Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    abd084d()
}

fun abd084d() {
    val q = readLine()!!.toInt()
    val lrList = (1..q).map { readLine()!!.split(" ").map { it.toInt() } }.map { Pair(it[0], it[1]) }
    val max = lrList.maxBy { it.second }!!.second

    val primes = genPrime(max)

    val cumulativeSum = LongArray(max + 2)
    for (i in 0..max) cumulativeSum[i + 1] = cumulativeSum[i] +
            if (i.toLong() in primes && (i.toLong() + 1) / 2 in primes) 1 else 0

    val answer = lrList.map {
        val (left, right) = it
        cumulativeSum[right + 1] - cumulativeSum[left]
    }

    println(answer.joinToString(System.lineSeparator()))
}

private fun genPrime(max: Int): LongArray {
    val sqrt = Math.ceil(Math.sqrt(max.toDouble())).toLong()
    val primes = mutableListOf<Long>()

    var target = (2..max.toLong()).toList()

    while (target.isNotEmpty() && target.first() <= sqrt) {
        val prime = target.first()
        primes.add(prime)
        target = target.filterNot { it % prime == 0L }
    }

    primes.addAll(target)

    return primes.toLongArray()
}