10^9 for each valid i

1≤ai≤10^9 for each valid i

1≤b,c≤N

1≤k≤10^9

For each query of type 2 if it is possible to go from b to c then we have to output the sum of elements from a[i] that were part of path.

For Example h[] = {1,5,4,8} , a[] = {1,2,3,4}, path taken : 1-->5-->8 (b=1,c=4)so sum will be 1+2+4 = 7.

And if we cannot reach to destination for example h[] = {1,5,4,4} b=1,c=4 so here we cannot reach to 4th index by following rules of movement hence output will be -1.

So, Now I think Question is clear. What i need to know is how to pre-process all this. i mean for every query of type 2 i can just create a loop and find we reaching from b to c is possible or not. But due to very large Queries the time complexity becomes O(n^2) of my approach which gives TLE. I need to know how to pre-process everything so that for every query of type 2 i just calculate the answer in constant time.

My O(n^2) approach.

while(Q--) // Q is total Queries
{
 int q,b,c,k; cin >> q;
 if(q == 1) // query type 1 
 {
   cin >> b >> k;
   a[b]=k;
 }
 else // query type 2
 {
   cin >> b >> c;
   int sum = a[c],curr=a[b];bool flag = 0;
   for( int i = b+1 ; i < c-1 ; i++ ) // loop to find sum if possible
   {
    if( h[i] > curr ) // h[i] is the just next greater.
    {
      sum+=a[i];
      curr=h[i];
      flag=1;
    }
   }

   if(flag) 
     cout << sum << "\n";
   else 
     cout << "-1\n"; 
}
}

So, My above approach works Fine when Q and N are below 1000, but when they are increased to 200000, this program gives TLE as for each query i am traversing a loop.

I need to remove this inner Loop, by doing some pre-processing before Query loop (while(Q--){..}). The problem is that i cant figure out how to pre-process the input data such that i am able to know that reaching from b to c is possible or not and if it is then calculating desired sum.

Please Help me out, I am scratching my head on this from past few days..