Prime Product Queries

You are given T test cases. Each test case contains two integers l and r representing an inclusive range. Your task is to compute the product of all prime numbers within the range [l, r] modulo \(10^9+7\). If there are no prime numbers in the range, output -1.

To solve this problem efficiently, you should precompute all prime numbers up to \(10^6\) using the Sieve of Eratosthenes. Then, process each query by iterating over the primes that lie in the given range and multiplying them under modular arithmetic.

Note: If there is no prime in the specified range, the output should be -1.

inputFormat

The first line contains an integer T denoting the number of test cases. Each of the following T lines contains two space-separated integers l and r describing the range.

Input Format: T l1 r1 l2 r2 ... lT rT

outputFormat

For each test case, print the product of all primes in the inclusive range [l, r] modulo \(10^9+7\) on a new line. If there are no primes, output -1.

## sample

3
1 10
10 20
20 30

210
46189
667

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