Range Product Queries

You are given an array of n integers and a sequence of queries. There are two types of queries:

• Update Query: 1 x y — update the element at position x with the value y.
• Range Query: 2 l r — compute the product of the elements from index l to r (1-indexed) modulo \(10^9+7\).

For range queries, you may use the formula \[ \text{product}(l, r)=\frac{P(r)}{P(l-1)} \pmod{10^9+7} \] where \(P(i)=a_1\times a_2\times\cdots\times a_i\) and the division is performed using the modular inverse. Implement the queries accordingly.

inputFormat

The input is given in the following format:

1. The first line contains an integer n denoting the number of elements in the array.
2. The second line contains n space-separated integers representing the array.
3. The third line contains an integer q denoting the number of queries.
4. The following q lines each contain three space-separated integers representing a query. The first integer is the query type (1 for update and 2 for range query). For an update query, the next two integers are x and y (set the element at position x to y). For a range query, the next two integers are l and r (query the product from index l to r).

outputFormat

For every range query (type 2), output the product of the specified subarray modulo \(10^9+7\> on a new line.

## sample

5
1 2 3 4 5
5
2 1 3
1 3 6
2 1 3
2 3 5
1 5 2

6
12
120

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